Optimised DWT using cooperative particle swarm optimiser ...jit.ac.in/journal/cse/106.pdfA. Velayudham, K. Madhan Kumar and R. Kanthavel particle swarm optimiser for hybrid domain

Int. J. Biomedical Engineering and Technology, Vol. X, No. Y, XXXX

Copyright © 200X Inderscience Enterprises Ltd.

Optimised DWT using cooperative particle swarm optimiser for hybrid domain based medical and natural image denoising

A. Velayudham* Department of Information Technology, Cape Institute of Technology, Levengipuram 627114, Tirunelveli District, India Email: [email protected] *Corresponding author

K. Madhan Kumar Faculty of Electronics and Communication Engineering, PET Engineering College, Vallioor, India Email: [email protected]

R. Kanthavel Rajalakshmi Institute of Technology, Chennai, India Email: [email protected]

Abstract: The quest for productive image denoising systems still is a valid challenge, at the intersection of practical investigation and measurements. In spite of the sophistication of the recently proposed systems, most calculations have not yet achieved an attractive level of applicability. In this research, an optimal wavelet filter coefficient design-based methodology is proposed for image denoising. The method utilises new wavelet filter whose coefficients are derived by discrete wavelet (Haar) transform using CPSO optimisation and bilateral filter. The optimal wavelet coefficient based denoising methods minimise the noise, while bilateral filter further decreases the noise and increases the PSNR without any loss of relevant image information. Overall, the proposed approach consists of two stages namely, (i) design of optimal wavelet filter, (ii) image denoising using a bilateral filter. At first, wavelet optimal coefficients are selected using cooperative particle swarm optimiser (CPSO). After that, the hybrid domain based algorithm (wavelet with bilateral filter) is applied to the noisy image which is helpful to obtain the denoised image. A comparative study of the performance of different existing approaches and the proposed denoised approach is made in terms of PSNR, SDME, SSIM and GP. When compared, the proposed algorithm gives better PSNR compared to the existing methods.

Keywords: image denoising; optimal wavelet; bilateral filter; cooperative particle swarm optimiser; wavelet coefficient; sub-bands.

Reference to this paper should be made as follows: Velayudham, A., Madhan Kumar, K. and Kanthavel, R. (201x) ‘Optimised DWT using cooperative

A. Velayudham, K. Madhan Kumar and R. Kanthavel

particle swarm optimiser for hybrid domain based medical and natural image denoising’, Int. J. Biomedical Engineering and Technology, Vol. x, No., y, pp.xx–xx.

Biographical notes: A. Velayudham obtained his Bachelor’s degree (2002) in Computer Science & Engineering from Manonmanium Sundaranar University, India. Then he obtained his Master’s degree (2004) in Computer Science & Engineering from Annamalai University, India. He completed his PhD in Information & Communication Engineering from Anna University, Chennai. Currently, he working as Professor in the Department of Information Technology at Cape Institute of Technology, Levengipuram affiliated to Anna University, Chennai. His specialisations include biometrics, steganography & neural networks. His current research interests are image processing, medical image denoising & soft computing.

K. Madhan Kumar obtained his Bachelor’s degree in Electronics and Communication Engineering (2001) from Manonmanium Sundaranar University. Then he obtained his Master’s degree in Optical Communication (2004) from Anna University. He completed his PhD from Anna University, Chennai. He is a Life Member at ISTE professional Society. Currently, he is a Professor at the Faculty of Electronics and Communication Engineering, PET Engineering College Vallioor. His specialisations include optical communication, microwave engineering and image processing. His current research interests are remote sensing, satellite image processing and optical networking.

R. Kanthavel received his Bachelor of Engineering degree in Electronics & Communication Engineering in 1996. Then he obtained his Master of Engineering degree in Communication Systems in 1999 from M.K. University, India. He completed his PhD in Information and Communication Engineering from Anna University, Chennai. His previous experience was in Government College of Engineering, Tirunelveli. He is currently the Vice-Principal of Rajalakshmi Institute of Technology, Chennai. He has published books for engineering students. His interests include embedded systems, wireless communication systems and computer networks.

1 Introduction

The noise elimination has established itself as an eminent pre-processing module for the multifarious image and video processing mechanisms. By the term ‘noise’ what is construed in the digital image processing scenario is any type of measure which repels an observed pixel from its unrefined value. In fact, it is very easy for the observed images to get quickly tainted by several types of noises in the course of the acquirement or communication. Conversely, the universal noise elimination continues to remain as a hard nut to crack. The ostensible for the phenomenon is that the noises which severely taint an image may be broadly grouped into several types of the additive Gaussian noise, impulse noise or multiplicative noise, each one endowed with its own unique traits (Zhang et al., 2014). Of late, the field of image processing has been offered a red carpet welcome thanks to the prominent part played by in the medical horizon, as a major chunk of the ailments are diagnosed with the help of medical images. However, the images can be deployed for the diagnosing process, if only it is entirely bereft of noise (Choubey

Optimised DWT using cooperative particle swarm optimiser

et al., 2011). Incidentally, the striking characteristics of excellent image de-noising techniques lie on its unique skills to eliminate the noise simultaneously conserving the edges. However, it is unfortunate that in the domain of medical images like X-rays, MRI scans, CT scans it has metamorphosed into a Herculean Task.

The noise tainting in CT scan images is habitually modelled by a Rice distribution which is approximated by a Gaussian distribution for the inferior image intensities and by a Rayleigh distribution for the high-intensity areas. The general distributions unfolding the speckle noise include the Rayleigh (Bao and Zhang, 2003), Poisson (Kempen et al., 1997), K-distribution (Keyes and Tucker, 1999), Nakagami (Shankar, 2000), Fisher-Tippet (Sanches and Marques, 2003), and the generalised gamma (GG) (Michailovich and Tannenbaum, 2006). The Additive Gaussian noise is referred to quantities with a zero- mean Gaussian distribution and suck kind of noise was supplemented to the images in the process of acquirement. The traditional linear filters do away with Gaussian noise with adverse consequences for the edge and texture data in an image. With the intention of tackling these hassles, a host of modified Gaussian noise elimination approaches have been investigated which are dedicated for the purpose of edge-preserving (DeDecker et al., 2011; Portilla et al., 2003; Luisier et al., 2007). In this regard, the Wavelet thresholding algorithm surfaces as one of the most preferred techniques, in which the prominent BLS-GSM approach (Portilla et al., 2003) is employed to adapt the neighbourhoods of coefficients at various positions and scales and to initiate the Bayesian least squares evaluation method to modernise the wavelet coefficients.

Nowadays, feasts of image denoising approaches are doing their elegant rounds which encompass the denoising in spatial and frequency domain (Gonzalez et al., 2007). The former technique is targeted at employing a weighted average of adjacent pixel values to achieve the ideal pixel value of certain image points. This working code is performed on the mean filter, median filter, Gaussian filter and the like (Xiao et al., 2010). The prominent denoising technique forming part of this category includes the Wiener filter and wavelet transform (Feng, 2011; Raj and Venkateswarlu, 2012). A plethora of investigations have been conducted which have deeply dealt with the image denoising approaches right from the frequency domain denoising techniques (Gonzalez and Woods, 2002) to those of recent innovation like the Developed wavelet (Zhang et al., 2003), curvelet (Starck et al., 2002) and ridgelet (Chen and Kegl, 2002) based techniques, sparse representation (Elad and Aharon, 2003) and the K-SVD (Aharon et al., 2006) approaches, shape-adaptive transform (Foi et al., 2007), bilateral filtering (Tomasi and Manduchi, 1998; Barash, 2002), non-local mean based techniques (Buades et al., 2005; Kervrann and Boulanger, 2006) and non-local collaborative filtering (Dabov et al., 2007), to name a few. Moreover, Bilateral filter (BF) based image de-noising also used in paper (Velayudham and Kanthavel, 2015; Elad, 2002) A number of improvements over the BF technique had been launched to effectively tackle visual data and smooth the rest areas to the extent feasible (Yang et al., 2011). In contrast, the BF was a dominant member of the family of the Gaussian noise elimination approaches laden with constraints habitually decided by the process of trial and error in reality. It merited significant attention that invariably constraints were not appropriate for the objective of noise elimination and edge conservation for all the areas within an image.

