相关论文: Type I and Type II Bayesian Methods for Sparse Sig…

Motivated by re-weighted $\ell_1$ approaches for sparse recovery, we propose a lifted $\ell_1$ (LL1) regularization which is a generalized form of several popular regularizations in the literature. By exploring such connections, we discover…

In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…

$\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity (the size of the support set), under which with high probability a sparse signal…

The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…

Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and…

Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same…

We consider high-dimensional distribution estimation through autoregressive networks. By combining the concepts of sparsity, mixtures and parameter sharing we obtain a simple model which is fast to train and which achieves state-of-the-art…

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…

In this paper we present the SPICE approach for sparse parameter estimation in a framework that unifies it with other hyperparameter-free methods, namely LIKES, SLIM and IAA. Specifically, we show how the latter methods can be interpreted…

Adaptive thresholding methods have proved to yield high SNRs and fast convergence in finding the solution to the Compressed Sensing (CS) problems. Recently, it was observed that the robustness of a class of iterative sparse recovery…

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the…

We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

The Type-I and Type-II censoring schemes are the most prominent and commonly used censoring schemes in practice. In this work, a mixture of Type-I and Type- II censoring schemes, named the Type I-Type II mixture censoring scheme, has been…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

The iterations of many first-order algorithms, when applied to minimizing common regularized regression functions, often resemble neural network layers with pre-specified weights. This observation has prompted the development of…

We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…