Abstract
Segmentation and denoising of signals often rely on the polynomial model which assumes that every segment is a polynomial of a certain degree and that the segments are modeled independently of each other. Segment borders (breakpoints) correspond to positions in the signal where the model changes its polynomial representation. Several signal denoising methods successfully combine the polynomial assumption with sparsity. In this work, we follow on this and show that using orthogonal polynomials instead of other systems in the model is beneficial when segmenting signals corrupted by noise. The switch to orthogonal bases brings better resolving of the breakpoints, removes the need for including additional parameters and their tuning, and brings numerical stability. Last but not the least, it comes for free!
Highlights
Polynomials are an essential instrument in signal processing
The neighboring segments should be identified such that they contrast in their “character.” For digital signal processing, such a vague word has to be mathematically expressed in terms of signal features, which differ from segment to segment
The improvement can be observed in all parameters in consideration
Summary
Polynomials are an essential instrument in signal processing. They are indispensable in theory, as in the analysis of signals and systems [1] or in signal interpolation and approximation [2, 3], but they have been used in specialized application areas such as blind source separation [4], channel modeling and equalization [5], to name a few. In [9, 13, 15], the authors build explicit signal segmentation/denoising models based on the standard polynomial basis 1, t, t2, . This article shows that modeling with orthonormal bases instead of the standard basis (which is clearly non-orthogonal) brings significant improvement in detection of the signal breakpoints and in the eventual denoising performance.
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