Image Compression & Decompression using DWT & IDWT Algorithm in Verilog HDL

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1 Image Compression & Decompression using DWT & IDWT Algorithm in Verilog HDL Mrs. Anjana Shrivas, Ms. Nidhi Maheshwari M.Tech, Electronics and Communication Dept., LKCT Indore, India Assistant Professor, Electronics and Communication Dept., LKCT Indore, India Abstract: The Discrete Wavelet Transform (DWT) algorithm is well known and commonly used for data and image compression. This paper presents an approach towards image compression & decompression using HDL simulation. DWT & IDWT in designed in HDL using filter method to compressed image. Daubechies (db)-4 tap filter is used in this design. Coefficients of Daubechies filters for DWT algorithm are fixed. Compressed & decompressed image is compared and it is found that a little blur is present in decompresed image but image is visible and it is comparable with the original image. Keywords: Wa vel et Transform, Filter Banks, DWT (Discrete Wa vel et Transform), IDWT, Daubechies (db) wa velet filter. Introduction Image compression is a technique of encoding an image to store it or send it using as fewer bits as possible. Presently the most common compression methods for still images fall into two categories: Discrete Cosine Transform (DCT) based techniques and methods based on wavelet transform. Widely used image compression technique JPEG achieves compression by applying DCT to the image, whereas wavelet transform methods generally use discrete wavelet transform (DWT) for this purpose. With the recent developments in wavelet compression, this method has arisen to be an efficient coding method for still image compression, outperforming today s DCT based JPEG standards. This state of the art compression technique is accomplished in three stages: 1) wavelet transform, ) zero tree coding and 3) entropy based coding. Wavelet transform decomposes the image into several multi-resolution sub bands in an octave manner, and perfectly reconstructs the original image from them. This multi-level decomposition is done using two dimensional wavelet filters (basis function), among which Haar and Daubechies filters are very popular. The appropriate choice of filters for the transform is very important in compression schemes to achieve high coding efficiency. Splitting of sub band into next higher level four sub bands using wavelet transform is shown in figure. Figure 01 Block diagram Two Dimensional DWT DWT and Filter Banks Wavelet Transformation is a method to represent any signal as the sum of sine waves of different frequencies. These frequencies can be divided into high band frequencies and Low band frequencies. The high band frequencies are called as the f[n] and the low frequencies are called the g[n]. The actual signal can be represented by the following equation. IJCSIET-ISSUE4-VOLUME1-SERIES4 Page 1

2 X[n] = f[n]e -jn + g[n]e -im Here the coefficients f[n] and g[n] are taken with the help of MATLAB tool. High Pass Filter Design The high pass filter is designed as a filter which allows the high pass components to pass and low frequency components to attenuate. The filter is designed with the help of MATLAB tool. The filter equation is found as written below F[n] = x[n-3] x[n-] x[n-1] x[n]. The coefficients of filter is taken using MATALB and above equation is implemented in a verilog hdl using Altera Quartus 9.1 software. Low Pass Filter Design The low pass filter is designed to allow the low frequency components to pass and attenuate the high frequency components. The coefficients of the low frequency components will be the coefficients g[n]. Mathematically we can write g[n] as follows: g[n] = x[n-3] x[n-]-0.41x[n- 1]-0.194x[n]. The frequency magnitude response of this filter was also verified to meet the required criteria as well as being orthogonal to the high pass filter. This filter is implemented in a verilog hdl file using Altera Quartus 9.1 software. The DWT is computed by successive low pass and high pass filtering of the discrete timedomain signal. This is called the Mallat algorithm or Mallat-tree decomposition. Its significance is in the manner it connects the continuous time mutiresolution to discretetime filters. In the figure, the signal is denoted by the sequence x[n], where n is an integer. The low pass filter is denoted by g[n] while the high pass filter is denoted by h[n]. At each level, the high pass filter produces detail information, while the low pass filter associated with scaling function produces coarse approximations. The reconstructions of the original signal from the wavelet coefficients. Basically, the reconstruction is the reverse process of decomposition. The approximation and detail coefficients at every level are up sampled by two, passed through the low pass and high pass synthesis filters and then added. This process is continued through the same number of levels as in the decomposition process to obtain the original signal. Multi-Resolution Analysis using Filter Banks Filters are one of the most widely used signal processing functions. Wavelets can be realized by iteration of filters with rescaling. The resolution of the signal, which is a measure of the amount of detail information in the signal, is determined by the filtering operations, and the scale is determined by up sampling and down sampling (sub sampling) operations. The DWT is computed by successive low pass and high pass filtering of the discrete time-domain signal as shown in figure 0. This is called the Mallat algorithm or Mallat-tree decomposition. Its significance is in the manner it connects the continuous time mutiresolution to discrete-time filters. In the figure, the signal is denoted by the sequence x[n], where n is an integer. The low pass filter is denoted by G0 while the high pass filter is denoted by H0. At each level, the high pass filter produces detail information; d[n], while the low pass filter associated with scaling function produces coarse approximations, a[n]. Figure 0 Three-level wavelet decomposition trees IJCSIET-ISSUE4-VOLUME1-SERIES4 Page

