International Journal of Computer Trends and Technology (IJCTT) volume 5 number 5 Nov 2013 Implementation of Lifting-Based Two Dimensional Discrete Wavelet Transform on FPGA Using Pipeline Architecture Raghavendra G 1, Mrs. Anita R 2 1 (PG Student, EPCET, Bangalore, India) 2 (Assoc. Prof, Dept. of ECE, EPCET, Bangalore, India) ABSTRACT: This paper presents the implementation of the high speed lifting-based two dimensional discrete wavelet transform (2D-DWT) algorithm on Field Programmable Gate Array (FPGA). Pipelining structure in DWT reduces hardware complexity and memory accesses and speeds up the performance. The conversion of raw image into Hex format is done using MATLAB and the Hex image is loaded into the FPGA Kit. The result of the 2D-DWT provides four filtered images and is passed to display. The algorithm has been realized in Verilog HDL and implemented using Xilinx Spartan-6 FPGA device. The lifting procedure to perform the DWT operation is folded architecture where in first stage each row of the raw image is processed to generate the approximate coefficients (L) and Detailed (H) and the output generated is stored back in the corresponding locations. In second stage each of the L and H is transposed and given to 1-D engine, which this time does the DWT operation row wise, but it results in column wise because of previous transpose operation. The DWT engine is run twice on L and H data to generate further subdivided images LL, LH, HL and HH. Keywords-Discrete wavelet transform (DWT); lifting scheme. I. INTRODUCTION The discrete wavelet transform is well known tool used in several application such as signal analysis, image processing and image compression. It is due to its characters of multiresolution analysis and nonblack-based analysis, and it has also become an ingredient of many new image compression standards, such as JPEG2000. Early implementations of the wavelet transform were based on filters convolution algorithms. But this approach requires a large amount of resources for computation. The algorithm requires the convolution of the filters at each resolution, used with the approximation image. A recent approach uses a reliable technique of lifting scheme for the implementation of the discrete wavelet transform (DWT)[1]. This method still constitutes an active area of research in mathematics and signal processing. This DWT based on lifting scheme presents many advantages over the convolutionbased approach such as computational efficiency, saving of memory, "in-place" computation of the DWT, integer-to-integer wavelet transform (IWT), symmetric forward and inverse transform, etc. Image compression techniques can compress with or without loss of data of original image. The lossy compression can achieve higher ratio than lossless compression. As a result, the 9/7 DWT which is recommended by JPEG2000 for lossy compression has been widely used in image compression area. The high-speed implementation of lifting-based 9/7 DWT on field-programmable gate array (FPGA) using multi-stage pipelining is ISSN: 2231-2803 http://www.ijcttjournal.org Page230
briefly described in further sections. The organization of the paper is as follows. Section 2 gives the introduction of the discrete wavelet transforms, section 3 the theoretical basis of the lifting-based discrete wavelet transforms are briefly presented. Section 4 describes the design of the 9/7 lifting DWT architectures. Section 5 describes the performance evaluation of the architecture are presented and finally, section 6 presents a conclusion for this paper. II. DISCRETE WAVELET TRANS FORM frequency content as the input signal; but the amount of data will be doubled. These compels the use of down sampling by a factor 2, applied to the outputs of the filters. The Two-Dimensional DWT (2D-DWT) is a multi-level decomposition technique. First, it converts the images from the spatial domain to the frequency domain. 1-level of wavelet decomposition produces four filtered and subsampled images, referred to as sub bands. Figure 1 shows the output of 1-level decomposition of 2D- DWT. The Discrete Wavelet Transform is based on the sub-band coding technique. It is found to yield a fast computation of Wavelet Transform. It is very easy to implement and it also reduces the computation time and overall hardware resources requirement. The DWT follows the filtering method by using filter banks for the construction of the time-frequency plane, with multi resolution. The DWT analyzes the given signal at different frequency bands with variable resolutions by decomposing the signal into two parts, (i) Approximation Co-efficient (ii) Detail Information Co-efficient. The decomposition of the original signal is segregated into different frequency bands which is obtained