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What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…

Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…

In this study, we consider a variant of unlabelled sensing where the measurements are sparsely permuted, and additionally, a few correspondences are known. We present an estimator to solve for the unknown vector. We derive a theoretical…

Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee…

In this paper we study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support…

In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…

This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…

Regression uses supervised machine learning to find a model that combines several independent variables to predict a dependent variable based on ground truth (labeled) data, i.e., tuples of independent and dependent variables (labels).…

We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…

In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…

Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…

We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The…

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…

In compressed sensing, one wishes to acquire an approximately sparse high-dimensional signal $x\in\mathbb{R}^n$ via $m\ll n$ noisy linear measurements, then later approximately recover $x$ given only those measurement outcomes. Various…

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Compressed sensing is an image reconstruction technique to achieve high-quality results from limited amount of data. In order to achieve this, it utilizes prior knowledge about the samples that shall be reconstructed. Focusing on image…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that…

For finite samples with binary outcomes penalized logistic regression such as ridge logistic regression (RR) has the potential of achieving smaller mean squared errors (MSE) of coefficients and predictions than maximum likelihood…