The main aim of this proposed study is based on image de-noising using hybrid optimal wavelet and bilateral filter. In this paper, at first we apply the wavelet transform to the input image. Inside the wavelet transform, the wavelet coefficients are optimised using cooperative particle swarm optimisation (CPSO). Here, PSO algorithm is combined with cooperative strategy. The cooperative strategy is achieved by splitting the


candidate solution vector into components, where each component is optimised by a particle. Cooperation is mainly in terms of exchanging information about best positions found by different groups. Then, the obtained four sub bands are given to the bilateral filer. The BF reduces the noise present in the images. The rest of the paper organised as follows; In Section 2, we present the image denoising based literature review and Section 3 shows the contribution of the research. In Section 4, we have described a background of the proposed methodology and proposed image de-noising frame work is explained in Section 5. The experimental results are analysed in Section 6 and conclusion part is present in Section 7.

2 Literature review

With an eye on overwhelming the constraints of the de-noising process, a host of investigations have been carried out which are well-reflected in the recent literature. Nadernejad and Nikpour *2012) invested time and energy for launching a novel approach employing the integration of the pixel concept and the partial differential equations (PDEs) with the intention of effective image de-noising. Ge et al. (2013) were instrumental in flagging off an innovative region-based active contour model for magnetic resonance image segmentation and denoising in accordance with the global minimisation framework and level set evolution. Landi and Piccolomini (2012) elegantly envisaged the non-negatively constrained Total Variation-based denoising of medical images tainted by the Poisson noise. The novel technique represented a Newton projection approach, where the internal mechanism was tackled by the Conjugate Gradient technique, preconditioned and executed in an effective manner for this specified application. The Wavelet thresholding technique represented one of the most desired techniques for the purpose of image denoising. Weipeng (2013) took pains to elaborate on the innovative image denoising technique of the refuge chamber by duly blending the wavelet transform and bilateral filtering. With the intent to preferably locate the infrared image of the refuge chamber, cut down its image noises and preserve additional image data, they beautifully brought in the novel approach of integrating two-dimensional discrete wavelet transform and the bilateral denoising. Zhang et al. (2014) excellently envisioned the adaptive bilateral filter based structure for the image denoising. In their innovative technique, denoising structure fundamentally comprised an impulse noise detector (IND), an edge connection process and an adaptive bilateral filter (ABF). Further, they toiled hard to launch an enhanced artificial bee colony (IABC) approach to adapt the constraints of the adaptive bilateral filters, thereby facilitating the efficient noise elimination and excellent edge conservation.

In addition, Velayudham and Kanthavel (2014) envisaged a novel de-noising method with Empirical mode decomposition (EMD) and Dual Tree Complex Wavelet Packets employing the medical images, where, noise corrective phase dependent on the EMD failed to significantly contribute to the accomplishment as most of the noise pixels were offered in a non-linear manner. Moreover, Subodh et al. (2012) have explained the ultrasound image de-noising based complex diffusion-based filter. Here, mainly used speckle noise for images. Naranchimeg et al. (2012) have explained the improved real-time method for noise reduction of directional Doppler audio signals. This method reduces the noise using low-pass filter with a variable threshold value based on maximum frequency of spectrum signals. The noise of Doppler audio signals was


reduced efficiently by using this algorithm. Moreover, El-said et al. (2012) have explained the Enhanced ultrasound images de-noising technique for speckle noise suppression in ultrasound images. This technique estimates automatically speckle noise amount in the ultrasound images by estimating important input parameters of the filter and then denoise the image using the sigma filter.

Motivated by the compelling concerned discussed above, in this document, an innovative parameter optimisation employing the Orthogonal Learning Particle Swarm Optimisation is elegantly launched for the purpose of the hybrid domain based image denoising. At the outset, the optimal wavelet transform is performed on the input image to generate the four sub-bands like the LL, LH, HL, and HH. In this technique, the Image Contour is fundamentally mirrored in the low-frequency segment, while the data is parked in the high-frequency segment, thereby leading to the improvement of the low-frequency decomposition coefficient. Now, the attenuation processing is performed to process the high-frequency decomposition coefficient, with a view to attaining the image augmentation. While filtering out noises, the bilateral filtering efficiently preserves the image features. At last, the inverse wavelet transform is applied to restore the source image with an eye on improving the image.

3 Contribution of the study

The main contribution of the study is given below;

This paper introduces a novel algorithm for image de-noising using combination of optimal wavelet transform with bilateral filter.

We develop a proposed methodology mainly contribute to medical image de-noising.

The proposed method can easily remove the noise from the image and improve the image quality.

The main contribution of this paper is in the use of a new neighbourhood relationship to develop a new multiscale bilateral filter for image de-noising

4 Background of the system

In this section, we will first present the background of the image denoising techniques used in this research. Then, the details of proposed algorithms will be presented.

4.1 Noise model

Consider an image is represented in terms of a matrix K with the entry ,i jK indicating

the intensity value of the pixel at ,i j . Given that an image is tainted by the additive Gaussian noise as per equation (1):

, , ,i j i j i jK A N (1)


where ,i jA characterises the pixel intensity of a noise-free image A at ,i j and ,i jN signifies the supplementary noise value generated from a zero-mean Gaussian distribution.

Further, the Gaussian noise represents the statistical noise possessing a probability density function (PDF) which is identical to that of the normal distribution, which is called the Gaussian distribution. Thus, the values that the noise can acquire are Gaussian-distributed.

The probability density function P of a Gaussian random variable K is given by:

2

2

12

2

k

GP K e

(2)

Where;

K Represents the grey level

Mean value

Standard deviation

In the case of the impulse noise, a fraction of the original pixel values are substituted by arbitrary values gathered from certain specified distribution. Let ,i jN represent the

intensity value of impulse noise at ,i j . The ,i jN is placed between the maximum intensity value maxI and the minimum intensity value minI . If ,i jN characterises only

minI or maxI , the noise model is termed as the salt–and–pepper noise. In addition, with the stipulation ensuring that ,i jN

gathers the arbitrary values from the interval min max,I I with the uniform distribution, the noise model is labelled as the uniform impulse noise. The impulse noisy image can be expressed as;

,

,, 1

i ji j

i j

N withprobability pK

N withprobability p

(3)

where p denotes the probability of a noise free image corrupted by impulse noise.

4.2 Wavelet transform

Let us assume that for a specified noise free input image ,{ , 1, 2,..., ,i jA A i M 1, 2,..., }j N gets tainted by the additive white Gaussian noise as per the rule furnished

in equation (4) shown below.

, , ,i j i j i jK A N (4)

where N is Gaussian noise and K is the noisy image. It has been assumed statistically that noise has independent and identical distribution pattern.