by successive high pass filtering g[n] and low pass filtering h[n] performed on the time domain signal. This combination of high pass filter g[n] and low pass filter h[n] forms a pair of analyzing filters. The output signal of each filter contains half the frequency content, but an equal amount of samples as that of the input signal. These two output signals contain the same Fig.1 1-level decomposition of 2-D DWT There are a lot of advantages of the sub band image decomposition using wavelet transform. Generally, it boost analysis for nonstationary image signal. It also provides a high compression rate. Its transform field is represented in multi resolution, which helps transmit data in any line even with a low transmission rate. The Discrete Wavelet Transform processes data on a variable time-frequency plane that matches the lower frequency components to coarser time resolutions and the high-frequency components to ISSN: 2231-2803 http://www.ijcttjournal.org Page231
finer time resolutions, thus achieving a multi resolution analysis. The Discrete Wavelet Transform has become powerful tool in a wide range of applications like image or video processing, medical imaging, telecommunication and numerical analysis etc. The DWT is advantageous over existing transforms, such as discrete Fourier transform (DFT) and DCT, because it performs a multi resolution analysis of a signal with localization in both time and frequency domain. III. LIFTING-BASED WAVELET TRANSFORM The second generation of wavelets under the category of lifting scheme, was introduced by Sweldens. The main feature of the lifting-based discrete wavelet transform scheme is to break up the high-pass and low-pass wavelet filters into a sequence of smaller filters that in turn can be converted into a sequence of upper and lower triangular matrices[4]. The basic idea behind the lifting scheme is to use data correlation to remove data redundancy, if any. This lifting algorithm is computed at three main phases, namely: (i) The split phase (ii) The predict phase (iii) The update phase. This is illustrated in Fig.2. Fig.2. Split, predict and update phases of the lifting based DWT. At first the Lifting Scheme structure splits the input signal samples into even and odd samples. Then Prediction function (P) is applied on even samples. It is called prediction because P function predicts odd samples using even samples. The prevailing difference between this prediction and the actual value of odd sample, creates a high frequency part of the signal is called "detail" coefficients (d). Then applying the U function on the resultant detail signal and combining the result with even samples update them so that the output coefficients (s) have the desired properties. Usually, the properties of s is the same as the properties of input signal (x) but with half the size. So the signal s is an approximation for x and is called approximation coefficient. A. Split phase. In the split phase, the data set x(n) is split into two subsets to separate the even samples x(2n) from the odd ones x(2n+1). B. Prediction phase. In the prediction stage, the main step is to eliminate redundancy left and give a more compact data representation. It is proposed to use the even subset x(2n) to predict the odd subset x(2n+1) using a prediction function P as described in equation(1). The difference between the predicted value of the subset and the original value is processed and replaces the latter d=x 0dd -P(X even ) (1) C. Update phase. The third stage of the lifting scheme is called the update phase. In this stage, the ISSN: 2231-2803 http://www.ijcttjournal.org Page232
coefficient x(2n) is lifted with the help of the neighboring wavelet coefficients as represented by equation(2). This phase is also referred as the primal lifting phase or update phase: s = Xeven+ U (d) (2) Where, U is the new update operator. IV. DESIGN OF THE PIPELINED ARCHITECTURE frequency-vertical high frequency component (LH), the horizontal high frequency-vertical low frequency (HL), and the horizontal high frequencyvertical high frequency (HH), respectively. Table1. Lifting Coefficients: Original9/7, Rational9/7 And Fixed Point Binary Of Rational9/7 The standard Lifting Scheme for the 9/7 wavelet filters is shown in Fig.3. In this, the four lifting coefficients α, β, γ, δ and the scaling factor k can be observed. The table.1 shows the Lifting Coefficients. Here the decimal is turned into binary by firstly multiplying the decimal by 216, and then it is converted into binary format. The conversion coefficient and the original coefficient have a certain degree of offset, but it will not impact the transform results. 