Image Restoration by Deep Projected GSURE

Ill-posed inverse problems appear in many image processing applications, such as deblurring and super-resolution. In recent years, solutions that are based on deep Convolutional Neural Networks (CNNs) have shown great promise. Yet, most of these techniques, which train CNNs using external data, are restricted to the observation models that have been used in the training phase. A recent alternative that does not have this drawback relies on learning the target image using internal learning. One such prominent example is the Deep Image Prior (DIP) technique that trains a network directly on the input image with the least-squares loss. In this paper, we propose a new image restoration framework that is based on minimizing a loss function that includes a "projected-version" of the Generalized Stein Unbiased Risk Estimator (GSURE) and parameterization of the latent image by a CNN. We propose two ways to use our framework. In the first one, where no explicit prior is used, we show that the proposed approach outperforms other internal learning methods, such as DIP. In the second one, we show that our GSURE-based loss leads to improved performance when used within a plug-and-play priors scheme.

1. Introduction

Inverse problems appear in many image processing applications, where the reconstruction of an unknown latent image x ∈ ℝⁿ from its given corrupted version y ∈ ℝ^m is required. In many image-restoration tasks the observed image y can be expressed by the following linear model

$$\begin{equation*}{\mathbf{y}} = {\mathbf{Hx}} + {\mathbf{e}},\tag{1}\end{equation*}$$ where H ∈ ℝ^m×n is a measurement operator with m ≤ n, and is an additive white Gaussian noise. For example, when H is a blur operator, it is a deblurring problem, and when H is an anti-aliasing filtering followed by sub-sampling it is a super-resolution (SR) problem.