Related papers: Solving Inverse Problems with Piecewise Linear Est…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
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…
We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in…
A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity…
We study the inverse problem of estimating a field $u$ from data comprising a finite set of nonlinear functionals of $u$, subject to additive noise; we denote this observed data by $y$. Our interest is in the reconstruction of piecewise…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved non convex…
In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an l1-regularized least squares cost function. This result can also be derived by employing a…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…
Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…
We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so…