Image Resolution Enhancement based on Edge Directed Interpolation using Dual

Tree – Complex Wavelet Transform Mr. Pilla Jagadeesh#1 and Dr. Jayanthi Pragatheeswaran#2 # Department of ECE, Pondicherry Engineering College Pondicherry, India

Abstract - Image resolution enhancement is a usable process for many image processing applications such as geoscience studies, astronomy and geographical information systems. One of the traditional methods used to increase the image resolution is image interpolation but the potential problem associated with it is to magnify the image many times without loss in image clarity. However, all the classical linear interpolation techniques like bilinear, bi-cubic interpolation methods generate blurred image. By employing dual-tree complex wavelet transform (DT-CWT) on a edge directional interpolation, it is possible to recover the high frequency components which provides an image with good visual clarity and thus super resolved high resolution images are obtained. The obtained simulation results comply with the above stated claim. A performance comparison of it is made with the recent work discussed in [7].

Keywords: Dual-tree complex wavelet transform (DT-CWT), resolution enhancement, Edge directed interpolation, Super resolved images.

I. INTRODUCTION With the recent advances in low-cost imaging solutions

and increasing storage capacities, there is an increased demand for better image quality in a wide variety of applications involving both image and video processing. While it is preferable to acquire image data at a higher resolution to begin with, one can imagine a wide range of scenarios where it is technically not feasible. In some cases, it is the limitation of the sensor due to low-power requirements as in satellite imaging, remote sensing, and surveillance imaging. An improvement in the spatial resolution for still images directly improves the ability to discern important features in images with a better precision. The low-resolution data can exist in the form of still images. Furthermore the observations can be corrupted by motion-induced artifacts either in the case of still images or videos.

Interpolation is the technique that which estimate the new pixel from the surrounding pixels available in the low resolution image. But the computational problem is increased as the order of interpolation factor increases. This problem can be overcome by interpolating the image in wavelet domain. But, super-resolution image reconstruction

is an ill-conditioned inverse problem, since the observation process of the original high resolution object consists of a noisy blurred low resolution observation affected by sampling artifacts, blurring and noise. This is mathematically modeled as a nonlinear process consisting of a convolution operator acting on the image, followed by a down sampling operation and the mixing of additive noise in the frequency domain approach using (discrete) Fourier transform and wavelet-transform based methods(using real wavelets).

This difficulty can be recovered by using complex wavelets because it has the properties of shift invariant and good directionality and by constructing the filters in the form of dual tree structure which provide complex-valued wavelets it eliminates the inverse problem by perfect reconstructing the both forward and reverse filter banks namely the transform called DT-CWT (dual-tree complex wavelet transform) [5-7]. In previous studies, the linear interpolations such as nearest neighbor, bilinear and bi-cubic interpolations [9] are used to enhance the resolution of the image were discussed in [2] but with these techniques produce many artifacts like blurring, blocking etc. To avoid these problems to some extent, a good old non-linear interpolation like edge directional interpolation [3] can be applied to images. This is the prime motivation of using edge directed interpolation technique. The main loss of after being super resolved images by applying interpolation causing smoothness in the visual clarity mainly edges. In one of the recent work [7], the authors have proposed a technique which is aimed at generating sharper edges and detailed super resolved satellite images than the dual tree complex wavelet transform (DT-CWT) with bi-cubic interpolation [4].

To the best of our knowledge, the features of edge directed interpolation is very less exploited and hence it is used in combination with DT-CWT in this paper and appreciable output has been observed. The obtained simulation results are compared with the results shown in the very recent work [7]. This paper is organized as follows: section II gives a brief review of the technique edge directional interpolation. Section III describes the proposed technique DT-CWT

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based satellite image resolution enhancement algorithm. Section IV provides some simulation results of the proposed approach and comparisons with the approach [7],[3], and [2]. Section V concludes this paper.

II .PRINCIPLE OF EDI TECHNIQUE

The researchers have so far tried with linear

interpolation techniques, such as nearest neighbour interpolation, bilinear and bi-cubic interpolations [9]. But these techniques suffer from blurring edges or introducing artifacts around edge area in the recent paper [7] the author has applied bi-cubic interpolation, which suffers from several problems. This paper attempts to rectify all the limitation of the work suggested in [7]. In this paper, a novel edge directional adaptive interpolation technique [1], to obtain a high resolution image is considered. EDI estimates the pixel along the edges by estimating the covariance of surrounding neighbours while it uses the image data themselves to direct the interpolation. The edge directional interpolation works as follows:

From the flow chart, the sliding windowing technique

like kernel function is applied and sobel is applied for the edge detection. If it is related to edge, bilinear interpolation is applied otherwise it will perform geometric transformations based on the estimated elevation angle to find the edges. After that, the interpolation is applied along these edges by estimating the covariance of surrounding neighbours as shown below:

