IEEE Trans Image Process - An iterative shrinkage approach to total-variation image restoration.

Tópicos

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Resumo

The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modeled by an ill-conditioned operator. In such a situation, the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some a priori information about its properties. Such a priori information--commonly referred to as simply priors--is essential for image restoration, rendering it stable and robust to noise. Moreover, using the priors makes the recovered images exhibit some plausible features of their original counterpart. Particularly, if the original image is known to be a piecewise smooth function, one of the standard priors used in this case is defined by the Rudin-Osher-Fatemi model, which results in total variation (TV) based image restoration. The current arsenal of algorithms for TV-based image restoration is vast. In this present paper, a different approach to the solution of the problem is proposed based upon the method of iterative shrinkage (aka iterated thresholding). In the proposed method, the TV-based image restoration is performed through a recursive application of two simple procedures, viz. linear filtering and soft thresholding. Therefore, the method can be identified as belonging to the group of first-order algorithms which are efficient in dealing with images of relatively large sizes. Another valuable feature of the proposed method consists in its working directly with the TV functional, rather then with its smoothed versions. Moreover, the method provides a single solution for both isotropic and anisotropic definitions of the TV functional, thereby establishing a useful connection between the two formulae. Finally, a number of standard examples of image deblurring are demonstrated, in which the proposed method can provide restoration results of superior quality as compared to the case of sparse-wavelet deconvolution.

Resumo Limpo

problem restor digit imag degrad measur play central role multitud practic import applic particular challeng instanc problem occur case degrad phenomenon model illcondit oper situat presenc nois make imposs recov valuabl approxim imag interest without use priori inform properti priori informationcommon refer simpli priorsi essenti imag restor render stabl robust nois moreov use prior make recov imag exhibit plausibl featur origin counterpart particular origin imag known piecewis smooth function one standard prior use case defin rudinosherfatemi model result total variat tv base imag restor current arsenal algorithm tvbase imag restor vast present paper differ approach solut problem propos base upon method iter shrinkag aka iter threshold propos method tvbase imag restor perform recurs applic two simpl procedur viz linear filter soft threshold therefor method can identifi belong group firstord algorithm effici deal imag relat larg size anoth valuabl featur propos method consist work direct tv function rather smooth version moreov method provid singl solut isotrop anisotrop definit tv function therebi establish use connect two formula final number standard exampl imag deblur demonstr propos method can provid restor result superior qualiti compar case sparsewavelet deconvolut

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