Wavelet Transform Image Compression Prototype Lanier Watkins, Kenneth R. Perry, John S. Hurley, Clark Atlanta University 223 J.P. Brawley Dr. SW Atlanta, GA 30304 B. Olson and B. Pain, Jet Propulsion Laboratory-California Institute of Technology 4800 Oak Grove Drive, Pasadena, CA 91109 ABSTRACT In this study, we seek to develop a low power, area efficient wavelet compression chip capable of reconstructing sharp images at acceptable noise levels. It can be used in conjunction with such devices as the 256 x 256 CMOS Active Pixel Sensor (APS) camera under developed at JPL [1], or because of its small size, incorporated on the image sensor itself. A software algorithm is used to simulate the hardware and yield predicted values prior to fabrication. We limit our focus to the two-coefficient Haar Wavelet and one level Subband Coding (SBC). These parameters allow us to best emulate hardware restrictions in software. As a result, the software algorithm should yield very close findings to those of the hardware. Zerotree Encoding, which is a less restrictive algorithm, is employed as a standard. Reported results from Zerotree Encoding for 8:1 compression of the 512 x 512 standard Lena image yield a Peak Signal-to-Noise Ratio (PSNR) of 43.3 dB. Our software results for 8:1 compression of the 256 x 256 Lena image yield a PSNR of 37 dB, which is quite good given the more restrictive nature of our algorithm. Keywords: wavelet transform, CMOS APS camera, low power, Subband Band Coding, prototyping INTRODUCTION Historically, image-processing methodologies have traditionally used the Discrete Cosine Transform (DCT) to accomplish synthesis and compression. However, recent efforts, including those of Watkins [2], Murenzi [3], and Namuduri [4] have shown that wavelet transform algorithms (continuous and discrete) may provide significant improvements over previously used algorithms. The software and hardware implementations used in this study are based on the use of the 2-coefficient Haar Wavelet and one level Subband Coding (SBC) [5]. This particular algorithm was chosen, because it is easily and accurately implemented in hardware. Zerotree Encoding, which is a less restrictive algorithm, utilizes the 9- coefficient Haar Wavelet and multi level SBC [6]. The Zerotree Encoding algorithm for 8:1 compression of the 512 x 512 Lena image yields a PSNR of 43.3 dB. In this effort the 256 x 256 Lena image, at 8:1, 4:1, and 2:1 compression ratios yield a PSNR of 37 dB, 37.3 dB, and 39 dB, respectively. Hence, the 2-coefficient Haar Wavelet and 1-level SBC compares favorably with other less restrictive algorithms. The chip is being designed for implementation in a NASA-JPL Active Pixel Sensor camera for image compression. Although it is not required for the chip to achieve very large compression ratios, minimum errors due to compression must be addressed. The results obtained from the software simulation reflect the probability that the proposed chip can indeed produce the necessary sharply reconstructed images with minimum errors in spite of the many restrictions introduced by the hardware. Ultimately, the completed prototype must undergo tests to measure performance and design efficiency. Our approach requires that such standard measurement tools as Root Mean Squared Error (RMSE) and Peak Signal-to-Noise Ratio 1 (PSNR) be used. The software algorithm will provide standard values that we can use to measure the performance and design efficiency of the chip. Discrete Wavelet Transform (Software) The Discrete Wavelet Transform has been implemented using Matlab. This implementation, shown in Figure 1 is based on Mallat’s Standard Wavelet Transform Algorithm [5]. Mallat’s algorithm uses quadrature mirror filters to provide wavelet analysis of an image. Large-scale analysis of the image is captured in the low frequency filtering, while small-scale analysis is captured in the high frequency filtering. The 2-coefficient Haar Wavelet consisting of both a lowpass filter [1 1] and a highpass filter [-1 1] is the preferred wavelet for this study because it can be readily implemented in hardware. The convolved lowpass filter and image produces the approximate or averaged coefficients while the convolved highpass filter and image produces detailed coefficients. The highpass and lowpass filters are called the decomposition filters because they break the image down or decompose the image into detailed and averaged coefficients, respectively. Similarly, the reconstruction lowpass and highpass filters [1 1] and [-1 1] respectively, can be used to rebuild the original image or to construct the wavelet function. The Matlab programming environment provided all the necessary tools needed to produce a menu driven software application. The image is read in as a 256 x 256 matrix and each row is convolved with a lowpass filter. The results are then stored in temporary matrix 1. The original image is then convolved with a highpass filter and stored in temporary matrix 2. Next, the columns of temporary matrices 1 and 2 are downsampled and stored into temporary matrices 3 and 4, respectively. The next step involves convolving the columns of temporary matrix 3 with lowpass and highpass filters, then storing the results into matrices 5 and 6, respectively. At this point, the columns of temporary matrix 4 are also convolved with lowpass and highpass filters. The results are stored in temporary matrices 7 and 8, respectively. Finally, the rows of temporary matrices 5-8 are downsampled and stored as subbands Lowpass Lowpass, Lowpass Highpass, Highpass Lowpass and Highpass Highpass, respectively. This procedure defines 1-Level Subband Coding using Mallat’s Algorithm. These four subbands can be recombined to produce the original image if and only if none of the subbands are quantized. There exist many different types of quantization schemes, each with its own This work was supported in part by the NASA Jet Propulsion Laboratory (Contract No. 961072).