Related papers: Iterative Thresholding for Demixing Structured Sup…
Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…
In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can…
Nonlinear hyperspectral unmixing has recently received considerable attention, as linear mixture models do not lead to an acceptable resolution in some problems. In fact, most nonlinear unmixing methods are designed by assuming specific…
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…
Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns.…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…
Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…
We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear…
We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such…
Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters.…
We study the efficient learnability of high-dimensional Gaussian mixtures in the outlier-robust setting, where a small constant fraction of the data is adversarially corrupted. We resolve the polynomial learnability of this problem when the…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Medical imaging involves high-dimensional data, yet their acquisition is obtained for limited samples. Multivariate predictive models have become popular in the last decades to fit some external variables from imaging data, and standard…