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