Simultaneous segmentation, compression, and denoising of signals using polyharmonic local sine transform and minimum description length (with E. Woei), submitted for publication, 2008.


We present a new approach to simultaneously segment, compress, and denoise an observed noisy signal by combining our compact signal representation scheme called the Polyharmonic Local Sine Transform (PHLST) and the Minimum Description Length (MDL) criterion. The PHLST algorithm 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 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 or without actually quantizing the relevant parameters. The resulting representation gives rise to simultaneous segmentation, compression, and denoising of the given data. We apply our algorithms to synthetic and real datasets and compare their performance against other competing methods for denoising and compression such as the wavelet transform using the MDL criterion. We observe that our PHLST algorithms perform better (in compression rate, relative L2-error, and visual quality) than the wavelet transform for oscillatory signals whereas their performance is comparable to that of the wavelet transform for piecewise smooth signals.

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