In the image tainted with the noise, the wavelet transform T is performed. The decomposition of the image into coefficients is carried out as illustrated in the following equation (5).

, ,i j i jD T K (5) The discrete wavelet transformation disintegrates the noisy image into diverse frequency sub-bands, marked as jLL , kLH , kHL and kHH , where 1,2,...k j . The subscript

indicates the thk frequency level and j represents the largest scale in the disintegration. All the sub-bands characterise diverse data on the image. The lowest frequency band

jLL relates to a rough estimate of the image. The kLH , kHL and kHH sub-bands indicate the horizontal, vertical and diagonal data of the image signal, correspondingly. The highest frequency band is represented by kHH . The kLL sub-band is additionally disintegrated in the recursive method into the sub-bands 1kLH , 1kHL and 1kHH . When a wavelet transform is initiated on an image the image is decayed into four sub-bands as illustrated in Figure 1.

Figure 1 2D analysis filters and image decomposition

After estimating the threshold value, the wavelet coefficient is varied in accordance with the shrinkage function S , as illustrated in the following equation (6).

, ,i j i jB S D (6) When the shrinkage of the wavelet coefficients comes to a close, it is transformed inverse to the original image domain as exhibited in equation (7) appearing hereunder.

1A T B (7)

where 1T is the inverse discrete wavelet transformation function and A is the restored image. The wavelet decomposition structure is shown in Figure 2.


Figure 2 Wavelet decomposition structure

Wavelet decomposition

LL LH

HL HH

Input image

4.3 Bilateral filter

The bilateral filtering owes its origin to the literary domain and is endowed with the nonlinear, non-iterative and local filtering traits and the constructive skills of edge conservation and the pulse noise repression (Tomasi and Manduchi, 1998). A bilateral filter invariably represents a non-linear, edge conserving and noise- sinking smoothing filter for the images. The intensity value of each pixel in an image is substituted by a weighted average of intensity values from the neighbourhood pixels, the weights being dependent on a Gaussian distribution. Significantly, the weights rely on both the Euclidean distance of pixels and the radiometric divergences. This has the effect of conserving the sharp edges by methodically looping through each pixel and adapting weights to the neighbouring pixels correspondingly.

The bilateral filter is defined as

1i

filteredi i i

xp

O x O x fr O x O x gs x xW

(8)

where the normalisation term

i

p i ix

W fr O x O x gs x x

(9)

where filteredO Filtered image

OOriginal input image to be filtered

x Coordinates of the current pixel to be filtered

Window centred in x

frRange kernel for smoothing differences in intensities.

gs Spatial kernel for smoothing differences in coordinates.

As discussed above, the weight pW is allocated by means of the spatial intimacy and the

intensity variance. Let us take the case of a pixel situated at ,i j which has to be


denoised in the image by means of its adjoining pixels one of which is situated at ,p q . Thereafter, the weight allocated for a pixel ,p q to denoise the pixel ,i j is furnished by means of equation (10) furnished hereunder.

22 2

2 2

, ,, , , exp exp

2 2d r

O i j O p qi p j qW i j p q

(10)

where

d and r smoothing parameters

,O i j and ,O p q intensity of pixels ,i j and ,p q

Using the above equation we obtain ,DO i j which is given in equation (11)

,

,

, , , ,,

, , ,p q

D

p q

p q W i j p qO i j

W i j p q

(11)

where ,DO i j signifies the denoised image of the pixel ,i j . The BF represents the adapted low-pass Gaussian filter for the domain filter and the range filter. The domain low-pass Gaussian filter allocates immense weights to the pixels spatially near the centre pixel. The range low pass Gaussian filter apportions enormous weights to the pixels identical to the centre pixel in the grey value. The BF is well-geared to efficiently eliminate the Gaussian noise, as it involves the fundamental task of grey filtering and the characterisation of the spatial layout of pixels. Further, the range deviation r across an edge tends to be comparatively greater than that along the edge, thereby empowering the BF-to to conserve the edge frameworks to a limited extent.

4.4 Standard PSO

The Particle Swarm Optimisation (PSO) is the most dynamic and extensively employed swarm intelligence technique flagged off by Kennedy and Eberhart in 1995 for outsmarting the optimisation hassles (Kennedy and Eberhart, 1995). The fundamental theory behind the innovative technique embraces a population, otherwise known as the swarm, of search points, labelled as the particles, on the lookout for the optimal solutions within the search space, concurrently. The particles move about in the search space with the presumption of an adaptable position shift, which is known as the velocity, at each iteration. The underlying hypothesis in the PSO is that each particle is competent to remember the best position found in history, or in other words, the best position that has ever been found by the whole swarm, termed as the global best, and the best position ever found by each particle, labelled as the personal best. With the intention of locating the global optimum of the optimisation menace, the particles learn from the personal best and global best positions. In particular, the learning systems in the canonical PSO may be put in a nutshell as detailed below.


Further, each particle commits to memory the best position it has ever visited, which

represents the position with the lowest function value. This data can be deemed as the

experience of the particle which is transmitted to the other particles. With this objective,

each particle is allocated a neighbourhood, which decides the indices of its mates which

are going to share its experience.

In normal PSO, each individual in the swarm is treated as a particle in a D-dimensional search space, and signified by a three tuple{ , , }i i iY V P . iY

1 2( , ,..., )i i iDy y y and 1 2( , ,..., )i i i iDV v v v indicate the position and velocity of the particle i , correspondingly. 1 2( , ,..., )i i i iDP p p p Signifies the personal best (

bestP ) of the particle i (that is, the best position achieved by the particle i ). 1 2( , ,..., )DG g g g Indicates the global best ( bestg ), that is, the best position followed by the whole swarm. The value of each element in the vector iV can be closed to the range of max max[ , ]v v to control the unnecessary roaming of particle outside the search space, and revised by

1 1 2 21 best besti i i i iV t w V t C R t P t Y t C R t g t Y t (12) where t Generation number, iV t Velocity of the thi particle, iY t Position of the thi particle, wInertia weight, 1 2,C C Acceleration coefficient, 1 2,R R randomly generated vectors, bestP Personal best of the thi particle, bestg Global best of the swarm.

The particle flies toward a novel position according to (13), and each value of the novel position should not go beyond the range of [min , max ]X X

1 1i i iY t Y t V t (13)

The position and velocity of each particle in the swarm are initialised arbitrarily at the beginning. After that, each particle i is led by its own flying practice bestP and the best particle bestg , i.e., revised by (12) and (13). This procedure is replicated till a user-defined stopping criterion is attained. The stages of standard PSO is as shown in Table 1.

Even though, there has been a volley of quick improvements and enhancements of the PSO technique over the last several decades with the novel technique having succeeded in effectively casting its lot with a feast of vibrant applications such as the water distribution network design (Montalvo et al., 2008), resource allocation (Gong et al., 2012), task assignment (Ho et al., 2008), maximum power point tracker for the photovoltaic system (Ishaque and Salam, 2013), optimal control (Cruz et al., 2013), DNA sequence compression (Zhu et al., 2011) and reconstruction of gene regulatory network (Palafox et al., 2013), image processing (Cagnina et al., 2014), text clustering (Yuhui, 2001) and the like (Weipeng, 2013), it turns out substandard performance when the optimisation issue is either flooded with a huge number of local optima or is high-dimensional and non-separable (Yang and Pedersen, 1997). This sorry state of affairs in regard to the inferior performance of the PSO is mainly on account of its feeble robustness to several problem frameworks (Bergh and Engelbrecht, 2004). Taking all


these into consideration and with an eye on scaling up the search performance of the standard PSO, in the current investigation, we have efficiently employed the CPSO algorithm. Table 1 Pseudo code for PSO algorithm

Input: Parameters of PSO algorithm Output: Best particle Start 1. Randomly initialise position and velocity of all particles

2. Evaluate the fitness values of all particles; let each particle’s bestP be its current position; let bestg be the best one among all particles

3. Updated each particle’s velocity and position using (12) and (13). 4. Calculate the fitness values of all particles

5. Update bestP . For each particle, if the fitness value of its new position is better than that of it’s bestP , then replace it’s bestP by the new position. 6. Update bestg . For each particle, if the fitness value of its new position is better than that of the bestg , then replace the bestg by the new position.

