Robust Blind Image Reconstruction from Low Resolution Corrupted Data Using Proximal Deep Networks

Image restoration problems are typically ill-posed, requiring the design of suitable priors. These priors are typically hand-designed and are fully instantiated throughout the process, and these hand-designed priors might not contain good approximations of the real data. We introduce a novel framework called proximal splitting network (PSN) for
handling inverse problems related to image restoration based on elements from the half quadratic splitting method and proximal operators of the prior term. Modeling the proximal operator of the prior term as a convolutional network, we defined an implicit prior to the image space as a function class during training. We assume the point spread function (PSF) is known for PSN. However, in blind image restoration, the PSF is completely unknown. To remedy this, we develop another approach where the PSF is not known. Recovering images typically requires estimates of the PSF. We present a method called
DR-Net, which does not require any such estimate and is further able to invert the effects of the blurring in blind image recovery tasks. These image recovery problems typically
have two terms, the data fidelity term (for faithful reconstruction) and the image prior (for realistic-looking reconstructions). We use the Douglas-Rachford iterations to solve these problems since it is a more generally applicable optimization procedure than methods such as the proximal gradient descent algorithm. Two proximal operators originate from these iterations, one for the data fidelity term and the second for the image prior. It is non-trivial to design a hand-crafted function to represent these proximal operators which
would work with real-world image distributions. We therefore approximate both theseproximal operators using deep networks. The last part of the thesis deals with face images
super-resolution, which is a special case of image reconstruction. We propose a novel neural network to recover face identity features. The proposed approach improves the performance of face recognition systems on low resolutions. Here, the neural network aims to minimize the identity difference between the recovered and the original images, where other approaches try to minimize the element-wise (pixel-by-pixel) difference. All the proposed methods are shown to be efficient and accurate for image restoration tasks.