3 Discrete Wavelet Transform Operation When a signal passes through these filters, it is split into two bands. The low pass filter, which corresponds to an averaging operation, extracts the coarse information of the signal. The high pass filter, which corresponds to a differencing operation, extracts the detail information of the signal. The output of the filtering operations is then decimated by two. A two-dimensional transform (see Figure 03) can be accomplished by performing two separate one-dimensional transforms. First, the image is filtered along the x dimension and decimated by two. Then, it is followed by filtering the sub-image along the y-dimension and decimated by two. Finally, we have split the image into four bands denoted by LL, HL, LH and HH after one-level decomposition. The Multiresolution decomposition approach in the two-dimensional signal is demonstrated in figures. After the first level of decomposition, it generates four sub bands LL1, HL1, LH1, and HH1. Considering the input signal is an image, the LL1 sub bands can be considered as a :1 sub sampled (both horizontally and vertically) version of image. The other three sub bands HL1, LH1, and HH1 contain higher frequency detail information. These spatially oriented (horizontal, vertical or diagonal) sub bands mostly contain information of local discontinuities in the image and the bulk of the energy in each of these three sub bands is concentrated in the vicinity of areas corresponding to edge activities in the original image. Since LL1 is a coarser approximation of the input, it has similar spatial and statistical characteristics to the original image. As a result, it can be further decomposed into four sub bands LL, LH, HL and HH as shown in figure 03 based on the principle of Multiresolution analysis. Accordingly the image is decomposed into any number of levels. The same computation can continue to further decompose LL into higher levels. Figure 03 Extension of DWT in two - dimensional signals Inverse Discrete Wavelet Transform Reconstruction of the original signal from the wavelet coefficients. Basically, the reconstruction is the reverse process of decomposition. The approximation and detail coefficients at every level are up sampled by two, passed through the low pass and high pass synthesis filters and then added. This process continued through the same number of levels as in the decomposition process to obtain the original signal. The Mallat algorithm works equally well if the analysis filters, G0 and H0 are exchanged with the synthesis filters, G1 and H1. H1 G1 Figure 04 Three-level wavelet decomposition trees Implementation of DWT Algorithm The DWT Algorithm is implemented using Verilog HDL on Altera s Quartus II 9.0 Web Edition tool. In DWT module it consists of low pass, high pass filter and a down sampler module. Low pass filter, high pass filter and down sample are coded in different module. After designing these modules a top level module is designed using low pass, high pass and down sample module to DWT. This top level module is the DWT module. The pixel value of the image is taken as a input of the DWT H1 G1 H1 G1 IJCSIET-ISSUE4-VOLUME1-SERIES4 Page 3