7. If the stopping criterion is satisfied, output bestg and its fitness value; otherwise, go to Step 3.

8. end Output: Best particle

4.5 CPSO algorithm

The same concept of PSO algorithm was creating a family of cooperative particle swarm optimiser (CPSO). Instead of having one swarm (of particles) trying to find the optimal dimension vector, the vector is split into its components so that swarms (of particle each) are optimising a 1-D vector. For instance, given a 3-dimension Sphere function 2 2 21 2 3( )f X x x x , whose global minimum point is [0, 0, 0]. Assume that the present position is iX = [2, 5, 2], its personal best position is iP = [0, 2, 5] and its neighbourhood’s best position is nP = [5, 0, 1]. The revised velocity is iV = [1, −8, 2] according to (5), and hence the novel position is i i iX X V = [3, −3, 4], resulting in a novel position with a cost value of 34 which is worse than Xi and Pi. As a result, the particle does not advantage from the learning from iP and nP in this generation. On the other hand, vectors iP and nP indeed acquire good information in their structures. For instance, if we can find out good dimensions of the two vectors, we can next join them to form a novel guidance vector of oP = [0, 0, 1] where the first coordinate 0 comes from iP while the second and the third harmonises 0 and 1 come from nP (with the corresponding dimension). Given the guidance of oP , the revised velocity turn out to be i o iV P X = [0, 0, 1] − [2, 5, 2] = [−2, −5, −1]; hence the novel position is i i iX X V = [0, 0, 1], resulting in a novel and better position with a cost ( ) 1f X that formulates the particle fly faster toward the global optimum [0, 0, 0].


5 Proposed image denoising frame work

The basic idea of our research is to image denoising using hybrid optimal wavelet and bilateral filter. The need for this study is to de-noising application such as medical imaging where good image visual quality is particularly emphasised. In this proposed work, we utilise medical image and natural images. Consider the input image ,O i j which contains Gaussian noise, we put forward an image de-noising algorithm

which combines bilateral filtering and optimal wavelet transform together. This algorithm first adopts optimal wavelet transform to decompose the original noise image into high and low-frequency components. After that, we optimise the wavelet coefficient using CPSO algorithm. Finally, the bilateral filter is used to remove the noise present in the image. The image de-noising approach is mainly divided into two stages such as (i) design of optimal wavelet filter and (ii) design of image denoising using a bilateral filter. The overall process of image denoising is shown in Figure 3.

Figure 3 Overall structure of the hybrid domain image denoising

5.1 Design of optimised wavelet filter

The main aim of this section is to find the optimal wavelet coefficient using cooperative particle swarm optimisation (CPSO) algorithm. Based on the coefficients only we can decompose the image. The optimal coefficient values are gives better results. The optimal wavelet filter design is carried out by integrating the important optimisation algorithms like CPSO. This traditional PSO algorithm called CPSO, which employing cooperative behaviour to significantly improve the performance of the system. This is achieved by using multiple swarms to optimise different components of the solution vector completely. Basically, the wavelet transform is applied to the noisy image it produce the four sub-bands, but which is not optimal sub-bands. Therefore, we use the CPSO optimisation approach to optimise the wavelet coefficients which is used to increase the PSNR values. The step by step process is explained below.

Step 1: Population initialisation and Parameters setting

The initial population of CPSO is generated uniformly at random in search space. At first, the lower bound ( iL ) and upper bound ( iU ) are set depending upon the wavelet


coefficient range. Here, Haar wavelet coefficients are used. To initialise CPSO, M N size population is generated, where, M is the dimension of the population and N is the population size. In our case, 4M and 10N . The sampling process of solution encoding is presented in Figure 4. Where ,i jL and ,i jU are lower and upper bound coefficients.

Figure 4 Solution encoding process

Step 2: Fitness calculation

From the initial solutions, the first 2 10 (i.e. 1,1L to 2,5U ) are assigned as Low pass filter coefficients and last 2 10 (i.e. 3,1L to 4,5U ) are assigned as high pass filter coefficients. Above selected low and high pass filter coefficients with DWT are given to image de-noising process. An assessment function is required when applying the CPSO to optimise the wavelet parameter to maximise the PSNR, to work out the fitness value of each particle in the swarm. When each image is given to the denoising process, the fitness function is calculated as follows:

2max

10 *10log w h

xy xy

E W WPSNRW W

(14)

where

wW and hW Width and height of the denoised image

xyW Original image pixel value at coordinate ( , )x y

*xyW Denoised image pixel value at coordinate ( , )x y

2maxE Largest energy of the image pixels (i.e., maxE =255 for 256 gray-level images)

Step 3: Selection of iP and nP

After calculating the fitness value of each particle, we select the personal best position iP based on the fitness value and its neighbourhood’s best position nP .


Step 4: Velocity update

To form an enhanced guidance vector oP the original PSO can be adapted as a CPSO with an OL approach that joins information of iP and nP . The particle’s flying velocity is hence changed as

( )d d di i d od iV V cr P X (15)

d d di i iX X V (16)

Where;

Inertia weight

c Randomly selected value which is fixed to be 2.0,

dr Random value consistently generated inside the interval [0,1]. d

iV Velocity of ith particle

diX Current position of the particle i

oP Guidance vector

The guidance vector oP is constructed for each particle i , correspondingly, from

iP and nP as

o i nP P P (17)

Where;

iP Personal best position

nP Neighbourhood’s best position

Cooperative operation

Step 5: Stopping criterion

The algorithm discontinues its execution only if a maximum number of iterations is achieved and the particle which is holding the best fitness value is selected and it is given as the best low and high pass coefficients feature to image de-noising.

5.2 Design of image de-noising framework

After the image decomposition, the four sub bands are given to the bilateral filter for remove noise present in the input image. At the time of filtering out the noises, the bilateral filtering is competent to efficiently preserve the image features. Nevertheless, being a weighted average technique dependent on the neighbourhood pixels, it gives rise to the lingering noises in certain regions. The luminous merits of the wavelet transform are focused on its unique characteristics of the time-frequency localisation and multi-resolution. The signals are disintegrated into two diverse segments such as the high-frequency and low-frequency segments by means of the wavelet transform. The high-frequency segment in the wavelet decomposition coefficient concurrently consists of the


image data and noises, while the low-frequency segment is essentially home to the edge data of the image. Hence, it is highly indispensable to differentiate the noise segment from the high-frequency coefficient. After optimal wavelet decomposition, we further perform bilateral filtering. Firstly, the original image receives optimal wavelet decomposition with one decomposition level. Next, bilateral filtering is used for high-frequency sub-band images HH, LH, and HL, but low-frequency sub-band image LL is not processed.

