Related papers: Sublinear Time, Measurement-Optimal, Sparse Recove…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $\mu$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise. This problem serves as a…
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…
In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
The goal of the trace reconstruction problem is to recover a string $x\in\{0,1\}^n$ given many independent {\em traces} of $x$, where a trace is a subsequence obtained from deleting bits of $x$ independently with some given probability…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $x\in\mathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,\ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1…
We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…
Much of the existing literature in sparse recovery is concerned with the following question: given a sparsity pattern and a corresponding regularizer, derive conditions on the dictionary under which exact recovery is possible. In this…
We consider the problem of recovering a function over the space of permutations (or, the symmetric group) over $n$ elements from given partial information; the partial information we consider is related to the group theoretic Fourier…
We give a proof of the conjecture of Nelson and Nguyen [FOCS 2013] on the optimal dimension and sparsity of oblivious subspace embeddings, up to sub-polylogarithmic factors: For any $n\geq d$ and $\epsilon\geq d^{-O(1)}$, there is a random…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \lambda xx^\top$ with $W$ drawn from…
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…
In this paper, we study the problem of online sparse linear regression (OSLR) where the algorithms are restricted to accessing only $k$ out of $d$ attributes per instance for prediction, which was proved to be NP-hard. Previous work gave…
In this work, we propose an algorithm for solving exact sparse linear regression problems over a network in a distributed manner. Particularly, we consider the problem where data is stored among different computers or agents that seek to…
We study the $\ell_0$-Low Rank Approximation Problem, where the goal is, given an $m \times n$ matrix $A$, to output a rank-$k$ matrix $A'$ for which $\|A'-A\|_0$ is minimized. Here, for a matrix $B$, $\|B\|_0$ denotes the number of its…