4 algorithm and this input is processed by low pass and high pass filter followed by a down sampler. The output of the high pass filter is wavelet coefficients and the output of the low pass filter is the scaling coefficients. Now in second stage the outputs of the low pass filter become the inputs for the second stage of DWT algorithm. In a similar way further DWT scaling and wavelet coefficients are computed. RTL view of DWT Algorithm 1 lp:lod hp:hid downsample:downs _ hp:hid1 lp:lod1 downsample1:downs1 _ hp:hid lp:lod downsample1:downs Figure 05 RTL of DWT Algorithm Implementation of IDWT Algorithm In IDWT module it consist of four basic input terminal input,,, and and it has idwt_out as a output port as shown in the figure 4.9. It computes the inverse discrete wavelet transform coefficients of the input image. In IDWT module it consists of reconstruction low pass and high pass filter and a upsampler module. Low pass filter, high pass filter and upsample are coded in different module. After designing these modules a top level module idwt is designed using low pass, high pass and upsample module to compute IDWT. This top level module is the IDWT module. The pixel value of the compressed image is taken as a input of the IDWT algorithm and this input is processed by first a up sampler followed by low pass and high pass filter. The output of the high pass filter and the output of the low pass filter is added together to get the first level decompression. Similarly again for second stage of decompression, output of the first stage is treated as a input for the second stage. RTL view of IDWT Algorithm g_g_g[63..0] g_g[63..0] g[63..0] upsample:ups1 sample_fout[63..0] lpr:lodr hpr:hidr upsample:ups Figure 06 RTL of two level IDWT Algorithm Results The grayscale cameraman image is taken to test the algorithm which is designed in verilog HDL. A portion of image size of 64x64 is taken with the help of MATLAB Tool to perform DWT & IDWT algorithm. The pixel of image is taking as input for the DWT algorithm designed in HDL and is compressed at two levels. After two level compressions, the image is represented by 16x16 pixels. The compressed simulated data is in binary format thus to visualize these compressed data image plotting tool of MATLAB is used. Again this compressed image is taken as a input for the IDWT algorithm and after two level of decompression. After decompression original image is retrieved with slightly difference in contrast. This difference in contrast is due to shifting of values during product in filter realization. Figure 5. and figure 5.3 shows the original image and compressed image using HDL simulation. DWT algorithm for image compression can be used at any level of compression. The DWT & IDWT algorithm is designed and verified with the help of simulation. This algorithm is designed in verilog HDL so it can be implemented on the hardware. This DWT algorithm gives the compressed result of input image. This result is verified with the help of simulation tool. Two level Image Compression using DWT Algorithm sample_fout[63..0] lpr:l1 hpr:h1 g_g_r[63..0] f_f_r[63..0] Test Image 1 IJCSIET-ISSUE4-VOLUME1-SERIES4 Page 4

5 Original Image (a) Compressed Image after Two levels DWT (b) Two level Image Decompression using IDWT Algorithm Test Image 1 Figure 07 Decompression using HDL Two level Image Compression using DWT Algorithm Test Image Original Image (a) Compressed Image after Two level DWT (b) Two level Image Decompression using IDWT Algorithm Test Image Figure 08 Decompression using HDL Conclusion The DWT and IDWT algorithm using the Daubechies (db)-4 tap wavelet is studied and designed in Verilog HDL using Quartus II 9.0 software. Filter based DWT is the simplest, it is selected for hardware implementation. The D DWT algorithm code was written in the Verilog HDL. It is then synthesized and simulated successfully. Pixels value of input images are taken, and DWT coefficients is calculated through DWT algorithm designed in Verilog HDL and the compressed images are used for IDWT using verilog HDL. Image compression and decompression with the help of HDL simulation is compared. It is found that the value of DWT and IDWT is approximately same in the implementation methodology; however, the intensity of the image decompressed image is higher than that of the original image. This is due to shifting of the values in HDL coding. Variable levels of compression can be easily achieved using HDL. The number of DWT stages can be varied, resulting in different number of sub bands. Different filter banks with different characteristics can be used. Efficient fast algorithm (pyramidal computing scheme) for the computation of discrete wavelet coefficients makes a wavelet transform based encoder computationally efficient. References [1] Abdullah AlMuhit, Md. Shabiul Islam and Masuri Othman, VLSI Implementation of Discrete Wavelet Transform (DWT) for Image Compression, nd International Conference on Autonomous Robots and Agents December 13-15, 004 Palmerston North, New Zealand on VLSI. IJCSIET-ISSUE4-VOLUME1-SERIES4 Page 5

6 []Sonja Grgic, Kresimir Kers, Mislav Grgic, Image Compression using Wavelets Bled Slovenia ISIE, [3]Martin Vetterli, Wavelets and Fiter Banks: Theory and Design, IEEE transaction on signal Processing, Vol. 40,No. 9, September 199 [4] Ibrahim Oz Cemil Oz Nejat Yumusak, Image Compression using -D Multi-Level Discrete Wavelet Transform (DWT), [5]R.C. Gonzalez and R. E. Woods, Digital Image Processing, Reading. MA Addison Wesley, 004. [6]David Salomon, Data Compression, The Complete Reference, nd Edition Springer-Verlag [7] ansform on 15 May 01. [8]Chris Solomon and Toby Breckon, Fundamentals of Digital Image Processing A Practical Approach with Examples in Matlab. [9] on 1 April 01. [8] Daubechihes I. (199), Ten Lectures on Wavelets SIAM [9]Mallat S. (1989), A theory of multiresolution signal decomposition, the wavelet representation, IEEE Pattern Anal. And Machine Intel., vol.11, no.7, ppv [10] Strang G., Nguyan T. (199), Wavelets and Filter Banks, Wellesley-Cambridge Press. [11]Antonini M., Barlaud M., Daubechies I., Image coding using wavelet transform, IEEE Trans Image Processing, pp IJCSIET-ISSUE4-VOLUME1-SERIES4 Page 6