EECS 651 Project Presentation Schedule and Abstracts Monday, April 18, 2005, 1:10-2:50 PM, Room 651 FXB 1:10-1:40 "Design of a CELP coder and study of its performance using different quantization methods" Awais Kamboh, Krispian Lawrence, Aditya Thomas & Philip Tsai In this term project we study the Code Excited Linear Prediction (CELP) speech coding technique. We design a basic CELP coder in MATLAB. MSE and Perceptual MSE are used as the performance measures for the coder. The Linear Predictive Coding (LPC) method, used in CELP, performs LP analysis of speech by extracting LP coefficients and employs quantization to reduce the number of bits needed to be transmitted. We examine the performance of the coder with respect to various quantization techniques. We will concentrate on scalar quantizers, TSVQ, DPCM and Transform Coders. 1:45-2:10 "Noisy Source Coding for Corrupted 45 rpm Records" Sonia Gupta, Scott Harlow, Idan Langberg We consider the data compression of noisy sources for the specific application of noisy 45-rpm records degraded by scratches and general needle wear. We consider the scalar quantization of both clean and corrupted sources optimized with both normal and modified distortion measures. Four different cases are compared and contrasted: the quantization of a clean source using a quantizer optimized for the clean signal, a corrupted source using a quantizer optimized for the clean signal, a corrupted source using a quantizer optimized for the corrupted source using an unmodified distortion measure, and a corrupted source using a quantizer optimized for the corrupted source using a modified distortion measure. The Generalized Lloyd Algorithm is used for these scalar designs. Our corrupted source is obtained by adding noise to a known clean signal. The noise added is t location-scale distribution noise with parameters obtained through characterizing typical noise from a 45-rpm record trail-in band. In designing with a modified distortion measure, an optimal estimator for the clean signal is obtained from the noisy signal using the clean signal and t location-scale noise distributions and a conditional expectation calculation. SNR results are calculated for four different rates and four different training vector sizes for each of the four different cases. 2:15-2:50 "Distributed Source Coding (Quantization using side information)" Anirudh Reddy, Awlok Josan, Chandan Damannagiri, Hugo Louro, Sidharth Misra Distributed Source Coding has become an important topic with the emergence of research in sensor networks. The first part of this project focuses on the design of fixed rate optimal scalar quantizers for correlated sources. Two cases are considered -- one in which the distortion in only one source is minimized with the second source acting as side information. In the second case average distortion in both sources is minimized. The second part of the project deals with the design of a good transform code for the distributed case. The standard Karhunen-Loeve Transform (KLT) is the optimal transform for Gaussian sources and in general good. However in Distributed Source Coding the KLT must be approximated. When side information is available at the decoder, the performance of conditional KLT, an approximation to the KLT, is analyzed. Finally we consider the design of a practical coding scheme (with side information at the decoder) using syndromes. The objective of this scheme is to partition the source codeword space into a bank of cosets and communicate the index of the coset containing the codeword to the decoder. The side information available at the decoder can be used to disambiguate which member in the coset is the correct codeword. We compare its rate-distortion performance with previous unstructured and structured quantizers. All the analysis is on jointly Gaussian sources with MSE being the fidelity criterion. Variation of the MSE with rate of encoding and extent of correlation of the source with the side information is also investigated. Tuesday, April 19, 12:35-1:30 PM, Room 3427 EECS 12:35-1 "An Investigation of Compression Artifacts in Transform Coded Images" Jarut Chaipipakorn, Edmund Lo, Ben Morris Transform coding is often used for image compression because of its relatively low complexity and excellent exploitation of source correlation. In creating a transform quantizer, the designer must first choose the type of transform to be used, next, the distribution of quantization levels in each scalar quantizer, and last, the distribution of rate among the scalar quantizers. In this project, we study how varying these main aspects of transform codes affects the amount and type of artifacts (such as blocking, artificial texture, and graying) produced in the decoded image. Specifically, we independently vary the type of transform used (DCT, HAAR, KLT, etc), the type of scalar quantizers used (uniform, Laplacian, LBG), and the total rate, to see the effect of each on the visibility of compression artifacts. With this information, we develop performance criteria to describe how much of an artifact is present in a given image. In order to reduce their appearance without increasing rate, we modify transform coding to allow each block to be encoded with a different transform. This allows some increase SNR and decrease artifacts but at the cost of additional computational complexity. In conclusion we present quantitative comparisons with JPEG and discuss the difficulty of removing compression artifacts. 