IEEE Trans Image Process - An iterative linear expansion of thresholds for l1-based image restoration.

Tópicos

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Resumo

This paper proposes a novel algorithmic framework to solve image restoration problems under sparsity assumptions. As usual, the reconstructed image is the minimum of an objective functional that consists of a data fidelity term and an l1 regularization. However, instead of estimating the reconstructed image that minimizes the objective functional directly, we focus on the restoration process that maps the degraded measurements to the reconstruction. Our idea amounts to parameterize the process as a linear combination of few elementary thresholding functions (LET) and to solve the linear weighting coefficients by minimizing the objective functional. It is then possible to update the thresholding functions and to iterate this process ( i-LET). The key advantage of such a linear parametrization is that the problem size reduces dramatically--each time we only need to solve an optimization problem over the dimension of the linear coefficients (typically less than 10) instead of the whole image dimension. With the elementary thresholding functions satisfying certain constraints, a global convergence of the iterated LET algorithm is guaranteed. Experiments on several test images over a wide range of noise levels and different types of convolution kernels clearly indicate that the proposed framework usually outperforms state-of-the-art algorithms in terms of both the CPU time and the number of iterations.

Resumo Limpo

paper propos novel algorithm framework solv imag restor problem sparsiti assumpt usual reconstruct imag minimum object function consist data fidel term l regular howev instead estim reconstruct imag minim object function direct focus restor process map degrad measur reconstruct idea amount parameter process linear combin elementari threshold function let solv linear weight coeffici minim object function possibl updat threshold function iter process ilet key advantag linear parametr problem size reduc dramaticallyeach time need solv optim problem dimens linear coeffici typic less instead whole imag dimens elementari threshold function satisfi certain constraint global converg iter let algorithm guarante experi sever test imag wide rang nois level differ type convolut kernel clear indic propos framework usual outperform stateoftheart algorithm term cpu time number iter

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