A user's guide for the signal processing software for image and speech compression developed in the Communications and Signal Processing Laboratory (CSPL), version 1

A complete documentation of the software developed in the Communication and Signal Processing Laboratory (CSPL) during the period of July 1985 to March 1986 is provided. Utility programs and subroutines that were developed for a user-friendly image and speech processing environment are described. Additional programs for data compression of image and speech type signals are included. Also, programs for the zero-memory and block transform quantization in the presence of channel noise are described. Finally, several routines for simulating the perfromance of image compression algorithms are included

Block Transform Coding of Presample Filtered Data

This dissertation addresses the application of non-adaptive transform coding for bit rate reduction of presampled filtered data. Transform coding is examined as an alternative to conventional pulse code modulation (PCM) for multi-source, fixed rate data acquisition systems. Typical bandlimiting presample filters introduce redundancy into the sequence of data samples. Linear transformation of successive N-length blocks of the data sequence and subsequent binary coding of the resulting components is shown to lead to reduced average bit rate for the same less distortion as PCM. Four Butterworth filters, two corresponding to eight bit PCM systems, and two corresponding to ten bit PCM systems, are considered. The orthonormal transforms (bases) examined are a filter derived Karhunen-Loueve, a discrete cosine, and a discrete Legendre transform. A reference for the previous use of the discrete Legendre basis for transform coding is not known. Transformation is modeled as a bank of basis dependent FIR filters for analysis. Thus, transform coding is interpreted in terms of spectral energy capture. The magnitude squared transfer function of the presample filter is assumed to define the worst case spectral envelope or power spectral density of the sampled filter output. This is incorporated into the model to establish an upper bound on the average component energy for the various bases. The bases are compared analytically using a bit rate reduction bound, adapted from Zelinski and Noll, and energy packing considerations. The analysis indicates that bit rate reduction is possible and that large block lengths are not required. The transform coding strategy for N = 16 is implemented on simulated and real data. Bit rate reduction on the order of 25 percent establishes merit for the transform coding strategy. Additionally, transform coding is observed to result in less distortion than PCM for signals having intervals of reduced spectral activity

Optimal block cosine transform image coding for noisy channels

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered

Suboptimality of the Karhunen-Loève transform for transform coding

We examine the performance of the Karhunen-Loeve transform (KLT) for transform coding applications. The KLT has long been viewed as the best available block transform for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. This paper treats fixed-rate and variable-rate transform codes of non-Gaussian sources. The fixed-rate approach uses an optimal fixed-rate scalar quantizer to describe the transform coefficients; the variable-rate approach uses a uniform scalar quantizer followed by an optimal entropy code, and each quantized component is encoded separately. Earlier work shows that for the variable-rate case there exist sources on which the KLT is not unique and the optimal quantization and coding stage matched to a "worst" KLT yields performance as much as 1.5 dB worse than the optimal quantization and coding stage matched to a "best" KLT. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for using a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding

On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression

We examine the rate-distortion performance and computational complexity of linear transforms for lossy data compression. The goal is to better understand the performance/complexity tradeoffs associated with using the Karhunen-Loeve transform (KLT) and its fast approximations. Since the optimal transform for transform coding is unknown in general, we investigate the performance penalties associated with using the KLT by examining cases where the KLT fails, developing a new transform that corrects the KLT's failures in those examples, and then empirically testing the performance difference between this new transform and the KLT. Experiments demonstrate that while the worst KLT can yield transform coding performance at least 3 dB worse than that of alternative block transforms, the performance penalty associated with using the KLT on real data sets seems to be significantly smaller, giving at most 0.5 dB difference in our experiments. The KLT and its fast variations studied here range in complexity requirements from O(n^2) to O(n log n) in coding vectors of dimension n. We empirically investigate the rate-distortion performance tradeoffs associated with traversing this range of options. For example, an algorithm with complexity O(n^3/2) and memory O(n) gives 0.4 dB performance loss relative to the full KLT in our image compression experiment

Reduction of block-transform image coding artifacts by using local statistics of transform coefficients

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