Proximal Gradient-Based Loop Unrolling with Interscale Thresholding

This work proposes an image restoration technique by introducing an interscale thresholding with a structured convolutional dictionary into a loop unrolled network based on the proximal gradient descent (PGD) method. A non-separable oversampled lapped transforms (NSOLT) in tree structure is adopted as the dictionary, where the interscale linear expansion of thresholds (LET) is applied as a Gaussian denoiser using the plug-and-play technique. The design parameters of the dictionary and thresholding function are made trainable, and image restoration systems are designed with the deep learning approach. Through the simulation of denoising and single image super-resolution (SISR), it is confirmed that the proposed method gives a high-performance feed-forward image restoration process with few design parameters.