Speeding up scaled gradient projection methods using deep neural networks for inverse problems in image processing

Conventional optimization based methods have utilized forward models with image priors to solve inverse problems in image processing. Recently, deep neural networks (DNN) have been investigated to significantly improve the image quality of the solution for inverse problems. Most DNN based inverse problems have focused on using data-driven image priors with massive amount of data. However, these methods often do not inherit nice properties of conventional approaches using theoretically well-grounded optimization algorithms such as monotone, global convergence. Here we investigate another possibility of using DNN for inverse problems in image processing. We propose methods to use DNNs to seamlessly speed up convergence rates of conventional optimization based methods. Our DNN-incorporated scaled gradient projection methods, without breaking theoretical properties, significantly improved convergence speed over state-of-the-art conventional optimization methods such as ISTA or FISTA in practice for inverse problems such as image inpainting, compressive image recovery with partial Fourier samples, image deblurring, and medical image reconstruction with sparse-view projections.