Adaptive Signal Decompositions with Applications in Compression

本研究探索了高性能、有损信号压缩的自适应方法，特别关注了依赖于信号扩展的各种方法。其中包括：(1)信号自适应扩展，包括量化和熵编码。这些是变换或子带/小波和小波包方案的概括。特别是对自适应小波包的研究，无论是从构造基的角度，还是从寻找最佳基的有效算法的角度。(2)过完备的展开或框架。重点是量化性能和计算复杂度。(3)一类使用逐次逼近的压缩算法。匹配追求的愤怒扭曲版本正在开发中；基于小波和小波封装的分层方法的推广正在研究中。(4)压缩自适应方案，包括自适应变换和量化。目标包括有损等效的算术编码，以及类似有损Lempel-Ziv算法的基于有损字典的预测压缩方案。

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.