Interpolation and Denoising of Piecewise Smooth Signals by Wavelet Regularization
نویسندگان
چکیده
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 nding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p (Lp), 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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