Exploiting the Stochastic Gradient Descent Algorithm for Spatially Varying Deconvolution

Spatially varying degradation is related to real-world problems, such medical, astronomical, underwater or metalens imaging, neutron radiography, motion blur, optical remote sensing, etc. However, usually, spatially invariant blur is used as a proxy due to its relative computational simplicity w.r.t. the original problem. A spatially-variant PSF (point spread function) can be approxi-mated by a finite set of spatially weighted convolutions. While such structure limits a direct use of the (Fourier) Convolution theorem, the associated forward model can indeed be exploited by iterative optimizers, such ADMM or FISTA, or by model-aware DL (deep learning) networks; these solutions still need large computational resources. In this paper we present a novel stochastic algorithm to solve the spatially varying deconvolution problem. Unlike other published stochastic deconvolution methods, which may be interpreted as a form of random walk, ours is based on manipulating the forward model to show that its gradient can be cast as a sum of independent functions, thus allowing a direct exploitation of the SGD (stochastic gradient descent). We also provide computational evidence (our code is publicly available) to support our theoretical analysis.