Step 1 Suppose low resolution image is jiX , and high

resolution image jiY , . Assume that magnification ratio is

two i.e., jiji XY ,2,2 = . Fig. 2(a) Finding covariance between pixels to estimate the new pixel From the above Fig.2a, by using equations at pixels (1-4) have to find the covariance to estimate the high resolution pixels computed using the formulae:

( )

1 1

2 1,2 1 2 1 2 .2( )0 0

ˆ i j k i k j lk l

y Y+ + + + += =

= α

(1)

The optimal linear MMSE interpolation between pixels depends on

1XX XR r−α =

(2)

Where, [ ] ( )3,0, ≤<= lkRR kl and

[ ] ( )30, <<= krr k denotes local covariance characteristics at high resolution. Step 2 After finding the covariance of the high resolution covariance klkl rR , is replaced by their low resolution

pixels ˆ ˆ,kl klR r which couple the pair of pixels along the same orientation but at different resolution. As the difference between the covariance of high resolution pixels and the low resolution pixels become negligible the resolution gets higher and higher. Step 3 Interpolate the other half by rotating the image by 45 as in Fig 2(b) and repeat the steps 1and 2 that results in new interpolated pixels with increased resolution. Fig. 2(b) Finding covariance between pixels to estimate the new pixel by rotating 45

Fig. 1 Flow chart of edge directional interpolation

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Step 4 Finally, the image is interpolated by the factor of two which results in a high resolution image.

The above steps are applied to the pixels related to edge areas and for non edge pixels, a simple linear interpolation technique such as bilinear interpolation is applied. Finally, by combining both the pixels related to edge areas and non-edge areas, it forms a new high resolution image with good visual clarity and with fewer artifacts such as blurring, smoothening is obtained.

III.PROPOSED EDGE DIRECTIONAL INTERPOLATION USING DT-CWT

The main loss of an image after being super resolved by applying interpolation is on its high-frequency components (i.e., edges), which is mainly due to the smoothing effects, caused by interpolation. Hence, in order to increase the quality of the super resolved image, preserving the edges is essential. DT-CWT has been employed in order to preserve the high-frequency components of the image. The DT-CWT has good directional selectivity and has the advantage over discrete wavelet transform (DWT). It also has limited redundancy. The DT-CWT is approximately shift invariant, unlike the critically sampled DWT. The redundancy and shift invariance of the DT-CWT mean that DT-CWT coefficients are inherently interpolable.

In the proposed image resolution enhancement technique, DT-CWT is used to decompose an input image into different sub-band images. Complex-valued high-frequency sub-band images contain the high-frequency components of the input image. Here, the interpolation is applied to the high-frequency sub-band images. In the wavelet domain, the low-resolution image is obtained by low-pass filtering of the high-resolution image. In other words, low-frequency sub-band images are the low resolution of the original image. Therefore, instead of using low-frequency sub-band images, which contain less information than the original input image, the interpolated input image is used. Hence, using the input image instead of

the low-frequency sub-band images increases the quality of the super-resolved image. The input image is interpolated using edge directional interpolation with the half of the interpolation factor used to interpolate high-frequency sub-bands, as illustrated in Fig. 3.The two up-scaled images are generated by interpolating the low-resolution original input image and the shifted version of the input image in horizontal and vertical directions. These two real-valued images are used as the real and imaginary components of the interpolated complex LL image, respectively, for the IDT-CWT operation.

By interpolating the input image by /2 and the high-frequency sub-band images by and then by applying IDT-CWT, the output image will contain sharp edges than the interpolated image obtained by interpolation of the input image directly. This is due to the fact that the interpolation of the isolated high-frequency components in the high-frequency sub-band images will preserve more high-frequency components after the interpolation of the respective sub-bands separately than interpolating the input image directly.

In summary, the proposed technique interpolates the input image as well as the high frequency sub-band images obtained through the DT-CWT process .The final high-resolution output image is generated by using IDT-CWT of the interpolated sub-band images and the input image. In the proposed algorithm, the employed interpolation i.e., edge directional interpolation is the same for all the sub-band and the input images. The interpolation and the wavelet function are two important factors to determine the quality of image.

The visual clarity and the peak signal to noise ratio (PSNR) results of proposed technique with edge directional interpolation outperforms the conventional nearest neighbour, bilinear, bi-cubic, and edge directional interpolation techniques.

Fig 3 Block diagram of the proposed resolution enhancement technique.

Interpolated input image

Low frequency sub-band

High frequencysub-band

Input image

Interpolated High frequency sub-band

High resolutionimage

DT-CWTIDT-CWT

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(a) (b)

(a) (b)

(a) (b)

(c)

(c)

Fig. 4(a) original resolution image. (b) Edge directional interpolation. (c) Super resolved image using the

proposed technique.

