WFRF:(Malek Mohammadi Mohammadreza)
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A Class of Nonconvex Penalties Preserving OverallConvexity in Optimization-Based Mean Filtering
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- Malek Mohammadi, Mohammadreza (författare)
- KTH,Reglerteknik,ACCESS Linnaeus Centre
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- Rojas, Cristian (författare)
- KTH,Reglerteknik,ACCESS Linnaeus Centre
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- Wahlberg, Bo (författare)
- KTH,Reglerteknik,ACCESS Linnaeus Centre
- (creator_code:org_t)
- Institute of Electrical and Electronics Engineers (IEEE), 2016
- 2016
- Engelska.
- Ingår i: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-587X .- 1941-0476. ; 65:24, s. 6650-6664
- Tidskriftsartikel (refereegranskat)
Abstract
Ämnesord
Stäng
- l1 mean filtering is a conventional, optimizationbasedmethod to estimate the positions of jumps in a piecewiseconstant signal perturbed by additive noise. In this method, the l1 norm penalizes sparsity of the first-order derivative of the signal.Theoretical results, however, show that in some situations, whichcan occur frequently in practice, even when the jump amplitudes tend to , the conventional method identifies false change points.This issue is referred to as stair-casing problem in this paper andrestricts practical importance of l1 mean filtering. In this paper, sparsity is penalized more tightly than the l1 norm by exploiting a certain class of nonconvex functions, while the strict convexity ofthe consequent optimization problem is preserved. This results in a higher performance in detecting change points. To theoretically justify the performance improvements over l1 mean filtering, deterministic and stochastic sufficient conditions for exact changepoint recovery are derived. In particular, theoretical results show that in the stair-casing problem, our approach might be able to exclude the false change points, while l1 mean filtering may fail. A number of numerical simulations assist to show superiorityof our method over l1 mean filtering and another state-of-theart algorithm that promotes sparsity tighter than the l1 norm. Specifically, it is shown that our approach can consistently detectchange points when the jump amplitudes become sufficiently large, while the two other competitors cannot.
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)
Nyckelord
- Change point recovery
- mean filtering
- nonconvex penalty
- piecewise constant signal
- sparse signal processing
- total variation denoising
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