Publication

A Projected Gradient Algorithm for Image Restoration Under Hessian Matrix-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis
2012
Conference Papers

Abstract

We have recently introduced a class of non-quadratic Hessian-based regularizers as a higher-order extension of the total variation (TV) functional. These regularizers retain some of the most favorable properties of TV while they can effectively deal with the staircase effect that is commonly met in TV-based reconstructions. In this work we propose a novel gradient-based algorithm for the efficient minimization of these functionals under convex constraints. Furthermore, we validate the overall proposed regularization framework for the problem of image deblurring under additive Gaussian noise.

Official source

https://infoscience.epfl.ch/entities/publication/762d9be5-ea13-48c3-ad69-f3e752f4c97b

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Michaël Unser, Stamatios Lefkimmiatis
2012
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/762d9be5-ea13-48c3-ad69-f3e752f4c97b

About this result

Related concepts (13)

Additive white Gaussian noise

Additive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics: Additive because it is added to any noise that might be intrinsic to the information system. White refers to the idea that it has uniform power spectral density across the frequency band for the information system. It is an analogy to the color white which may be realized by uniform emissions at all frequencies in the visible spectrum.

Gaussian noise

In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed. The probability density function of a Gaussian random variable is given by: where represents the grey level, the mean grey value and its standard deviation.

Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

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