Related papers: $\ell^1$ penalty for ill-posed inverse problems

Sparsification of neural networks is one of the effective complexity reduction methods to improve efficiency and generalizability. We consider the problem of learning a one hidden layer convolutional neural network with ReLU activation…

In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…

We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on {\em blind} calibration, using measures performed on a few…

In compressed sensing, the l0-norm minimization of sparse signal reconstruction is NP-hard. Recent work shows that compared with the best convex relaxation (l1-norm), nonconvex penalties can better approximate the l0-norm and can…

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…

Inverse Reinforcement Learning (IRL) is the problem of finding a reward function which describes observed/known expert behavior. The IRL setting is remarkably useful for automated control, in situations where the reward function is…

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to…

We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals…

We study the problem of recovering a block-sparse signal from under-sampled observations. The non-zero values of such signals appear in few blocks, and their recovery is often accomplished using a $\ell_{1,2}$ optimization problem. In…

In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell_1$ norm…

We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic…

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a…

We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an encoder-decoder network by including an $\ell^1$-penalty.…

This paper presents an error analysis of classical and learned Tikhonov regularization schemes for inverse problems. We first demonstrate, both theoretically and numerically, that using a fixed regularization parameter across varying noise…

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…

In this paper, we consider the minimization of a Tikhonov functional with an $\ell_1$ penalty for solving linear inverse problems with sparsity constraints. One of the many approaches used to solve this problem uses the Nemskii operator to…

The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood…

Blind deconvolution is a ubiquitous problem of recovering two unknown signals from their convolution. Unfortunately, this is an ill-posed problem in general. This paper focuses on the {\em short and sparse} blind deconvolution problem,…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…