Interpolation and Denoising of Piecewise Smooth Signals by Wavelet Regularization

Hyeokho Choi; Richard Baraniuk

Interpolation and Denoising of Piecewise Smooth Signals by Wavelet Regularization

Hyeokho Choi, Richard Baraniuk

Houston Methodist

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of finding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B _p ^α(L _p), p ≥ 1, the optimization corresponds to convex programming in the wavelet domain. The algorithm simultaneously achieves signal interpolation and wavelet denoising, which makes it particularly suitable for noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.

Original language	English (US)
Title of host publication	Proceedings of SPIE - The International Society for Optical Engineering
Editors	M.A. Unser, A. Aldroubi, A.F. Laine
Pages	16-27
Number of pages	12
Volume	5207
Edition	1
State	Published - 2003
Event	Wavelets: Applications in Signal and Image Processing X - San Diego, CA, United States Duration: Aug 4 2003 → Aug 8 2003

Other

Other	Wavelets: Applications in Signal and Image Processing X
Country/Territory	United States
City	San Diego, CA
Period	8/4/03 → 8/8/03

Keywords

Besov
Denoising
Interpolation
Regularization
Wavelet

ASJC Scopus subject areas

Electrical and Electronic Engineering
Condensed Matter Physics

Cite this

@inproceedings{6d6c14dc0aed4600b88fc6ee47c4b327,

title = "Interpolation and Denoising of Piecewise Smooth Signals by Wavelet Regularization",

abstract = "In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of finding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p α(L p), p ≥ 1, the optimization corresponds to convex programming in the wavelet domain. The algorithm simultaneously achieves signal interpolation and wavelet denoising, which makes it particularly suitable for noisy sample data, unlike classical approaches such as bandlimited and spline interpolation. ",

keywords = "Besov, Denoising, Interpolation, Regularization, Wavelet",

author = "Hyeokho Choi and Richard Baraniuk",

year = "2003",

language = "English (US)",

volume = "5207",

pages = "16--27",

editor = "M.A. Unser and A. Aldroubi and A.F. Laine",

booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",

edition = "1",

note = "Wavelets: Applications in Signal and Image Processing X ; Conference date: 04-08-2003 Through 08-08-2003",

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TY - GEN

T1 - Interpolation and Denoising of Piecewise Smooth Signals by Wavelet Regularization

AU - Choi, Hyeokho

AU - Baraniuk, Richard

PY - 2003

Y1 - 2003

N2 - In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of finding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p α(L p), p ≥ 1, the optimization corresponds to convex programming in the wavelet domain. The algorithm simultaneously achieves signal interpolation and wavelet denoising, which makes it particularly suitable for noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.

AB - In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of finding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p α(L p), p ≥ 1, the optimization corresponds to convex programming in the wavelet domain. The algorithm simultaneously achieves signal interpolation and wavelet denoising, which makes it particularly suitable for noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.

KW - Besov

KW - Denoising

KW - Interpolation

KW - Regularization

KW - Wavelet

UR - https://www.scopus.com/pages/publications/1242330936

UR - https://www.scopus.com/inward/citedby.url?scp=1242330936&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:1242330936

VL - 5207

SP - 16

EP - 27

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Unser, M.A.

A2 - Aldroubi, A.

A2 - Laine, A.F.

T2 - Wavelets: Applications in Signal and Image Processing X

Y2 - 4 August 2003 through 8 August 2003

ER -

Interpolation and Denoising of Piecewise Smooth Signals by Wavelet Regularization

Abstract

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Keywords

ASJC Scopus subject areas

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