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1 Volume 6, Issue 9, September 2016 ISSN: X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: Implementation of 8-Point Approximate DCT for Image Compression D.Vaithiyanathan *, Dheepansundaravelu.P Department of Electronics and Communication Engineering. College of Engineering Guindy, Anna University, Chennai, Tamil Nadu, India Abstract The Discrete Cosine Transform is the basic operation used by video and image compression standard, such as JPEG, MPEG1-2-4, H and others. In this paper 8-point approximate DCT compression scheme is implemented. The lower computational complexity is achieved by eliminates the need for multiplication and shifting operation and can be implemented only through addition operation itself. This approximate DCT method outweighs other approximate DCT methods by a significant increase in the Peak Signal to Noise ratio (PSNR). Keywords Discrete Cosine Transform, DCT approximation, Low Complexity, Image Compression, Hardware Implementation, Pipelining, Field Programmable Gate Arrays (FPGAs) I. INTRODUCTION Multimedia data processing, which encompasses almost every aspects of our daily life such as communication broad casting, data search, advertisement, video games, etc., has become an integral part of our life style. The most significant part of multimedia systems is application involving image or video, which require computationally intensive data processing. Moreover, as the use of mobile device increases exponentially, there is a growing demand for multimedia application to run on these portable devices. In order to reduce the volume of multimedia data over wireless channel compression techniques are widely used. Efficiency of a transformation scheme can be directly gauged by its ability to pack input data into as few coefficients as possible. This allows the quantizer to discard coefficients with relatively small amplitudes without introducing visual distortion in the reconstructed image. In image compression, the image data is divided up into 8x8 blocks of pixels. From this point on, each colour component is processed independently, so a "pixel" means a single value, even in a colour image. A DCT is applied to each 8x8 block. DCT converts the spatial image representation into a frequency map: the low-order or "DC" term represents the average value in the block, while successive higher-order "AC' terms represent the strength of more and more rapid changes across the width or height of the block. The highest AC term represents the strength of a cosine wave alternating from maximum to minimum at adjacent pixels. There are several efficient DCT algorithms being developed and a noticeable literature is available. Although fast algorithms can significantly reduce the computational complexity of computing the DCT, floating-point operations are still required. Despite their accuracy, floating-point operations are expensive in terms of circuitry complexity and power consumption. Therefore, minimizing the number of floating-point operations is a sought property in a fast algorithm. One way of circumventing this issue is by means of approximate transforms. The approximate DCT methods under consideration are (i) the transform in [1]; (ii) the 2008 Bouguezel-Ahmad-Swamy (BAS) DCT approximation [2] (iii) the parametric transform for image compression [3] (iv) the Cintra-Bayer (CB) approximate DCT based on the rounding-off function [4] (v) the modified CB approximate DCT [5]. II. APPROXIMATE DCT TRANSFORM The reduction in computational complexity comes with the cost of PSNR. One way to guarantee good candidates is to restrict the search to matrices whose entries do not require multiplication operations. Another important parameter is the number of retained coefficients. Hence, this paper adopted the number of retained coefficients equal to 10 as suggested by Bouguezel et al., All the methods here consist of a transformation matrix that can be put in the following format: [Diagonal matrix] x [Low complexity matrix] The diagonal matrix usually contains irrational numbers in the form 1/ m where m is a small positive integer. Therefore, in this case, the complexity of the approximation is bounded by the complexity of the low-complexity matrix [1]. Since the entries of the low complexity matrix comprise only powers of two in {0, ±1/2, ±1, ±2}, null multiplicative complexity is achieved [1]. Many reported papers [1-12] derive a novel low-complexity approximate DCT. For such end, reported works proposed a search over the 8x8 matrix space in order to find candidate matrices that possess low 2016, IJARCSSE All Rights Reserved Page 441

