Related papers: Learning a Sparse Representation of Barron Functio…
This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Traditional machine learning methods usually minimize a simple loss function to learn a predictive model, and then use a complex performance measure to measure the prediction performance. However, minimizing a simple loss function cannot…
One of the crucial tasks in many inference problems is the extraction of sparse information out of a given number of high-dimensional measurements. In machine learning, this is frequently achieved using, as a penality term, the $L_p$ norm…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
We present a novel method for the classification and reconstruction of time dependent, high-dimensional data using sparse measurements, and apply it to the flow around a cylinder. Assuming the data lies near a low dimensional manifold…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…
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…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…
Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision or biomedical imaging. One of the main challenges to perform this task is to design efficient numerical…
Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…
In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. Here, we discuss a sparse approximation method for computational time-reversal imaging. The method is formulated…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…