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Some results on source coding, vector quantization and progressive image transmission
Abstract
In this dissertation, we investigate three problems in data compression, namely, source coding, vector quantization, and progressive image transmission. In source coding, we find the optimal performance of a data compression system for cyclostationary Gaussian sources. This is accomplished by first defining a rate distortion function, R(D), for cyclostationary sources, and then proving the source coding theorem and its converse for these sources. These theorems state the following facts: given a distortion $D>0,$ there exists a code with rate arbitrarily close to the R(D); and, there exists no code with rate less than R(D). From these two theorems, we conclude that the rate distortion function defined in this dissertation is the optimal performance for the cyclostationary Gaussian sources. In vector quantization, we develop a new tree-structured vector quantizer (VQ) design algorithm which operates under rate and storage constraints. This new algorithm has the following features: first, it has low computation complexity; second, it can control storage complexity; third, its performance is close to the performance of the best known VQ. The design of this VQ uses tree-growing approach and grows the tree one stage (layer) at a time. Before the design, the storage and rate constraints at each stage are specified. Then, we minimize the distortion at each stage under these constraints. The minimization of the distortion involves the optimal rate and storage allocation, which is implemented through the use of the dynamic programming technique. As the third problem in data compression, we develop a new progressive image transmission (PIT) design algorithm in which the resolution and resource constraints at each stage can be specified/controlled. The type of resource can be the rate or distortion, and the storage size. The first step of the design of this algorithm is to use the wavelet transform to obtain a pyramid structure representation of an image. Then, at the design of each stage, we optimally allocate the resources available at the current stage to all the subimages which constitute the image to be reconstructed. The resources allocated to the subimages are then used to design the first or the subsequent layers of the TSVQ's to successively refine these subimages. Since the existing PIT algorithms can only control the rate or the resolution (but not both) at each stage, this algorithm is a generalization of the existing algorithms and can be used in a wider range of applications.
Subject Area
Electrical engineering
Recommended Citation
Hwang, Wen-Jyi, "Some results on source coding, vector quantization and progressive image transmission" (1993). Doctoral Dissertations Available from Proquest. AAI9408291.
https://scholarworks.umass.edu/dissertations/AAI9408291