Deep BCD-Net Using Identical Encoding-Decoding CNN Structures for Iterative Image Recovery

Using learned convolutional operators for iterative signal/image recovery is a growing trend in computational imaging [1]-[6] due to its outperforming signal recovery performances over conventional non-trained regularizers (e.g., sparsity promoting regularizers) [4]-[6]. The iterative image recovery approaches using a learned convolutional operator or convolutional neural network (CNN) closely relate to challenging (nonconvex) block optimization. The authors in [4]-[6] proposed a fast and convergence-guaranteed block proximal gradient method using a majorizer to quickly and stably recover images with the aforementioned image recovery approaches. Nonetheless, the corresponding iterative algorithm needs several hundreds of iterations to converge, detracting from its practical use. By unfolding iterative signal recovery algorithms, there exist several works in combining neural network approaches into them [7]-[14]. By optimizing image mapping networks-- consisting of encoding and decoding kernels, thresholding operators, etc.--at each iteration (or layer), the methods moderate the aforementioned convergence issue, aiming to give "best" signal estimates at each layer.