Centralized and Distributed Semiparametric Compression of Piecewise Smooth Functions

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.