IEEE Trans Image Process - Deconvolving images with unknown boundaries using the alternating direction method of multipliers.

Tópicos

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Resumo

The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for inverse problems, namely, image deconvolution and reconstruction under non-smooth convex regularization. ADMM achieves state-of-the-art speed by adopting a divide and conquer strategy, wherein a hard problem is split into simpler, efficiently solvable sub-problems (e.g., using fast Fourier or wavelet transforms, or simple proximity operators). In deconvolution, one of these sub-problems involves a matrix inversion (i.e., solving a linear system), which can be done efficiently (in the discrete Fourier domain) if the observation operator is circulant, i.e., under periodic boundary conditions. This paper extends ADMM-based image deconvolution to the more realistic scenario of unknown boundary, where the observation operator is modeled as the composition of a convolution (with arbitrary boundary conditions) with a spatial mask that keeps only pixels that do not depend on the unknown boundary. The proposed approach also handles, at no extra cost, problems that combine the recovery of missing pixels (i.e., inpainting) with deconvolution. We show that the resulting algorithms inherit the convergence guarantees of ADMM and illustrate its performance on non-periodic deblurring (with and without inpainting of interior pixels) under total-variation and frame-based regularization.

Resumo Limpo

altern direct method multipli admm recent spark interest flexibl effici optim tool invers problem name imag deconvolut reconstruct nonsmooth convex regular admm achiev stateoftheart speed adopt divid conquer strategi wherein hard problem split simpler effici solvabl subproblem eg use fast fourier wavelet transform simpl proxim oper deconvolut one subproblem involv matrix invers ie solv linear system can done effici discret fourier domain observ oper circul ie period boundari condit paper extend admmbas imag deconvolut realist scenario unknown boundari observ oper model composit convolut arbitrari boundari condit spatial mask keep pixel depend unknown boundari propos approach also handl extra cost problem combin recoveri miss pixel ie inpaint deconvolut show result algorithm inherit converg guarante admm illustr perform nonperiod deblur without inpaint interior pixel totalvari framebas regular

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