Related papers: Learnable Descent Algorithm for Nonsmooth Nonconve…

We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric…

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the…

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…

Most existing non-blind restoration methods are based on the assumption that a precise degradation model is known. As the degradation process can only be partially known or inaccurately modeled, images may not be well restored. Rain streak…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures…

As an integral component of blind image deblurring, non-blind deconvolution removes image blur with a given blur kernel, which is essential but difficult due to the ill-posed nature of the inverse problem. The predominant approach is based…

We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal…

Image deconvolution is still to be a challenging ill-posed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and…

This paper presents a new variational inference framework for image restoration and a convolutional neural network (CNN) structure that can solve the restoration problems described by the proposed framework. Earlier CNN-based image…

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…

This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…