External Division of Two Bregman Proximity Operators for Poisson Inverse Problems
This work addresses Poisson inverse problems in signal processing and imaging, offering an incremental improvement over existing methods for sparse recovery.
The paper tackled the problem of recovering sparse vectors from linear models with Poisson noise by introducing an external-division operator to reduce bias from ℓ₁-norm regularization, achieving more stable convergence and significantly superior performance on synthetic data and image restoration compared to KL-based methods.
This paper presents a novel method for recovering sparse vectors from linear models corrupted by Poisson noise. The contribution is twofold. First, an operator defined via the external division of two Bregman proximity operators is introduced to promote sparse solutions while mitigating the estimation bias induced by classical $\ell_1$-norm regularization. This operator is then embedded into the already established NoLips algorithm, replacing the standard Bregman proximity operator in a plug-and-play manner. Second, the geometric structure of the proposed external-division operator is elucidated through two complementary reformulations, which provide clear interpretations in terms of the primal and dual spaces of the Poisson inverse problem. Numerical tests show that the proposed method exhibits more stable convergence behavior than conventional Kullback-Leibler (KL)-based approaches and achieves significantly superior performance on synthetic data and an image restoration problem.