MIMO VLSI Based on SPIHT algorithm for using Two ... · MIMO VLSI Based on SPIHT algorithm for using Two-Dimensional Lifting-Based Discrete Wavelet Transform International Journal

International Journal of Applied Sciences, Engineering and Management ISSN 2320 – 3439, Vol. 02, No. 05, September 2013, pp. 95 – 100

IJAEM 020503 Copyright @ 2013 SRC. All rights reserved.

MIMO VLSI Based on SPIHT algorithm for using Two-Di mensional Lifting-Based Discrete Wavelet Transform

C. HARINATH BABU1, K. K. VARA LAKSHMI 2 1M.tech , Dept of ECE, AVR & SVR College of Engineering, Nandyal, A. P., India.

2Associate Professor, Dept of ECE, AVR & SVR College of Engineering, Nandyal, A. P., India. Abstract: This brief paper proposes an efficient multi-input/multi-output VLSI Folded Architecture (MIMOFA) for two-dimensional lifting-based discrete wavelet transforms (DWT). In comparison with other 2-D DWT folded architecture, the advantages of the proposed architecture are 100% hardware utilization, fast computing time (10 times of the parallel filters), regular data flow, and low control complexity, making this folded architecture suitable for next generation image compression systems. The novelty is the simplicity and generality to construct the MIMOA, which is a high-speed the design and implementation of an image transform coding algorithm based on the discreet wavelet transform (DWT) SPIHT is computationally very fast and among the best image compression algorithms known today. According to statistic analysis of the output binary stream of SPIHT encoding, propose a simple and effective method combined with Huffman encode for further compression

Keywords: Discrete wavelets transform, very-large-scale integration (VLSI), High-speed, lifting scheme, multi-input/multi-output, SPIHT algorithm, folded architecture. Introduction THE discrete wavelet transform (DWT) has been widely used for image coding. This is due to the fact that the DWT supports features like progressive image transmission, ease of compressed image manipulation, region of interest coding, etc[1], [2].A potential problem, however, is the high computational complexity of the DWT. Therefore, the study on specified VLSI implementations of DWT is important and inevitable. Up to now, many VLSI architectures for DWT have been proposed to meet the real time requirement in many applications [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], 13]. Among these 2D DWT, most designs are proposed for the convolution-based or FIR-based DWT [2], [3]. Recently, a methodology For implementing lifting-based DWT has been proposed in [4], [5], [6], [7], [8], [9], [10], [11], [12], because the lifting-based DWT has many advantages including in-place computation, integer-to integer transform[5], reduction of the number of arithmetic operations, and the size of registers, etc. All these reported architectures are designed for a fixed processing speed and cannot be easily extended to achieve a higher processing speed. The high processing speed has been achieved in [12] when parallel FIR structures are used. However, FIR structures result in the increase of the hardware cost. The aim of this brief paper is to construct an efficient multi input/ multi-output VLSI architecture (MIMOA) based on lifting Scheme, which meets the high processing speed requirement with controlled increase of hardware cost and simple control signals. High processing speed can be achieved when multiple row data samples are processed simultaneously. And time multiplexing technique is adopted to control the increase of the hardware cost For the MIMOA. Furthermore, the control signals are simple, since the regular architecture is a combination of simple single-input/ single-output (SISO) modules and two-input/two-output (TITO) modules. It provides a

variety of hardware implementations to meet different processing speed requirements by selecting The discrete cosine transforms (DCT) [11] is a technique for converting a signal into elementary frequency components. It is widely used in image compression. Here we develop some simple functions to compute the DCT and to compress images [12]. These functions illustrate the power of Mathematical in the prototyping of image processing algorithms. In recent years, wavelet transform [13][14] as a branch of mathematics developed rapidly, which has a good localization property[15] in the time domain and frequency domain, can analyze the details of any scale and frequency. So, it superior to Fourier and DCT. It has been widely applied and developed in image processing and compression. Wavelet Transform (WT) has received more and more significant attention in signal compression. However, many differences lie in the performance of different wavelets. There is a need to select the optimal matched wavelet bases to analyze the signal and the signal needs to be expressed with the fewest coefficients, i.e. sparse coefficients. The signal compression with wavelet is a procedure in which the input signal is expressed with a sum of a few of power terms for wavelet function. The more similar the bases function is to input signal, the higher the compression ratio is. But, at higher compression ratios we may experience more errors, i.e. mean square error will be high at the receiving end and hence PSNR will be very low. "Set Partitioning in Hierarchical Trees" [15]. In this method, more (wide-sense) zero-trees are efficiently found and represented by separating the tree root from the tree, so, making compression more efficient. Experiments are shown that the images through the wavelet transform, the wavelet coefficients� value in high frequency region are generally Small , so it will appear seriate "0" situation in quantify [18]. SPIHT does not adopt a special

