Related papers: Iterative regularization for convex regularizers

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Regularisation is commonly used in iterative methods for solving imaging inverse problems. Many algorithms involve the evaluation of the proximal operator of the regularisation term in every iteration, leading to a significant computational…

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…

This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…

In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This regularizer is intended to promote solutions conforming to…

Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or…

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been recently shown that exact recovery is possible by…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive…

Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…