1:05-1:30 "Video Encoding Using 2nd Order Trajectories" Carter, Grikschat, Stepanian Motion estimation is an important technique used in the current video coding standards. It takes advantage of the temporal correlation in a sequence of images. It can be thought of as a form of a predictor that is used in a DPCM framework. This project will investigate ways to reduce rate in video coding while maintaining reasonable image quality. Specifically, we will reduce the number of error-images coded and use quadratic motion trajectories (as opposed to the current use of linear displacement) to decode and restore the decimated sequence of images. Our goal is to reduce rate at the expense in image quality for every other frame. The experiments will explore the tradeoff between a lower rate vs. MSE and other distortion metrics such as PSNR. We will also relate any rate gain to the increase in complexity of each method. These results will be benchmarked against the results of simulating methods similar to those used in current standards such as MPEG and H.264. Tuesday, April 19, 3:05-3:55 PM, Room 3427 EECS 3:05-3:30 "Design and Analysis of Tree-Structured Vector Quantization" Pratik Kamdar, Saradwata Sarkar, Shruti Sheorey Tree-Structured Vector Quantization (TSVQ) is one of the most effective techniques for reducing the search complexity in Vector Quantizers. It is not surprising, therefore, that several TSVQ algorithms have been studied and investigated in the Source Coding literature. In this project, we consider different methods for growing and pruning TSVQ. Fixed-rate and variable-rate TSVQ are grown and pruned for varying rates and dimensions. We compare Rate-Distortion performances for each method. The theoretical performance is obtained using Bennett's integral and is compared with the experimental results. We investigate the shapes of the cells of pruned TSVQs using histogram plots of normalized error vector lengths. Finally we examine the Rate-Distortion graphs obtained in progressive reconstruction where successively better approximations to the input vector are provided as the digital information arrives. 3:35-55 "On the Rate Allocation of Transform Coding for Noisy Channels" Ilju Na While transform coding has been proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. In 1990, Vaishampayan and Farvardin presented an optimization scheme for the siutation that a transform code is used over a binary symmetric channel (BSC). More specifically, what they developed were (1) a numerical algorithm for optimizing the rate allocation based on the steepest descent algorithm and (2) the design of optimal scalar quantizers over noisy channels, a.k.a., channel-optimized scalar quantizer (COSQ). However, there has been no high-resolution theory that predicts the optimal rate allocation for the noisy channel transform code. Recently, in 1997, Hochwald and Zeger developed high-resolution theory for noisy channel quantizers. Although the Hochwald-Zeger theory applies to a kind of joint source-channel code that does not exactly match the noisy channel quantizer presumed by Vaishampayan and Farvardin, (in fact, a robust VQ consisting of a source-optimized VQ and a robust index assignment was considered), it sounds reasonable that a rate allocation based on the Hochwald-Zeger theory will make a reasonably good prediction of the rate allocation found by Vaishampayan and Farvardin. In this project, we investigate the optimal rate allocation of transform codes for noisy channels. The procedure consists of two steps: (1) finding the expressions for the least distortion of scalar quantizers with tranmission rate R when used over a BSC, and (2) finding the optimal rate allocation R_i based on the result of the previous step. The optimization method will be the use of 'equal-slope condition' taught in the class. After finding the optimal rate allocation of transform codes for noisy channels, it will be compared with that of transform codes for noiseless channel. Also, the above theoretical rate allocation for noisy channels can be compared with the numerical rate allocation found by Vaishampayan and Farvardin.