(c)

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Fig.4 shows that super resolved image using proposed technique in (c) are much sharper than the original low-resolution image in (a) and the interpolated images in (b) in which the proposed technique interpolates the high frequency sub-band images with edge directional interpolation to improve the visual clarity at edges than the interpolation directly on the image. By comparing the visual qualitative results from fig 4 (b) and (c) it is proved that the proposed technique shows more clarity than the edge directional interpolation and 4.2dB higher than the PSNR obtained for bi-cubic interpolation with DT-CWT and 10.0dB improvement compare to EDI without DT-CWT.

In order to show effectiveness of the proposed method over the conventional resolution enhancement methods, three satellite images with different features are used for comparison. Table 1 compares the PSNR Performance of the proposed technique with conventional nearest neighbour, bilinear, bi-cubic and edge directional interpolation techniques.

Table 1 Compares the PSNR (dB) Performance of

the proposed technique with conventional methods.

TECHNIQUES/IM

AGE

SATELLITE

IMAGE

PSNR(dB)

SATELLITE

IMAGE(2)

PSNR(dB)

SATELLITE

IMAGE (3)

PSNR(dB)

Nearest Neighbor 15.3 13.0 17.1

Bi-linear 15.5 13.5 17.7

Bi-cubic 15.7 13.3 17.9

EDI 17.6 13.6 19.5

Bi-cubic with

DTCWT

25.6 28.3 28.7

EDI With DTCWT 27.8 30.0 32.2

IV.RESULTS AND DISCUSSIONS

Simulation results presented in this section are obtained using MATLAB 8.0. The proposed algorithm tested on the images taken from [8]. In this paper, enhancement of image resolution based on edge directional interpolation using Dual Tree-Complex Wavelet Transform (DT-CWT) on three different satellite images are shown with interpolation factor of two, and also the performance analysis of dual tree complex wavelet transform are compared with the results of interpolation techniques which is directly applied on the image are done using qualitative and quantitative parameters.

V.CONCLUSION

This paper proposes a new super resolution technique based on edge directional interpolation of high frequency sub-band images obtained by DT-CWT and the input image is used to generate a super-resolved image [10]and it has been tested on different satellite images and compared with the traditional interpolation techniques nearest neighbor, bilinear, bi-cubic, edge directional interpolation and bi-cubic with DT-CWT. Where the proposed technique, shows good performance in terms of PSNR and Visual clarity. The main reason of the resolution enhancement with DT-CWT is able to preserve more high frequency components than the interpolation without DT-CWT.

REFERENCES

[1] J.Allebach and P.W. Wong, “Edge-directed interpolation,”

proceeding of ICIP’1996, pp.707-710. [2] M.Unser, A.Aldroubi and M.Eden, “image interpolation and

resampling,” IEEE Trans. on image processing, vol.6, pp.1322-1326, September, 1997.

[3] X.Li and M.Orchrard, “New edge-directed interpolation,” IEEE Trans. image process, vol.10, no.10, pp.1521-1527, Oct.2001.

[4] Y. Piao, I. Shin, and H. W. Park, “Image resolution enhancement using inter-sub band correlation in wavelet domain,” in Proc. International conference on image processing, 2007, vol. 1, pp. 445-448.

[5] N. Kingsbury, “Complex wavelets for shift invariant analysis and filtering of signals,” Appl. Compute. Harmonic Anal., vol. 10, no. 3, pp. 234–253, May 2001.

[6] T. H. Reeves and N. G. Kingsbury, “Prediction of coefficients from coarse to fine scales in the complex wavelet transform,” in Proc. IEEE International conference on acoustics, speech and signal processing, Jun. 5–9, 2000, vol. 1, pp. 508–511.

[7] Hasan Demirel and Gholamreza Anbarjafari, ”Satellite Image Resolution Enhancement Using Complex Wavelet Transform”, IEEE Trans. geoscience and remote sensing letters,vol.7,no.1,January 2010,pp 123- 126.

[8] Http://www.emap-int.com/products/HighResImagery/eMap International is pleased to offer competitively priced high resolution imagery from a growing \ Constellation of satellites.

[9] Robert. G. Keys, “Cubic Convolution interpolation for digital image processing,” IEEE Trans. On acoustics, speech, and signal processing, Vol.ASSP-29, No.26, Dec-1981

[10] Gholamreza Anbarjafari and Hasan Demirel, “Image Super Resolution Based On interpolation Of Wavelet Domain and Spatial Domain Input Image,” IEEE Trans .image processing., vol.32, no.3, June 2010.

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