In the bilateral filter, at the outset, we estimate the spatial domain and Gaussian filter in the grey value domain. The filtered image output in the spatial domain is achieved by means of Equation 18 appearing here under.

1 ,

d

S x H b x dN x

(18)

,dN x b x d

(19)

where

S x Input image

H x Output image

,b x Geometric distance between adjacent central point and its adjacent point

dN x Normalisation constant

Filtered image output in grey value domain is given in following;

1 ,

r

S x H g H H x dN x

(20)

,rN x g H H x d

(21)

where

,g H H x Brightness similarity between adjacent centre x and an adjacent point

rN x Normalisation constant

After that, we combine the (20) and (21) to get the bilateral filtering based spatial domain and similarity degree simultaneously, i.e.,

1 , ,S x H b x g H H x d

N x

(22)

, ,N x b x g H H x d

(23)


Equation (23) illustrates the weighting coefficient of the bilateral filter N x which is dependent on the spatial distance and grey value distance between pixels concurrently. The image processed by means of this approach filters the noises and preserves the marginal data. In the long run, the soft thresholding technique is applied to the wavelet coefficient as per equation (24) shown below.

, , ,,

,0

j p j p j pj p

j p

sign c c wc

w

(24)

The soft thresholding technique is elegantly employed to eradicate the noise from the image. When the wavelet disintegration comes to a close, the high-frequency sub-band image is subject to the bilateral filtering. Subsequent to the conclusion of the adoption of the wavelet decomposition coefficient, by means of the inverse wavelet transform, the source image ,D i j is recovered so as to realise the improved image. The pseudo code for proposed work is given in Table 2. Table 2 Pseudo code for proposed image denoising

Input:

Input image ,O i j Parameters of the wavelet transform Parameters of the CPSO algorithm Parameters of the bilateral filter Output:

Denoised image ,D i j Assumption;

Initial velocity 0iV

Start:

1.get the input image ,O i j

2. add the Gaussian noise to the ,O i j 3. apply the optimal wavelet transform { Generate the initial population of CPSO (refer Table 1)

Assign iL and iU depends upon the wavelet coefficient range

Calculate the fitness value using (14) } 4.Repeat


Table 2 Pseudo code for proposed image denoising (continued)

{

5.update the velocity diV based on the CPSO

( )d d di i d od iV V cr P X

6.Calculating the new solution diX based on d

iV d d di i iX X V

7. repeat 8. Stop the criteria if the optimal coefficient is obtained 9. select the optimal subband such as LL, LH, HL and HH 10. select only high-frequency band for further processing 11. high-frequency sub-bands are given to the bilateral filter { calculate spatial domain using (18) calculate grey value domain using (20) combine both the domain using (22)

Remove the noise based on the soft thresholding . obtain the denoised subbands } 12. apply reconstruction process { Inverse wavelet transform is applied to the sub-bands

Obtain the de-noised image ,D i j } Output:

Denoised image ,D i j Stop.

6 Result and discussion

The practical implication of proposed image de-noising is presented in this section. The performance of the image is tested under various noise conditions and here we are using two types of test images, including medical images and natural images. The experimental images used in the simulations are generated by contaminating the original images by noise with an appropriate noise density depending on the experiment. The proposed image denoising technique has been implemented in the working platform of MATLAB (version7. 12). This technique is performed on a windows machine having configuration processor® Dual-core CPU, RAM: 1 GB, Speed: 2.70 GHz with Microsoft Window7 professional operating system. We have utilised the size of the image “512×512”, whose


images are publicly available. Table 3 shows the input images used in the proposed work. Here, we experimentally compare our proposed de-noising framework with several alternative filters. Table 3 Used medical and natural images of the proposed work

Our proposed work consists of two phases such as design of optimal wavelet filter and image denoising framework. We foremost, improve the wavelet coefficient using CPSO optimisation algorithm, which will give the optimal sub-bands and this process is to improve the quality of the image. After that, the optimal subband is given to the bilateral filter; it will remove the noise present in the image. Finally, soft thresholding method is used to produce the denoised image. Here, we utilise the eight publically available “512×512” greyscale images such as baboon image, Barbara image, cameraman image, house image, Lena image and three medical images for testing the qualitative-quantitative evaluation. These images are corrupted by Gaussian noise, impulse noise and salt and pepper noise with different noise levels respectively. Additionally, a standard set of noisy images is created to eliminate the bias produced by different expressions of noise. Four widely used objective evaluation criteria, the peak- signal to noise ratio (PSNR), Structural Similarity (SSIM), Second Derivative Measure of Enhancement (SDME) and Gain Parameter (GP) are given as follows;

PSNR: The description of peak signal to noise ratio (PSNR) is given below;

2max

10 *10log w h

xy xy

E I IPSNR

I I

where wI and hI Width and height of the de-noised image

xyI Original image pixel value at coordinate ( , )x y

*xyI Denoised image pixel value at coordinate ( , )x y

2maxE Largest energy of the image pixels


SSIM: The description of Structural Similarity (SSIM) is given below;

ˆ1

2 2 2 2ˆ ˆ1 2

2 2ˆ,

I I I I

I II I

CSSIM I I

C C

where I denotes the original image, Î denotes the denoised image. I and Î are the

mean value of the image I and Î respectively. I and Î are the standard deviation of

the image I and Î respectively. 1C and 2C are the two parameters. SDME: The description of Second Derivative Measure of Enhancement (SDME) is

given below;

max; , , , min; ,

1 2 max; , , , min; ,

21 20ln2

k l center k l k l

k l center k l k l

I I ISDME

k k I I I

Where the denoised image is divided into ( 1 2k k ) blocks with odd size, max; ,k lI and

min; ,k lI correspond to the maximum and minimum values of pixels in each block whereas

; ,center k lI is the value of the intensity of the pixel in the centre of each block. GP: The description of the gain parameter (GP) is the ratio of original noise and the

remainder noise.

var10 log10

ˆvar

nGP

I n I n

where

n Original noise

I n Original image

Î n Noise reduced image

6.1 Experimental results

The basic idea of our research is to de-noise the image using optimal wavelet transform with bilateral filter. Here, first, we show the experimental outcome of the proposed approach using optimal wavelet with a bilateral filter. In our work, we present the CPSO algorithm to optimise the parameters of the wavelet transform which is improving the quality of the image. Table 4 presents the denoised image results using natural images corrupted with 20% Gaussian noise and Table 5 illustrates the performance of medical images corrupted with 20% Gaussian noise. Similarly, Tables 6 and 7 presents the experimental output of the denoising approach using without CPSO optimisation algorithm in wavelet filter.


Table 4 Experimental results of natural images using proposed approach

Table 5 Experimental results of medical images using proposed approach


Table 6 Experimental results of natural images without using CPSO method

Table 7 Experimental results of medical images without using CPSO method


Figure 5 shows the proposed approach based on the PSNR measures. Here we compare our proposed approach with a Particle swarm optimisation algorithm. The PSO algorithm has the advantages of easily realising and quickly converging but standard PSO algorithm easily traps into local optima and also is not robust and quickly converging. To overcome the difficulties present in the PSO in our work, we use CPSO algorithm. This algorithm is very good convergence and improves the quality of the image. In Figure 5, we obtain the maximum PSNR of 32 dB which is very much high compared to when using the PSO algorithm. As the number of iteration increases, PSNR value also increases. From the graph, we clearly understand our proposed approach achieves the maximum PS NR compared to existing approaches.

