Abstract
Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular nondifferentiable convex cost function. This letter describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.
| Original language | English (US) |
|---|---|
| Article number | 7807310 |
| Pages (from-to) | 216-220 |
| Number of pages | 5 |
| Journal | IEEE Signal Processing Letters |
| Volume | 24 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1 2017 |
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Keywords
- Convex
- denoising
- sparse
- total variation (TV)
ASJC Scopus subject areas
- Signal Processing
- Applied Mathematics
- Electrical and Electronic Engineering
Cite this
Total Variation Denoising Via the Moreau Envelope. / Selesnick, Ivan.
In: IEEE Signal Processing Letters, Vol. 24, No. 2, 7807310, 01.02.2017, p. 216-220.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Total Variation Denoising Via the Moreau Envelope
AU - Selesnick, Ivan
PY - 2017/2/1
Y1 - 2017/2/1
N2 - Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular nondifferentiable convex cost function. This letter describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.
AB - Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular nondifferentiable convex cost function. This letter describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.
KW - Convex
KW - denoising
KW - sparse
KW - total variation (TV)
UR - http://www.scopus.com/inward/record.url?scp=85015248024&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85015248024&partnerID=8YFLogxK
U2 - 10.1109/LSP.2017.2647948
DO - 10.1109/LSP.2017.2647948
M3 - Article
AN - SCOPUS:85015248024
VL - 24
SP - 216
EP - 220
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
SN - 1070-9908
IS - 2
M1 - 7807310
ER -