Interpolation and denoising of piecewise smooth signals by wavelet regularization

Hyeokho Choi; Richard G. Baraniuk

doi:10.1117/12.504752

13 November 2003 Interpolation and denoising of piecewise smooth signals by wavelet regularization

Hyeokho Choi; Richard G. Baraniuk

Author Affiliations +

Proceedings Volume 5207, Wavelets: Applications in Signal and Image Processing X; (2003) https://doi.org/10.1117/12.504752
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

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^α_p(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.

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Hyeokho Choi, Hyeokho Choi, Richard G. Baraniuk, Richard G. Baraniuk, } "Interpolation and denoising of piecewise smooth signals by wavelet regularization", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.504752; https://doi.org/10.1117/12.504752

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