PACO : Signal Restoration via PAtch COnsensus
Ignacio Ramírez Paulino
Submitted to IEEE Transactions on Signal Processing- 2018
Research group(s):  Tratamiento de Imagenes (gti)
Department(s):  Procesamiento de Señales
Download the publication : Ram18a.pdf [1.9MB]  

Abstract

Many signal processing algorithms operate by breaking the target signal into possibly overlapping segments (typically called windows or patches), processing them separately, and then stitching them back into place to produce a unified output. In most cases where pach overlapping occurs, the final value of those samples that are estimated by more than one patch is resolved by averaging those estimates; this includes many recent image processing algorithms. In other cases, typically frequency-based restoration methods, the average is implicitly weighted by some window function such as Hanning, Blackman, etc. which is applied prior to the Fourier/DCT transform in order to avoid Gibbs oscillations in the processed patches. Such averaging may incidentally help in covering up artifacts in the restoration process, but more often will simply degrade the overall result, posing an upper limit to the size of the patches that can be used. In order to avoid such drawbacks, we propose a new methodology where the different estimates of any given sample are forced to be identical. We show that, together, these consensus constraints constitute a non-empty convex feasible set, provide a general formulation of the resulting constrained optimization problem which can be applied to a wide variety of signal restoration tasks, and propose an efficient algorithm for finding the corresponding solutions. Finally, we describe in detail the application of the proposed methodology to three different signal processing problems, in some cases surpassing the state of the art by a significant margin

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