Orthogonality is superiority in piecewise-polynomial signal segmentation and denoising
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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!
KeywordsSignal segmentation, Signal smoothing, Signal approximation, Denoising, Piecewise polynomials, Orthogonality, Sparsity, Proximal splitting, Convex optimization
Document typePeer reviewed
Document versionFinal PDF
SourceEURASIP Journal on Advances in Signal Processing. 2019, vol. 2019, issue 6, p. 1-15.
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