C. Harinath Babu, K. K. Vara Lakshmi


method to treat with it, but direct output. In this paper, focus on this point, propose a simple and effective method combined with Huffman encode for further compression. A large number of experimental results are shown that this method saves a lot of bits in transmission, further enhanced the compression performance. Lifting Scheme of DWT Lifting scheme is a relatively new method to construct wavelet bases, which was first introduced by Sweldens in 1990s [4]. This scheme is called the second-generation wavelet, which leads to a fast in-place implementation of the DWT. According to [4], any DWT of perfect reconstruction can be decomposed into a finite sequence of lifting steps. This decomposition corresponds to a factorization for the poly-phase matrix of the target wavelet filter into a sequence of alternating upper and lower triangular matrices and a constant diagonal matrix. The two-input/two-output lifting architecture of the CDF97 is shown in Fig 1. Fig. 2. Architecture for the horizontal filtering Fig. 1: The two-input/two-output lifting architecture of the CDF97

Fig.2: The architecture for the horizontal filtering

Fig.3: Input data flow of the architecture for the horizontal filtering

Fig. 4: Output data flow of the architecture for the horizontal filtering.

Proposed Efficient Mimoa for 2D Lifting-Based DWT A 2D DWT consists of horizontal filtering along the rows followed by vertical filtering along the columns. Convolution-based DWT or lifting-based DWT is used to implement the filters traditionally. the lifting- based DWT is considered. The proposed architecture is suitable for any lifting-based DWT. The throughput rate is denoted by a 1D variable M, which is an even integer. Architecture for the Horizontal Filtering along the Rows (M =8) First, CDF97 is applied to the row dimension, which is a 1D DWT. The architecture for the horizontal filtering along the rows consists of eight SISO modules. The input data flow elements from each row are processed by one SISO module. We can accordingly get output data flow of the architecture for the horizontal filtering, where mi;j denotes the computation results after we apply CDF97 to the row dimension. Many SISO architectures for the 1D DWT are proposed. An efficient SISO architecture is proposed in [10] by employing the fold technique. Therefore, we adopt it in our SISO modules, which consist of two multipliers, four adders, and ten registers. Folded Architecture

Fig. 5: Folded Architecture The discrete wavelet transform (DWT) is being increasingly used for image coding. This is due to the fact that DWT supports features like progressive

MIMO VLSI Based on SPIHT algorithm for using Two-Dimensional Lifting-Based Discrete Wavelet Transform


image transmission (by quality, by resolution), ease of compressed image manipulation, region of interest coding, etc. DWT has traditionally been implemented by convolution. Such an implementation demands both a large number of computations and a large storage features that are not desirable for either high-speed or low-power applications. Recently, a lifting-based scheme that often requires far fewer computations has been proposed for the DWT. The main feature of the lifting based DWT scheme is to break up the high pass and low pass filters into a sequence of upper and lower triangular matrices and convert the filter implementation into banded matrix multiplications. Such a scheme has several advantages, including “in-place” computation of the DWT, integer-to-integer wavelet transform (IWT), symmetric forward and inverse transform, etc. Therefore, it comes as no surprise that lifting has been chosen in the upcoming. The proposed architecture computes multilevel DWT for both the forward and the inverse transforms one level at a time, in a row-column fashion. There are

two row processors to compute along the rows and two column processors to compute along the columns. While this arrangement is suitable or filters that require two banded-matrix multiplications filters that require four banded-matrix multiplications require all four processors to compute along the rows or along the columns. The outputs generated by the row and column processors (that are used for further computations) are stored in memory modules. The memory modules are divided into multiple banks to accommodate high computational bandwidth requirements. The proposed architecture is an extension of the architecture for the forward transform that was presented. A number of architectures have been proposed for calculation of the convolution-based DWT. The architectures are mostly folded and can be broadly classified into serial architectures (where the inputs are supplied to the filters in a serial manner) and parallel architectures.

