IEEE Trans Image Process - A fast majorize-minimize algorithm for the recovery of sparse and low-rank matrices.

Tópicos

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Resumo

We introduce a novel algorithm to recover sparse and low-rank matrices from noisy and undersampled measurements. We pose the reconstruction as an optimization problem, where we minimize a linear combination of data consistency error, nonconvex spectral penalty, and nonconvex sparsity penalty. We majorize the nondifferentiable spectral and sparsity penalties in the criterion by quadratic expressions to realize an iterative three-step alternating minimization scheme. Since each of these steps can be evaluated either analytically or using fast schemes, we obtain a computationally efficient algorithm. We demonstrate the utility of the algorithm in the context of dynamic magnetic resonance imaging (MRI) reconstruction from sub-Nyquist sampled measurements. The results show a significant improvement in signal-to-noise ratio and image quality compared with classical dynamic imaging algorithms. We expect the proposed scheme to be useful in a range of applications including video restoration and multidimensional MRI.

Resumo Limpo

introduc novel algorithm recov spars lowrank matric noisi undersampl measur pose reconstruct optim problem minim linear combin data consist error nonconvex spectral penalti nonconvex sparsiti penalti major nondifferenti spectral sparsiti penalti criterion quadrat express realiz iter threestep altern minim scheme sinc step can evalu either analyt use fast scheme obtain comput effici algorithm demonstr util algorithm context dynam magnet reson imag mri reconstruct subnyquist sampl measur result show signific improv signaltonois ratio imag qualiti compar classic dynam imag algorithm expect propos scheme use rang applic includ video restor multidimension mri

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