2 computation cost. Let us define the cost of a transformation matrix as the number of arithmetic operations required for its computation. One way to guarantee good candidates is to restrict the search to matrices whose entries do not require multiplication operations. An important parameter in the image compression routine is the number of retained coefficients in the transform domain. In several applications, the number of retained coefficients is very low. For instance, considering 8x8 image blocks, 1. In image compression using support vector machine, only the first 8-16 coefficients were considered. 2. Mandyam et al. proposed a method for image reconstruction based on only three coefficients. 3. Bouguezel et al. employed only 10 DCT coefficients when assessing image compression methods. Hence the DCT approximated, low computational complexity transform matrix is given by [1]: C* = D*. T* = D *..(1) The Diagonal matrix is given by, D * = diag [1/, 1/, 1/2, 1/, 1/, 1/, 1/2, 1/ ] The above transform matrix requires addition operations only. Hence the need of multiplications and shift operations are completely eliminated, thereby reducing arithmetic complexity. The given transform is for 8X8 structure and the same can be replicated for 16X16, 32X32 and so on. On comparing with other approximate DCT model like CB-2011, BAS-2011, the above transform provides almost same peak signal to noise ratio but considerable reduction in arithmetic complexity need 14 additions only is given in equation 1 [1]. The comparison of arithmetic computational complexity with other approximate methods is given in Table I. Table I. Comparison of Computational Complexity Transform Add. Multi. Shifts Total BAS-2008 [2] BAS-2011 [3] CB-2011 [4] CB-2012 [5] Transform in [1] Transform in [10] III. IMPLEMENTATION OF DCT PROCESS For quality analysis, images were submitted to a JPEG-like technique for image compression. The resulting compressed images are then assessed for image degradation in comparison to the original input image. Thus, 2D versions of the discussed methods are required. An 8x8 image block has its 2D transform mathematically expressed by [1]: T. A. T T, Where T is a considered transformation. The input images were divided into 8x8 sub-blocks, which were submitted to the 2D transforms. For each block, this computation furnished 64 coefficients in the approximate transform domain for a particular transformation. According to the standard zigzag sequence, only the initial coefficients in each block were retained and employed for image reconstruction. This range of corresponds to high compression. All the remaining coefficients were set to zero. The inverse procedure was then applied to reconstruct the original image [1-12]. A. Overall process of the DCT implementation The above said process of compression and reconstruction of the image using DCT approximate transform is shown in Fig 1 & Fig 2. Here the Input image for e.g. Lena image of size 256x256 is taken. This image is divided into 8x8 image sub blocks. Each sub block is then DCT approximated by low complexity DCT approximate transform matrix given in equation 1 [1]. 2016, IJARCSSE All Rights Reserved Page 442 (2)

3 Fig. 1. Image compression process Flow Fig. 2. Image Reconstruction process Flow After DCT transform, 64 DCT coefficients were obtained. These 64 DCT coefficients are quantized using standard JPEG quantization matrix as given in equation (3). The standard quantization matrix is preferred, because it provides better quality with balanced compression. These quantized coefficients are then trimmed out using zigzag sequence, keeping only first 10 DCT coefficients as proposed by Bouguezel et al. Q = (3) These trimmed quantized DCT coefficients (10 no s) are used for reconstruction of the image. De-quantization uses the same standard quantization matrix of equation 3. Then the inverse DCT is performed using the same low complexity DCT transform matrix. All the 8X8 sub blocks of image are then merged to get the reconstructed image. B. Verilog Implementation Process flow: The basic flow of the verilog implementation is shown in Fig.3. Here the input gray scale image of size 256x256 is converted.coe file format using MATLAB functions and loaded into block RAM of hardware core using Verilog HDL. The block RAM is being read by Read/Write controller to get loaded into the internal array of size 256x256. In order to process the image by taking 8x8 blocks at a time, an 8x8 block read controller is used. This block read controller reads 8x8 blocks present in the internal array one by one, until all the 1024 blocks are read [13-18]. The output from 8x8 block read converter is given to block to parallel input converter. This module takes the 8x8 block and converts them into 64 parallel inputs. While converting them to parallel manner, the inputs of format 0 to 255 are converted to -128 to 127 formats. It is because since the DCT can operate only in the range of -128 to 127. These 64 parallel inputs are then sent to DCT core at a shot, so that it can process the image. The 64 line outputs from DCT are given to IDCT core, which gives the resultant reconstructed image for size 8x8. The 64 parallel outputs coming from IDCT core are converted to 8x8 block format using the parallel to block converter. By converting to block format, it also converts them to 0 to 255 format back. Then the 8x8 block write controller receives the input from parallel to block converter and writes them onto the internal array. After the successful processing of all x8 block, the internal array matrix is being written on to the Block RAM by the Read/write controller. IV. DCT & IDCT CORE ARCHITECTURE The DCT and IDCT core being used in the Compression and Reconstruction process are designed for an input size of 64 i.e. 8x8 block. It is because; the DCT approximate transform matrix is of size 8x8 only. 2016, IJARCSSE All Rights Reserved Page 443

4 A. Discrete Cosine Transform (DCT) CORE architecture The architecture of DCT core is shown in Fig. 4. The DCT core receives an input of 64 parallel lines, each being 13 bit of -128 to 127 format (13 th bit being sign bit). The 2D DCT implemented here is of row-column transformation model. Initially the data is processed Row wise. After row transformation, it is being given to transpose buffer, which converts the row elements to column elements. Again it is being operated by column transformation, to produce the DCT coefficients. For both row and column transformation, same approximate DCT transform as given in equation 2 is being used, as the transform matrix is a orthogonal matrix. Fig.3. Verilog Implementation Process flow Fig.4. DCT core Architecture 2016, IJARCSSE All Rights Reserved Page 444

