Centralized and Distributed Semiparametric Compression of Piecewise Smooth Functions

• Published in: IEEE transactions on signal processing Vol. 59; no. 7; pp. 3071 - 3085
• Main Authors: Chaisinthop, V, Dragotti, P L
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximations; Coders; Coding, codes; Compressing; compression; Decoders; Decoding; Detection, estimation, filtering, equalization, prediction; distributed source coding; Encoders; Estimation; Exact sciences and technology; Information, signal and communications theory; Linear approximation; Longitudinal waves; Nonlinearity; parametric estimation; piecewise smooth functions; Quantization; Signal and communications theory; Signal processing; Signal, noise; Telecommunications and information theory; Video compression; Wavelet transforms; wavelets; Performance evaluation; Source coding; Distributed source signal; Rate distortion theory; Approximations; Decoding; parametric estimation; Wavelet transformation; distributed source coding; piecewise smooth functions; wavelets; Signal processing; compression
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2144590

This paper introduces novel wavelet-based semiparametric centralized and distributed compression methods for a class of 1-D piecewise smooth functions. Classical centralized compression schemes are based on a relatively complex, nonlinear encoder and a simple, linear decoder. Recently, a new paradigm in compression called distributed source coding has emerged. This setup involves multiple encoders, where each one partially observes the source, and a centralized decoder. First, we focus on the dual situation of the centralized compression with a simple encoder and a complex decoder. We show that, by incorporating parametric estimation into the decoding procedure, it is possible to achieve the same rate-distortion performance as that of a conventional wavelet-based compression scheme. Second, we consider the distributed compression scenario, where each independent encoder partially observes the 1-D piecewise smooth function. We propose a new wavelet-based distributed compression scheme that uses parametric estimation to perform joint decoding. Our analysis shows that it is possible for the proposed scheme to achieve the same compression performance as that of a joint encoding scheme.