相关论文: Solution of linear ill-posed problems using overco…

We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it…

Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for…

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…

Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers…

A new method is proposed in this paper to learn overcomplete dictionary from training data samples. Differing from the current methods that enforce similar sparsity constraint on each of the input samples, the proposed method attempts to…

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…

This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…

The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…

In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from…

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such…

This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov…

The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the…

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…

Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…

Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…