5 Fig. 5 IDCT core Architecture After DCT transform, quantization of the DCT coefficients are done using the standard quantization matrix as given in equation 3. Quantization is achieved by dividing each element in the transformed image matrix D by the corresponding element in the quantization matrix and then rounding to the nearest integer value. The quantization is mathematically expressed as below C i,j = round (D i,j / Q i,j )... (4) Where D is the DCT coefficients of the transformed image, Q is the quantization matrix. These quantized DCT coefficients are then trimmed out, which is keeping only few DCT coefficients and making the remaining as zeroes. This trimming procedure is done using the zigzag procedure. In our case, we kept only first 10 DCT coefficients. B. Inverse Discrete Cosine Transform (IDCT) CORE Architecture The architecture of IDCT core is shown in Fig. 5. The input to the IDCT core is the Trimmed Quantized 64 DCT coefficients from DCT core module. Initially De-quantization is done using the same quantization matrix. This dequantisation is otherwise called as Decompression. The De-quantization is mathematically expressed as below: R i,j = Q i,j X C i,j... (5) The 2D Inverse DCT is performed similar to DCT using Row-column transform model. V. MATLAB RESULTS AND COMPARISONS The compression performance is evaluated for gray scale images that can be grouped into three image types. Cameraman and Lena are low frequency (LF) images, Barbara and Parrots are medium frequency (MF) and Mandrill and Satellite are high frequency (HF) images. The fast DCT transform [1] has been implemented in Matlab and the performance parameters such as Peak Signal to Noise Ratio (PSNR) is determined. Fig.6 Results of Lena Images after retaining various no. of DCT coefficients 2016, IJARCSSE All Rights Reserved Page 445

6 In this section, the devised transforms were applied to achieve compression for all the three type (LF, MF and HF) of benchmark images obtained from a standard public image bank was considered. These are 256x256 8 bit per pixel (8bpp) images in bitmap (BMP) format. Image Table II. PSNR values for the various no of DCT coefficients being retained No. of Retained DCT coefficients Lena Mandrill Cameraman woman Table III PSNR values for the various DCT approximation methods operated upon various images Transform Lena Mandrill Cameraman Fig. 7. Plot Showing The Variation Of PSNR With No. Of DCT Coefficients Retained Transform in [1] CB CB BAS 2011(a=0) BAS A. Image Results for Various levels of DCT Coefficients Compression of images is taken in the aspect of number of DCT coefficients retained for the reconstruction of image. Here Lena image of size 256x256 (bmp image) is compressed by retaining various degrees of DCT coefficients, which were shown in Fig 6. It is found that higher the number of DCT coefficients retained, higher is the quality of the decompressed image. The comparative results of the PSNR values for various standard test images with varying number of DCT coefficients retained is given in Table II. The plot in Fig 7 shows the variation of PSNR with the no of DCT coefficients being retained. (a) BAS (b) BAS-2011 (c) CB-2011 (d) CB-2012 (e) Transform in [1] (PSNR= ) (PSNR= ) (PSNR= ) (PSNR= ) (PSNR= ) (a) BAS (b) BAS-2011 (c) CB-2011 (d) CB-2012 (e) Transform in [1] (PSNR= ) (PSNR=26.349) (PSNR= ) (PSNR= ) (PSNR= ) Fig. 8. Showing Various DCT approximation methods operated over Cameraman and Lena Image with only 10 DCT coefficients retained B. Comparison of other DCT approximation methods The standard test images are compressed, decompressed and reconstructed using only 10 DCT coefficients. The reconstructed images using the fast DCT approximate method [1] and existing are illustrated in Fig. 8 and the PSNR 2016, IJARCSSE All Rights Reserved Page 446