1D-DWT architecture can be designed as a pipelined structure following the lifting scheme. This basic design is shown in Fig.4. This basic architecture can be utilizes 8 adders, 6 multipliers and 14 registers. Fig.3. 9/7 lifting DWT. Since the image signals are twodimensional, the 2D wavelet transform are required. The 2D wavelet transform is computed by recursive application of 1D wavelet transform. After the 2D wavelet transform of the first level, the original image is divided into four equal parts. There are the horizontal low frequency-vertical low frequency component (LL), the horizontal low Fig.4. Basic pipeline architecture of 1D-DWT For 1 st clock cycle the even and odd pixel value of the image stored in c 0 and c 1 registers are moved to c 2 and c 3 registers, respectively. For 2nd clock cycle the data present in c 0 and c 2 gets added ISSN: 2231-2803 http://www.ijcttjournal.org Page233
and then multiplied with the coefficient α and this result is added with data present in the c 3 register. This result is stored in the predicted data in c 5 register. For 3rd clock cycle the data present in c 5 get added with c 7 and multiply with the coefficient β and the results adds with data present in the c 4 register stores the updated data in c 6 register. For 4 th clock cycle the data present in c 6 get added with c 8 and multiply with the coefficient γ and the results adds with data present in the c 9 register stores the 2 nd time predicted data in c 11 register. For 5 th clock cycle the data present in c 11 moved into c 13 multiply with 1/k coefficient and gives high pass A UART module to load a input a raw image. A raw image memory to store the input image, DWT processing engine which performs dwt operation on Row and Column, The control block to sequence and control DWT operations Output memory to store the HH, HL, LH and LL images. V. IMPLEMENTATION RESULTS output (detail coefficient) and c 11 get added with c 13 and multiply with the coefficient δ and the results adds with data present in the c 10 register stores the 2 nd time updated data in c 12 multiply with k coefficient and gives low pass output (approximation coefficient). The input image having size of 256*256, it is read by using Matlab command and it is used for input image to 1D-DWT and 2D-DWT. A high speed 9/7 lifting 2D-DWT algorithm which is implemented on FPGA-based platforms with multi-stage pipelining structure. It is realized in Verilog HDL language and optimized in terms of memory requirements., the proposed architecture has higher operating frequency, the design raises operating frequency around 1.5 times more fast, than architecture which without multi-stage pipeline. The hardware architecture is suitable for high speed implementation. The final results is as shown in fig.1. The original image is divided into approximation and detail sub images. Therefore first filter is applied along the rows and then applied along the columns, thus the operation results in four bands, low- low(ll),lowhigh(lh),high-low(hl) and high-high(hh).four sub-images are obtained, the approximation, the vertical sub image, the horizontal sub image and diagonal sub image. Fig 5.Proposed 2D-DWT Block Diagram ISSN: 2231-2803 http://www.ijcttjournal.org Page234
VI. CONCLUSION DWT is an extremely important part of modern Image compression and computing. By having the ability to decompose and compress images to a fraction of their original size, valuable (and expensive) disk space can be saved. In addition, transportation of images from one computer to another becomes easier and less time consuming. DWT based compression technique algorithm provides a very effective way to compress with minimal loss in quality. Although the actual implementation of the JPEG2000 algorithm is more difficult than other image formats, and the actual compression of images is expensive computationally, the high compression ratios that can be routinely attained using the JPEG2000 algorithm easily compensate for the amount of time spent implementing the algorithm and compressing an image. It successfully implements a significant part JPEG2000 algorithm on Spartan6 FPGA chip. [4] S.Khanfir, M. Jemni, Reconfigurable Hardware Implementations for Lifting-Based DWT Image Processing Algorithms, ICESS 08, 2008, pp. 283-290. REFERENCES [1] A. S. Lewis and G. Knowles, Image compression using the 2-D wavelet transform, IEEE Trans. Image Process., 1992, 1(3), pp. 244 250 [2] T. Park and S. Jung, High speed lattice based VLSI architecture of 2D discrete wavelet transform for real-time video signal processing, IEEE Trans. Consum. Electron. 2002, 48(4), pp. 1026 1032 [3] K. A. Kotteri, S. Barua,et.al,"A Comparison of Hardware Implementations of the Biorthogonal 9/7 DWT: Convolution Versus Lifting,"IEEE Trans. on circuit and systems,2005,52(5),256-260 ISSN: 2231-2803 http://www.ijcttjournal.org Page235