Related papers: An Improved Sample Complexity for Rank-1 Matrix Se…
The paper explores the problem of \emph{spectral compressed sensing}, which aims to recover a spectrally sparse signal from a small random subset of its $n$ time domain samples. The signal of interest is assumed to be a superposition of $r$…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…
This paper considers the problem of recovering an unknown sparse p\times p matrix X from an m\times m matrix Y=AXB^T, where A and B are known m \times p matrices with m << p. The main result shows that there exist constructions of the…
Measuring the similarity of the internal representations of deep neural networks is an important and challenging problem. Model stitching has been proposed as a possible approach, where two half-networks are connected by mapping the output…
We explore the impact of coarse quantization on matrix completion in the extreme scenario of dithered one-bit sensing, where the matrix entries are compared with time-varying threshold levels. In particular, instead of observing a subset of…
Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…
This article proposes a novel algorithm for solving mismatch problem in compressed sensing. Its core is to transform mismatch problem into matched by constructing a new measurement matrix to match measurement value under unknown measurement…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…
Sketching techniques have gained popularity in numerical linear algebra to accelerate the solution of least squares problems. The so-called $\varepsilon$-subspace embedding property of a sketching matrix $S$ has been largely used to…
Numerical computing of the rank of a matrix is a fundamental problem in scientific computation. The datasets generated by the internet often correspond to the analysis of high-dimensional sparse matrices. Notwithstanding recent advances in…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…
The combination of the sparse sampling and the low-rank structured matrix reconstruction has shown promising performance, enabling a significant reduction of the magnetic resonance imaging data acquisition time. However, the low-rank…
Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…
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…
The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…
In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…