7 comparisons are presented in Table III. The approximate transform of our work is positioned in the SDCT family by means of PSNR. From the Fig. 8 it clearly shows that the transform in [1] has better PSNR than BAS-2011, CB-2011 and CB-2012 for almost all the compression ratios and when compared to the existing CB Hence from the results, we are able to prove that the transform of our work has better PSNR values on comparing with the CB-2012, which also has the computational complexity of 14 additions only and it also outperforms the existing transform by a 0.796dB improvement in the PSNR value. VI. VERILOG SIMULATION RESULTS AND ANALYSIS The entire process of compression and reconstruction of image has been implemented using Verilog HDL on Xilinx ISE simulator. The simulation results are shown in Fig. 9, where after pipeline is completely loaded, we can get output for every clock cycle. Fig. 9. Verilog Simulation output results using Xilinx ISE simulator VII. CONCLUSIONS In this work, we have worked upon 8X8 transformation matrix, which requires only 14 additions, thus avoiding the need for multiplication and shift operations. The hardware implementation of approximate DCT for image compression is a simple, efficient architecture having lower computation complexity and has closed or better performance than the existing transforms. REFERENCES [1] Uma Sadhvi Potluri, Arjuna Madanayake, Renato, J. Cintra, FábioM. Bayer, Sunera Kulasekera, and Amila Edirisuriya, Improved 8-Point Approximate DCT for Image and Video Compression Requiring Only 14 Additions, IEEE Transactions On Circuits And Systems, Vol. 61, No. 6, June 2014 [2] S. Bouguezel, M. O. Ahmad, and M. N. S. Swamy, Low-complexity 8x8 transform for image compression, Electron. Lett., vol. 44, no.21, pp , [3] S. Bouguezel,M. O. Ahmad, and M. N. S. Swamy, A low-complexity parametric transform for image compression, in Proc. ISCAS, May 2011, pp [4] R. J. Cintra and F. M. Bayer, A DCT approximation for image compression, IEEE Signal Processing Lett., vol. 18, no. 10, pp , Oct [5] F. M. Bayer and R. J. Cintra, DCT-like transform for image compression requires 14 additions only, Electron. Lett., vol. 48, no. 15, pp , [6] S. Bouguezel, M. O. Ahmad, and M. N. S. Swamy, A multiplicationfree transform for image compression, in Proc. 2nd Int. Conf. Signals,Circuits Systems, Nov. 2008, pp [7] S. Bouguezel,M. O. Ahmad, and M. N. S. Swamy, A novel transform for image compression, in Proc. 53rd IEEE Int. Midwest Symp. Circuits Systems (MWSCAS), Aug. 2010, pp [8] Edirisuriya, A. Madanayake, R. J. Cintra, and F.M. Bayer A multiplication- free digital architecture for D DCT/DST transform for HEVC, in Proc. IEEE 27th Conv. Electr. Electr. Eng. Israel, 2012, Nov. 2012, pp [9] S. Bouguezel, M. O. Ahmad, and M. N. S. Swamy, A multiplicationfree transform for image compression, in Proc. 2nd Int. Conf. Signals,Circuits Systems, Nov. 2008, pp [10] D.Vaithiyanathan, R. Seshasayanan, S. Anith and K. Kunaraj, A low-complexity DCT approximation for image compression with 14 additions only, In Proc. of Inter. Conf. on Green Computing, Communication and Conservation of Energy (ICGCE), Chennai, India, pp , Dec [11] D. Vaithiyanathan and R. Seshasayanan, Low power DCT architecture for image compression, In Proc. of International conference on Advanced Computing and Communication Systems, Coimbatore, India, pp. 1-6, Dec , 2013 [12] D.Vaithiyanathan, K.Kunaraj, S.Anith & R.Seshasayanan, Multiplierless 8-Point DCT Architecture for Fast Image Compression, International Journal of Applied Engineering Research, vol. 9, no. 20, 2014, pp [13] Vijaya Prakash A.M., K.S. Gurumurthy A Novel VLSI Architecture for Image compression Model using low power Discrete Cosine Transform in International Scholarly and Scientific Research & Innovation 4(12) 2010, Vol: , IJARCSSE All Rights Reserved Page 447

8 [14] Venkata Pavan Kumar, Ch. Venkateswarlu Design of Low power 2-D DCT architecture using Reconfigurable Architecture in IOSR Journal of Electronics and Communication Engineering (IOSRJECE) ISSN : , ISBN No : Volume 3, Issue 1 (Sep-Oct 2012), PP [15] T. Pradeepthi, Addanki Purna Ramesh Pipelined Architecture of 2D DCT, Quantization and zig zag processor for JPEG Image compression using VHDL in International Journal of VLSI design & Communication Systems (VLSICS) Vol.2, No.3, September 2011 [16] Papiya Chakraborty A survey analysis for Lossy image compression using Discrete Cosine Transform in International Journal of Scientific & Engineering Research Volume 3, Issue 9, September [17] Vikram Angala, Harika. T, Low power DCT architecture for Image/video coders in IPASJ International Journal of Electronics & Communication (IIJEC), Volume 2, Issue 10, October [18] B. Raghu Kanth, S R Sastry Kalavakolanu, M. Aravind Kumar, D.N. Bhushan Babu, JPEG image compression using Verilog in International Journal Of Engineering Science & Advanced Technology [IJESAT], Volume-2, Issue-5, , IJARCSSE All Rights Reserved Page 448