Figure 5 Experimental results of iteration vs. PSNR

6.2 Comparative analysis

To evaluate the performance of our proposed approach, we compare our results with our previous methods. Here we compare our work with three approaches such as two previous published papers (EMD+DTCWP (Velayudham and Kanthavel, 2014), LPG+DTCWP (Velayudham and Kanthavel, 2015)) and PF+BF (without CPSO). In (Velayudham and Kanthavel, 2014), image denoising technique using Dual Tree Complex Wavelet Packets, Empirical Mode Decomposition and Sobel operator was explained. Here, histon process was used in order to surmount the smoothing filter type and it not affects the lower dimensions. Similarly, Velayudham and Kanthavel (2015) introduced a three-stage image denoising method by applying Dual Tree Complex Wavelet Packets (DTCWP) and LPG-PCA method. DTCWP and histon calculation were used as a method to identify the noisy pixel information and remove small amount of noise in first stage. The second stage yields an initial estimation of the image by removing most of the noise and the third stage is further refined from the output of the second stage. The three stages have the same process except for the parameter of noise


level. Moreover, without optimisation method same as our proposed approach only different is optimisation. Furthermore, in these approaches, they characterise the local features of the image based on the wavelet coefficients. Therefore, we have chosen to compare the performance of our proposed algorithm against these methods. From the results, one can observe that EMD+DTCWP (Velayudham and Kanthavel, 2014), LPG+DTCWP (Velayudham and Kanthavel, 2015) methods are obtaining slightly different results. Our method is different from the above three methods. To improve the quality of the image here, we used optimisation algorithm. Figures 6 to 9 show the comparative results of our proposed work against existing approaches.

Figure 6 Performance analysis of PSNR plot for proposed against existing using 20% Gaussian noise

Figure 7 Performance analysis of PSNR plot for proposed against existing using 40% Gaussian noise


Figure 8 Performance analysis of PSNR plot for proposed against existing using 20% salt and pepper noise

Figure 9 Performance analysis of PSNR plot for proposed against existing using 40% salt and pepper noise

Figures 6 to 9 show the performance of PSNR for various noise levels. Even though PSNR can certainly measure the intensity difference between two images, it really is well-known that it may perhaps don't identify the visual perceptual quality of the image. We improve the PSNR values pertaining to different images within different noise level such as 20% and 40%. In Figure 6, we obtain the maximum PSNR of 36 dB for Medical image (3) and the scheme using the EMD+DTCWP (Velayudham and Kanthavel, 2014) gives a PSNR of 20.9230 dB, LPG+DTCWP (Velayudham and Kanthavel, 2015) gives 24 dB and PF+BF (without CPSO) gives 24 dB. Similarly, in Figure 7 we obtain the maximum PSNR of 35 dB for a medical image. Considering Figures 6 to 9 we have justified that we have obtained maximum PSNR values for our proposed approach. The approach PF+BF (without CPSO) is same as the proposed approach only thing is there is no optimisation. The optimisation algorithm is for improving the quality of the image and PSNR value. It can be proven that our proposed method has outperformed the existing approaches.


Table 8 Comparative results for images with 20% of Gaussian noise

Appr

oach

es

Perf

orm

ance

M

easu

res

Babo

on

imag

e Ba

rbar

a

imag

e C

amer

aman

im

age

Hou

se im

age

Lena

imag

e M

edic

al

imag

e (1

) M

edic

al

imag

e (2

) M

edic

al

imag

e (3

)

EMD

+DTC

WP

PSN

R

27.6

9787

27

.939

29

27.2

6956

25

.489

2 28

.891

51

23.6

3809

21

.566

7 20

.923

0 SS

IM

0.22

453

0.26

231

0.23

128

0.20

123

0.22

671

0.24

7881

0.

2334

63

0.26

4351

SD

ME

16.2

761

15.8

527

18.9

4358

16

.578

8 11

.563

21

16.2

2532

16

.245

39

16.3

454

GP

6.34

108

4.23

783

5.28

171

5.54

453

6.13

5743

4 5.

5773

6 9.

5743

4 7.

5687

43

LPG

+DTC

WP

PSN

R

25.5

6378

21

.476

29

24.5

6956

28

.689

2 25

.655

18

23.8

6480

26

.264

6 24

.346

0 SS

IM

0.23

563

0.24

674

0.21

541

0.22

455

0.25

8476

0.

2814

278

0.25

7834

0.

2374

43

SDM

E 15

.767

66

17.5

485

19.5

4794

3 13

.655

7 16

.346

73

19.6

4887

14

.477

65

18.4

444

GP

5.65

5867

3.

6578

56

6.45

774

7.23

542

7.35

6379

6.

5738

8 9.

5743

4 8.

3463

65

PF+B

F (W

ithou

t C

PSO

)

PSN

R

25.4

274

20.1

978

23.8

335

21.1

482

19.1

206

20.1

982

22.5

805

24.2

37

SSIM

0.

2115

3 0.

2518

9 0.

2287

6 0.

2153

2 0.

2051

0 0.

2288

9 0.

2476

38

0.24

6435

SD

ME

14.8

750

13.5

6704

16

.587

1 17

.851

1 12

.863

921

15.1

2632

11

.145

39

11.2

5462

G

P 5.

1084

3 6.

7834

0 5.

2817

1 6.

5345

3 4.

5743

48

7.57

3644

8.

1344

9 5.

4366

49

Prop

osed

ap

proa

ch

PSN

R

30.3

074

30.9

781

32.9

535

31.6

48

32.2

025

34.0

980

33.8

020

36.3

272

SSIM

0.

3315

38

0.31

6218

0.

3226

14

0.31

133

0.29

7102

0.

3089

92

0.30

7118

0.

2794

85

SDM

E 24

.781

51

23.7

0429

23

.757

12

25.7

231

22.3

9315

19

.083

28

20.3

3906

14

.846

27

GP

7.04

8436

9.

1340

16

9.19

9716

7.

8385

3 8.

3400

83

11.6

4452

11

.449

29

8.64

9273


Table 9 Comparative results for images with 40% of Gaussian noise

Appr

oach

es

Perf

orm

ance

M

easu

res

Babo

on

imag

e Ba

rbar

a

imag

e C

amer

aman

im

age

Hou

se

imag

e Le

na

imag

e M

edic

al

imag

e (1

) M

edic

al

imag

e (2

) M

edic

al

imag

e (3

)

Exis

ting

App

roac

h

PSN

R

25.4

274

20.1

978

23.8

335

21.1

482

19.1

206

20.1

982

22.5

805

24.2

37

SSIM

0.

2115

3 0.

2518

9 0.

2287

6 0.

2153

2 0.

2051

0 0.

2288

9 0.

2476

38

0.24

6435

SD

ME

14.8

750

13.5

6704

16

.587

1 17

.851

1 12

.863

921

15.1

2632

11

.145

39

11.2

5462

G

P 5.

1084

3 6.

7834

0 5.

2817

1 6.

5345

3 4.

5743

48

7.57

3644

8.

1344

9 5.

4366

49

Exis

ting

App

roac

h

PSN

R

27.6

9787

27

.939

29

27.2

6956

25

.489

2 28

.891

51

23.6

3809

21

.566

7 20

.923

0 SS

IM

0.22

453

0.26

231

0.23

128

0.20

123

0.22

671

0.24

7881

0.

2334

63

0.26

4351

SD

ME

16.2

761

15.8

527

18.9

4358

16

.578

8 11

.563

21

16.2

2532

16

.245

39

16.3

454

GP

6.34

108

4.23

783

5.28

171

5.54

453

6.13

5743

4 5.

