Related papers: Functional Nonlinear Sparse Models
This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an…
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…
This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic…
We study the problem of detection of a high-dimensional signal function in the white Gaussian noise model. As well as a smoothness assumption on the signal function, we assume an additive sparse condition on the latter. The detection…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…
In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that…