Related papers: Sparse Convolution for Approximate Sparse Instance
In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II for reconstructing the input vector $\mathbf x\in\mathbb R^N$, $N=2^J$, with short support of length $m$ from its discrete…
Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
We consider the recovery of a nonnegative vector x from measurements y = Ax, where A is an m-by-n matrix whos entries are in {0, 1}. We establish that when A corresponds to the adjacency matrix of a bipartite graph with sufficient…
We consider the problem of sparse phase retrieval, where a $k$-sparse signal ${\bf x} \in {\mathbb R}^n \textrm{ (or } {\mathbb C}^n\textrm{)}$ is measured as ${\bf y} = |{\bf Ax}|,$ where ${\bf A} \in {\mathbb R}^{m \times n} \textrm{ (or…
The \Problem{knapsack} problem is a fundamental problem in combinatorial optimization. It has been studied extensively from theoretical as well as practical perspectives as it is one of the most well-known NP-hard problems. The goal is to…
Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically…
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…
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms to recover its nonzero coefficients and corresponding exponents. As an application, we adapt this interpolation algorithm to the problem of…
Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any $n$-dimensional vector that is $k$-sparse (with $k\ll n$) can be fully recovered using…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
Suffix tree (and the closely related suffix array) are fundamental structures capturing all substrings of a given text essentially by storing all its suffixes in the lexicographical order. In some applications, we work with a subset of $b$…
We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…
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…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
Convolutional sparse coding (CSC) is an important building block of many computer vision applications ranging from image and video compression to deep learning. We present two contributions to the state of the art in CSC. First, we…