5773

6 9.

5743

4 7.

5687

43

With

out

CPS

O

PSN

R

19.1

206

20.1

982

22.5

805

24.2

37

27.6

9787

27

.939

29

27.2

6956

25

.489

2 SS

IM

0.22

876

0.21

532

0.20

510

0.22

889

0.24

7638

0.

2623

1 0.

2312

8 0.

2615

38

SDM

E 12

.863

921

15.1

2632

11

.145

39

11.2

546

15.7

6766

17

.548

5 19

.547

94

14.8

750

GP

4.57

4348

7.

5736

44

8.13

449

5.43

664

6.34

108

4.23

783

5.28

171

5.54

453

Prop

osed

ap

proa

ch

PSN

R

33.1

3075

31

635.

978

34.4

6748

9 29

.546

6 32

.202

5 35

.465

46

34.4

3636

34

.555

SS

IM

0.32

5536

0.

2965

621

0.35

7582

6 0.

3346

3 0.

2834

657

0.26

8795

8 0.

2595

74

0.25

4685

SD

ME

22.4

6778

1 25

.587

042

25.5

4897

5 29

.367

2 25

.643

931

18.6

4708

3 26

.436

36

18.8

6356

7 G

P 65

57.0

484

8.53

4570

1 10

.253

475

8.64

885

8.36

737

16.3

6365

7 15

.684

8 7.

4637


Table 10 Comparative results for images with 20% of salt and pepper noise

Appr

oach

es

Perf

orm

ance

M

easu

res

Babo

on im

age

Barb

ara

imag

e C

amer

aman

im

age

Hou

se

imag

e Le

na

imag

e M

edic

al

imag

e (1

) M

edic

al im

age

(2)

Med

ical

im

age

(3)

Exis

ting

App

roac

h

PSN

R

25.5

6378

21

.476

29

24.5

6956

28

.689

2 25

.655

18

23.8

6480

26

.264

6 24

.346

0 SS

IM

0.23

563

0.24

674

0.21

541

0.22

455

0.25

8476

0.

2814

278

0.25

7834

0.

2374

43

SDM

E 15

.767

66

17.5

485

19.5

4794

3 13

.655

7 16

.346

73

19.6

4887

14

.477

65

18.4

444

GP

5.65

5867

3.

6578

56

6.45

774

7.23

542

7.35

6379

6.

5738

8 9.

5743

4 8.

3463

65

Exis

ting

App

roac

h

PSN

R

26.4

637

26.4

66

27.2

6956

26

.325

28

.891

51

28.5

637

24.5

4775

22

.462

64

SSIM

0.

2445

6 0.

2556

3 0.

2312

8 0.

2246

0.

2267

1 0.

2957

4 0.

2843

3 0.

2543

51

SDM

E 17

.646

74

16.5

673

18.9

4358

19

.435

7 11

.563

21

18.3

463

12.4

36

18.3

454

GP

4.56

74

5.54

7 5.

2817

1 6.

5435

6.

1357

434

6.57

736

10.5

4664

6.

5687

43

With

out

CPS

O

PSN

R

19.1

206

20.1

982

22.5

805

24.2

37

27.6

9787

27

.939

29

27.2

6956

25

.489

2 SS

IM

0.22

876

0.21

532

0.20

510

0.22

889

0.24

7638

0.

2623

1 0.

2312

8 0.

2615

38

SDM

E 12

.863

921

15.1

2632

11

.145

39

11.2

546

15.7

6766

17

.548

5 19

.547

94

14.8

750

GP

4.57

4348

7.

5736

44

8.13

449

5.43

664

6.34

108

4.23

783

5.28

171

5.54

453

Prop

osed

ap

proa

ch

PSN

R

31.3

324

33.8

542

30.4

636

34.4

678

32.2

025

35.0

5677

33

.802

0 35

.785

SS

IM

0.34

1639

0.

3172

432

0.34

2456

3 0.

2973

3 0.

2971

02

0.33

564

0.30

7118

0.

2594

85

SDM

E 25

.795

56

22.8

6543

25

.454

6 24

.746

3 22

.393

15

22.5

578

20.3

3906

15

.846

34

GP

7.14

6431

10

.466

7 11

.354

8.

4654

7 8.

3400

83

14.4

634

11.4

4929

9.

4463

4


Table 11 Comparative results for images with 40% of salt and pepper noise

Appr

oach

es

Perf

orm

ance

M

easu

res

Babo

on

imag

e Ba

rbar

a

imag

e C

amer

aman

im

age

Hou

se

imag

e Le

na

imag

e M

edic

al

imag

e (1

) M

edic

al im

age

(2)

Med

ical

im

age

(3)

Exis

ting

App

roac

h

PSN

R

26.4

637

26.4

66

27.2

6956

26

.325

28

.891

51

28.5

637

24.5

4775

22

.462

64

SSIM

0.

2445

6 0.

2556

3 0.

2312

8 0.

2246

0.

2267

1 0.

2957

4 0.

2843

3 0.

2543

51

SDM

E 17

.646

74

16.5

673

18.9

4358

19

.435

7 11

.563

21

18.3

463

12.4

36

18.3

454

GP

4.56

74

5.54

7 5.

2817

1 6.

5435

6.

1357

434

6.57

736

10.5

4664

6.

5687

43

Exis

ting

A

ppro

ach

PSN

R

27.6

9787

27

.939

29

27.2

6956

25

.489

2 28

.891

51

23.6

3809

21

.566

7 20

.923

0 SS

IM

0.22

453

0.26

231

0.23

128

0.20

123

0.22

671

0.24

7881

0.

2334

63

0.26

4351

SD

ME

16.2

761

15.8

527

18.9

4358

16

.578

8 11

.563

21

16.2

2532

16

.245

39

16.3

454

GP

6.34

108

4.23

783

5.28

171

5.54

453

6.13

5743

4 5.

5773

6 9.

5743

4 7.

5687

43

With

out

CPS

O

PSN

R

25.5

6378

21

.476

29

24.5

6956

28

.689

2 25

.655

18

23.8

6480

26

.264

6 24

.346

0 SS

IM

0.23

563

0.24

674

0.21

541

0.22

455

0.25

8476

0.

2814

278

0.25

7834

0.

2374

43

SDM

E 15

.767

66

17.5

485

19.5

4794

3 13

.655

7 16

.346

73

19.6

4887

14

.477

65

18.4

444

GP

5.65

5867

3.

6578

56

6.45

774

7.23

542

7.35

6379

6.

5738

8 9.

5743

4 8.

3463

65

Prop

osed

ap

proa

ch

PSN

R

30.3

074

30.9

781

32.9

535

31.6

48

32.2

025

34.0

980

33.8

020

34.3

272

SSIM

0.

3315

38

0.31

6218

0.

3226

14

0.31

133

0.29

7102

0.

3089

92

0.30

7118

0.

2794

85

SDM

E 24

.781

51

23.7

0429

23

.757

12

25.7

231

22.3

9315

19

.083

28

20.3

3906

14

.846

27

GP

7.04

8436

9.

1340

16

9.19

9716

7.

8385

3 8.

