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Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with…

Compressed sensing (CS) has been introduced to accelerate data acquisition in MR Imaging. However, CS-MRI methods suffer from detail loss with large acceleration and complicated parameter selection. To address the limitations of existing…

The purpose of these notes is to provide background on understanding the primal-dual algorithm of Chambolle and Pock [1] for imaging scientists. The presentation focuses on providing intuition and an algorithmic system that is amenable to…

This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual…

In this paper, we study design of deep neural networks for tasks of image restoration. We propose a novel style of residual connections dubbed "dual residual connection", which exploits the potential of paired operations, e.g., up- and…

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping…

Convolutional neural networks have been proven effective in a variety of image restoration tasks. Most state-of-the-art solutions, however, are trained using images with a single particular degradation level, and their performance…

A common approach to solve inverse imaging problems relies on finding a maximum a posteriori (MAP) estimate of the original unknown image, by solving a minimization problem. In thiscontext, iterative proximal algorithms are widely used,…

We propose a new type of efficient deep-unrolling networks for solving imaging inverse problems. Conventional deep-unrolling methods require full forward operator and its adjoint across each layer, and hence can be significantly more…

Most traditional algorithms for compressive sensing image reconstruction suffer from the intensive computation. Recently, deep learning-based reconstruction algorithms have been reported, which dramatically reduce the time complexity than…

We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such,…

The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…

Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem. Recently, deep neural networks have been applied to this problem with superior results, owing to the…

The feed-forward architectures of recently proposed deep super-resolution networks learn representations of low-resolution inputs, and the non-linear mapping from those to high-resolution output. However, this approach does not fully…

Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters,…

Deep neural networks (DNN) have achieved great success in image restoration. However, most DNN methods are designed as a black box, lacking transparency and interpretability. Although some methods are proposed to combine traditional…

Deep neural networks (DNNs) have shown very promising results for various image restoration (IR) tasks. However, the design of network architectures remains a major challenging for achieving further improvements. While most existing…

Deep residual networks (ResNets) have significantly pushed forward the state-of-the-art on image classification, increasing in performance as networks grow both deeper and wider. However, memory consumption becomes a bottleneck, as one…

The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo $2\pi$ observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by…

We study inertial versions of primal-dual proximal splitting, also known as the Chambolle--Pock method. Our starting point is the preconditioned proximal point formulation of this method. By adding correctors corresponding to the…