Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory


Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.

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Additional Information: This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Uncontrolled Keywords: edge,jump,shift,step,change,level,Mathematics(all),Engineering(all),Physics and Astronomy(all)
Publication ISSN: 1471-2946
Last Modified: 21 Jun 2024 07:09
Date Deposited: 28 Jan 2013 15:39
Full Text Link: http://rspa.roy ... t/467/2135/3088
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2011-11-08
Authors: Little, Max A. (ORCID Profile 0000-0002-1507-3822)
Jones, Nick S.



Version: Published Version

License: Creative Commons Attribution

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