3400

83

11.6

4452

11

.449

29

8.64

9273


Table 12 Comparative results for images with 20% of impulse noise

Appr

oach

es

Perf

orm

ance

M

easu

res

Babo

on

imag

e Ba

rbar

a

imag

e C

amer

aman

im

age

Hou

se

imag

e Le

na

imag

e M

edic

al

imag

e (1

) M

edic

al

imag

e (2

) M

edic

al

imag

e (3

)

Exis

ting

App

roac

h

PSN

R

26.4

637

22.0

66

22.9

56

26.3

25

28.0

61

24.4

57

24.7

75

26.2

64

SSIM

0.

156

0.26

34

0.31

28

0.24

6 0.

2671

0.

2957

4 0.

1433

0.

2351

SD

ME

18.4

674

13.6

73

19.9

48

20.3

57

15.5

61

19.3

463

16.4

62

11.3

454

GP

6.67

4 4.

047

3.81

7 5.

4635

5.

7434

6.

736

9.46

64

6.74

3

Exis

ting

App

roac

h

PSN

R

22.9

787

27.9

029

22.9

56

20.4

192

27.1

51

21.8

09

19.5

667

26.2

30

SSIM

0.

232

0.22

31

0.11

28

0.22

3 0.

206

0.28

81

0.33

463

0.25

1 SD

ME

14.2

61

18.5

27

20.7

41

19.0

88

16.3

21

11.5

32

19.5

391

14.8

54

GP

5.79

08

6.78

3 7.

8171

3.

753

5.74

34

7.07

36

5.17

434

6.08

743

With

out

CPS

O

PSN

R

27.6

9787

27

.939

29

27.2

6956

25

.489

2 28

.891

51

23.6

3809

21

.566

7 20

.923

0 SS

IM

0.22

453

0.26

231

0.23

128

0.20

123

0.22

671

0.24

7881

0.

2334

63

0.26

4351

SD

ME

16.2

761

15.8

527

18.9

4358

16

.578

8 11

.563

21

16.2

2532

16

.245

39

16.3

454

GP

6.34

108

4.23

783

5.28

171

5.54

453

6.13

5743

4 5.

5773

6 9.

5743

4 7.

5687

43

Prop

osed

ap

proa

ch

PSN

R

29.3

474

31.8

781

33.9

535

30.6

48

31.5

677

34.0

980

33.8

020

35.5

84

SSIM

0.

3115

38

0.29

6218

0.

3125

78

0.29

133

0.26

467

0.30

8992

0.

3071

18

0.27

9485

SD

ME

25.7

8151

24

.104

29

21.4

646

24.7

231

21.6

689

19.0

8328

20

.339

06

14.8

4627

G

P 6.

0484

36

8. 8

781

9.19

9716

7.

5788

8.

8956

7 11

.644

52

11.4

4929

8.

6492

73


Table 13 Comparative results for images with 40% of impulse noise

Appr

oach

es

Perfo

rman

ce

Mea

sure

s Ba

boon

im

age

Barb

ara

imag

e Ca

mer

aman

im

age

Hou

se

imag

e Le

na

imag

e M

edic

al

imag

e (1

) M

edic

al im

age

(2)

Med

ical

im

age

(3)

Exis

ting

App

roac

h

PSN

R

25.5

6378

21

.476

29

24.5

6956

28

.689

2 25

.655

18

23.8

6480

26

.264

6 24

.346

0 SS

IM

0.23

563

0.24

674

0.21

541

0.22

455

0.25

8476

0.

2814

278

0.25

7834

0.

2374

43

SDM

E 15

.767

66

17.5

485

19.5

4794

3 13

.655

7 16

.346

73

19.6

4887

14

.477

65

18.4

444

GP

5.65

5867

3.

6578

56

6.45

774

7.23

542

7.35

6379

6.

5738

8 9.

5743

4 8.

3463

65

Exis

ting

App

roac

h

PSN

R

25.4

274

20.1

978

23.8

335

21.1

482

19.1

206

20.1

982

22.5

805

24.2

37

SSIM

0.

2115

3 0.

2518

9 0.

2287

6 0.

2153

2 0.

2051

0 0.

2288

9 0.

2476

38

0.24

6435

SD

ME

14.8

750

13.5

6704

16

.587

1 17

.851

1 12

.863

921

15.1

2632

11

.145

39

11.2

5462

G

P 5.

1084

3 6.

7834

0 5.

2817

1 6.

5345

3 4.

5743

48

7.57

3644

8.

1344

9 5.

4366

49

With

out

CPS

O

PSN

R

26.4

637

26.4

66

27.2

6956

26

.325

28

.891

51

28.5

637

24.5

4775

22

.462

64

SSIM

0.

2445

6 0.

2556

3 0.

2312

8 0.

2246

0.

2267

1 0.

2957

4 0.

2843

3 0.

2543

51

SDM

E 17

.646

74

16.5

673

18.9

4358

19

.435

7 11

.563

21

18.3

463

12.4

36

18.3

454

GP

4.56

74

5.54

7 5.

2817

1 6.

5435

6.

1357

434

6.57

736

10.5

4664

6.

5687

43

Prop

osed

ap

proa

ch

PSN

R

30.3

074

30.9

781

32.9

535

31.6

48

32.2

025

34.0

980

33.8

020

33.5

678

SSIM

0.

3315

38

0.31

6218

0.

3226

14

0.31

133

0.29

7102

0.

3089

92

0.30

7118

0.

2794

85

SDM

E 24

.781

51

23.7

0429

23

.757

12

25.7

231

22.3

9315

19

.083

28

20.3

3906

14

.846

27

GP

7.04

8436

9.

1340

16

9.19

9716

7.

8385

3 8.

3400

83

11.6

4452

11

.449

29

8.64

9273


The main idea of our research is to perform image denoising using optimal wavelet with a bilateral filter. The practical implication of proposed methodology is given in this section. In our work, we utilise the three types of noise such as Gaussian noise, salt, and pepper noise and impulse noise at different levels of noise variance. Tables 8 to 13 presents the various performance measure utilise the image denoising process. In Table 8, we obtain the maximum PSNR of 36.32 dB, SDME of 25.7231 and GP of 11.64452 whose value is high compared to EMD+DTCWP (Velayudham and Kanthavel, 2014), LPG+DTCWP (Velayudham and Kanthavel, 2015) and PF+BF (without CPSO). In Table 9, we increase the noise level at 40% and we apply the proposed algorithm to the images, where the performance slightly changes. Here we obtain the maximum PSNR of 35.46 dB, which is also high, compared to the existing approach. Moreover, in Tables 10 and 11, the performances in terms of PSNR, SSIM, SDME, and GP are calculated while applying salt and pepper noise at the different noise level. The outcomes of proposed method were better compared to the approaches as shown in Tables 10 and 11. Similarly, in Tables 12 and 13, the performances in terms of PSNR, SSIM, SDME and GP are measured while applying impulse noise at different levels of noise. The results have proved that the proposed method clearly outperformed the existing approaches as shown in Tables 12 and 13.

7 Conclusion

In this paper, we have proposed a new image denoising method, making use of optimal wavelet transform and bilateral filter. The proposed technique contains two phases, particularly, optimal wavelet design as well as image denoising framework. During the optimal wavelet design process, we use the CPSO algorithm to optimise the wavelet parameters. Here, we optimally obtain the four subbands such as LL, LH, HH, and HH. Among the four sub-bands, we select the three high bands for the further processing. Finally, we apply the bilateral filter to the sub-bands and produce the de-noised outputs. For testing, we have utilised 5 natural images and 3 medical images and this technique has achieved good results compared to existing methods. The proposed method has clearly outperformed the existing methods by yielding having better values.

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