IEEE Trans Image Process - Poisson image reconstruction with Hessian Schatten-norm regularization.

Tópicos

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Resumo

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupted by Poisson noise. In this paper, we propose an efficient framework for Poisson image reconstruction, under a regularization approach, which depends on matrix-valued regularization operators. In particular, the employed regularizers involve the Hessian as the regularization operator and Schatten matrix norms as the potential functions. For the solution of the problem, we propose two optimization algorithms that are specifically tailored to the Poisson nature of the noise. These algorithms are based on an augmented-Lagrangian formulation of the problem and correspond to two variants of the alternating direction method of multipliers. Further, we derive a link that relates the proximal map of an l(p) norm with the proximal map of a Schatten matrix norm of order p. This link plays a key role in the development of one of the proposed algorithms. Finally, we provide experimental results on natural and biological images for the task of Poisson image deblurring and demonstrate the practical relevance and effectiveness of the proposed framework.

Resumo Limpo

poisson invers problem aris mani modern imag applic includ biomed astronom one main challeng obtain estim under imag set measur degrad linear oper corrupt poisson nois paper propos effici framework poisson imag reconstruct regular approach depend matrixvalu regular oper particular employ regular involv hessian regular oper schatten matrix norm potenti function solut problem propos two optim algorithm specif tailor poisson natur nois algorithm base augmentedlagrangian formul problem correspond two variant altern direct method multipli deriv link relat proxim map lp norm proxim map schatten matrix norm order p link play key role develop one propos algorithm final provid experiment result natur biolog imag task poisson imag deblur demonstr practic relev effect propos framework

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