Semi-parametric compression of piecewise smooth functions

This paper introduces a new wavelet-based compression scheme that combines the use of linear approximation and parametric estimation. Our proposed scheme differs from the conventional wavelet-based schemes in two ways: first, the encoder uses linear approximation and second, the decoding process is non-linear as it is combined with parametric estimation. We consider a simple model of one-dimensional (1-D) piecewise smooth function and show that, with our scheme, it is possible to achieve the same decay in the distortion-rate bound as conventional wavelet-based schemes that employ non-linear approximation. A practical compression algorithm that achieves the distortion bound and uses the new concept of sampling of signal with finite rate of innovation is also presented together with the simulation results.