Adaptive Signal Decompositions with Applications in Compression

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This research explores adaptive methods for high performance, lossy signal compression, and in particular, focuses on a variety of methods that rely on signal expansions. Among these are: (1) signal adaptive expansions that include quantization and entropy coding. These are generalizations of transform or subband/wavelet and wavelet packet schemes. In particular, adaptive wavelet packets are being studied, both from the point of a view of constructing bases and that of finding good and efficient algorithms to find the best bases. (2) Overcomplete expansions or frames. The focus is on quantization performance and computational complexity. (3) The class of compression algorithms that use successive approximation. A rage-distortion version of matching pursuit is being developed; generalizations of hierarchical methods based on wavelets and wavelet packers are being investigated. (4) Adaptive schemes for compression, including adaptive transforms and quantization. Goals include a lossy equivalent of arithmetic coding, and a lossy dictionary based predictive compression scheme that resembles a lossy Lempel-Ziv algorithm.