Explicit solutions of one-dimensional total variation problem

Artyom Makovetskii; Sergei Voronin; Vitaly Kober

doi:10.1117/12.2187866

22 September 2015 Explicit solutions of one-dimensional total variation problem

Artyom Makovetskii, Sergei Voronin, Vitaly Kober

Proceedings Volume 9599, Applications of Digital Image Processing XXXVIII; 959926 (2015) https://doi.org/10.1117/12.2187866
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

Abstract

This work deals with denosing of a one-dimensional signal corrupted by additive white Gaussian noise. A common way to solve the problem is to utilize the total variation (TV) method. Basically, the TV regularization minimizes a functional consisting of the sum of fidelity and regularization terms. We derive explicit solutions of the one-dimensional TV regularization problem that help us to restore noisy signals with a direct, non-iterative algorithm. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of noisy signals.

Citation Download Citation

Artyom Makovetskii, Sergei Voronin, and Vitaly Kober "Explicit solutions of one-dimensional total variation problem", Proc. SPIE 9599, Applications of Digital Image Processing XXXVIII, 959926 (22 September 2015); https://doi.org/10.1117/12.2187866

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