Simultaneous segmentation, compression, and denoising of signals using polyharmonic local sine transform and minimum description length criterion

We propose a new approach to simultaneously segment, compress, and denoise a given noisy signal by combining our compact signal representation scheme called polyhannonic local sine transform (PHLST) and the minimum description length (MDL) criterion. PHLST first generates a redundant set of local pieces of an input signal each of which is supported on a dyadic subinterval and is approximated by a combination of an algebraic polynomial of low order (e.g. linear or cubic) and a trigonometric polynomial. This combination of polynomials compensates their shortcomings and yields a compact representation of the local piece. To select the best nonredundant combination of the local pieces from this redundant set, we use the MDL criterion with and without actually quantizing the relevant parameters. The resulting representation gives rise to simultaneous segmentation, compression, and denoising of the original data. We shall demonstrate its superiority over the best basis algorithm using the local cosine dictionary with the sparsity criterion