Plug-and-play inertial forward–backward algorithm for Poisson image deconvolution

Poisson image deconvolution remains an ill-posed research problem consisting of a nonquadratic data-fidelity term and an implicit regularization function. Recently, the plug-and-play (PnP) framework has provided a new method to reformulate the regularizer model to incorporate efficient denoisers. We develop a PnP inertial forward–backward approach (PnP_IFB) for Poisson noise reconstruction. The key advantages over the conventional alternating direction method of multipliers (ADMM)-based scheme are circumventing the matrix inversion operation and requiring less parameter tuning. The scheme can achieve a numerical convergence rate that is comparable to other acceleration strategies such as the fast iterative shrinkage-thresholding algorithm, but it does not depress the reconstruction quality. Moreover, this characteristic acceleration remains efficient when dealing with some nonconvex regularizers. Then, we demonstrate its effectiveness against other state-of-the-art approaches with respect to their deconvolution performance using synthetic images, and the experimental results prove the superiority of the method when using appropriate denoisers.