Fig 6: data processing for horizontal process MIMOA for 2D Lifting-Based DWT If the particular application requires higher processing speed, the throughput rate M will be larger than 8. The proposed MIMOA is composed of M SISO modules, M/2 TITO modules, some multiplexers, and delay registers, which is shown in below fig.“2N/M D” in represents that the number of delay registers is 2N/M. The number of registers required in one SISO module is 10. Spiht Algorithm Description of the Algorithm Image data through the wavelet decomposition, the coefficient of the distribution turn into a tree. According to this feature, defining a data structure: spatial orientation tree. 4-level wavelet decomposition of the spatial orientation trees structure are shown in Figure1.We can see that each coefficient has four children except the “red� marked coefficients in the LL sub band and the coefficients in the highest sub bands (HL1;LH1; HH1). The following sets of coordinates of coefficients are used to represent set partitioning method in SPIHT algorithm. The location

of coefficient is notated by (i,j),where i and j indicate row and column indices, respectively. H: Roots of the all spatial orientation trees O(i, j) :Set of offspring of the coefficient (i, j), O(i, j) = {(2i, 2j), (2i, 2j + 1),(2i + 1, 2j), (2i + 1, 2j + 1)}, except (i, j) is in LL; When (i,j) is in LL sub band, O(i; j) is defined as: O(i, j) = {( i, j + ��), (i + ℎ��, j), (i +ℎ�� , j + ��)}, where �� and ℎ�� is the width and height of the LL sub band, respectively. D (i, j): Set of all descendants of the coefficient (i, j),

Fig. 7: Parent-child relationship in SPIHT



A significance function �� (�) which decides the Significance of the set of coordinates, �, with respect to the threshold 2� is defined by: ��() = , �� ,� ∈ ��,� ≥ �� , �� Where ci,j is the wavelet coefficient. In this algorithm, three ordered lists are used to store the significance information during set partitioning. List of insignificant sets (LIS), list of insignificant pixels (LIP), and list of significant pixels (LSP) are those three lists. Note that the term „pixel� is actually indicating wavelet coeffcient if the set partitioning algorithm is applied to a wavelet transformed image. Algorithm: SPIHT 1).Initialization: 1. output n= [log2 max{|(��,� )|}] 2. set LSP =∅; 3. set LIP = (i,j) ∈ H; 4. set LIS = (i,j) ∈ H, where D(i; j) ≠ ∅ and set each entry in LIS as type A ; 2) Sorting Pass: 1. for each(i, j) ∈LIP do: (a) output �� (�, �) (b) if �� (�, �) = 1 then move (i, j) to LSP and output Sign ( ��,� ) 2. for each (i, j) ∈ LIS do: (a) if (i, j) is type A then i. output �� (�(�, �)) ii. if then�� (� �, � ) = 1 then A. for each (k, l) ∈ O(i, j) . output �� (�, �) . if �� (�, �) = 1 then append (k, l) to LSP, output Sign(�� ,�),and �� ,� = �� ,� − 2� sign(�� ,�) .else append (k; l) to LIP B. move (i, j) to the end of LIS as type B (b) if (i, j) is type B then i. output �� (� �, � ) ii. if �� (� �, � ) = 1 then . append each (k, l) ∈ O(i, j) to the end of LIS as type A . remove (i,j) from LSP 3) Refinement Pass: for each (i,j) in LSP, except those included in the last sorting pass . output the n-th MSB of |��,� | 4) Quantization Pass: 1. decrement n by 1 2. goto step 2) Analyses of SPIHT Algorithm Here a concrete example to analyze the output binary stream of SPIHT encoding. The following is 3-level wavelet decomposition coefficients of SPIHT encoding. n = [log2 max {|c(i,j)|}] = 5, so, The initial threshold value:� = 25, for � , the output binary stream: 11100011100010000001010110000, 29 bits in all. By the SPIHT encoding results, we can see that the output bit stream with a large number of seriate

"0" situation, and along with the gradual deepening of quantification, the situation will become much more severity, so there will have a great of redundancy when we direct output. Modified SPIHT Algorithm For the output bit stream of SPIHT encoding with a large number of seriate "0" situation, we obtain a conclusion by a lot of statistical analysis: „000� appears with the greatest probability value, usually will be about 1/4.Therefore, divide the binary output stream of SPIHT every 3 bits as a group, every group recorded as a symbol, a total of eight kinds of symbols, statistical probability that they appear, and then encoded using variable-length encoding naturally reached the further compressed, in this paper, variable-length encoding is Huffman encoding. Using the output bit stream of above example to introduce the new encoding method process. 1) First, divide the binary output stream every 3 bits as a group: 111 000 111 000 100 000 010 101 100 00. In this Process, there will be remain 0, 1, 2 bits can not participate. So, in order to unity, in the head of the output bit stream of Huffman encoding cost two bits to record the number of bits that do not participate in group and those remainder bits direct output in end. 2) The emergence of statistical probability of each symbol grouping results are as follows: P(„000�)= 0.3333 P(„001�)= 0 P(„010�)= 0.1111 P(„011�)= 0 P(„100�)= 0.2222 P(„101�)= 0.1111 P(„110�)= 0 P(„111�)= 0.2222 Results The experimental results show the standard Lena image 128×128 grayscale image compression with different comparison parameters. Average code length which is calculated as follows: PSNR = 10 log10 [ square of (255)/MSE] CR = (Number of bits in the original image) / (Number of bits in the compressed image) By using the above formulae in the proposed algorithm the following parameters are calculated for the Lena image and given in the following table. Algorithm Parameters CR MSE PSNR Compressed

image size DCT

2.4059 3.4401 36.1236 6810

DWT 1.4080

0.7479 48.1308 11636

SPIHT 1.3507

0.0874 58.7156 12130

Table 2: Result analysis for Lena image of size

128×128

MIMO VLSI Based on SPIHT algorithm for using Two-Dimensional Lifting-Based Discrete Wavelet Transform


Conclusion An efficient MIMOA for 2D lifting-based DWT is proposed in the paper. It provides a variety of hardware implementations to meet different processing speed requirements with controlled increase of hardware cost and simple control signals. The MIMOA designed for 1-level 2D DWT can be easily extended to construct the architecture for multi-level 2D DWT in our future work. To evaluate the performance of the proposed architecture, different 2D DWT architectures have been compared. The results have demonstrated that the MIMOA has a good performance in terms of the reduction of computing time and hardware cost, which will be an efficient alternative for future high-speed applications. The proposed lossy image compression algorithm is simple and effective method for gray-scale image compression and is combined with Huffman encoding for further compression in this paper that saves a lot of bits in the image data transmission. There are very wide range of practical value for today that have a have number of image data is to be transmitted. References

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K.K.Vara Laxmi is working as an Associate Professor in the Department of Electronics & Communication Engineering at A.V.R & S.V.R college of Engineering & Technology, Nandyal, Kurnool (dist), She has 4 international journal publications to her credit. She

has Completed M.Tech (DSCE) degree in from RGM college of engineering 2008, B.Tech from Electronics &Communication Engineering from jntu anantapur in 2002. Her main research interest includes communication systems.

Harinath Babu is pursuing his M.Tech degree in VLSI System Design. A.V.R & S.V.R college of Engineering & Technology, Nandyal, B.Tech from Electronics & Communication Engineering from ALFA College of Engineering and Technology, Allagadda in 2011. His research

interest includes Digital Image processing and VLSI systems.

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MIMO VLSI Based on SPIHT algorithm for using Two ... · MIMO VLSI Based on SPIHT algorithm for using Two-Dimensional Lifting-Based Discrete Wavelet Transform International Journal