Related papers: Nearly Optimal Sparse Fourier Transform

This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…

Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…

Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…

This paper is concerned with the fast computation of Fourier integral operators of the general form $\int_{\R^d} e^{2\pi\i \Phi(x,k)} f(k) d k$, where $k$ is a frequency variable, $\Phi(x,k)$ is a phase function obeying a standard…

Despite their success, kernel methods suffer from a massive computational cost in practice. In this paper, in lieu of commonly used kernel expansion with respect to $N$ inputs, we develop a novel optimal design maximizing the entropy among…

Compressive phase retrieval is a popular variant of the standard compressive sensing problem in which the measurements only contain magnitude information. In this paper, motivated by recent advances in deep generative models, we provide…

Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an…

In this note, we provide details of the $k$-dimensional Weisfeiler-Leman Algorithm and its analysis from Immerman-Lander (1990). In particular, we present an optimized version of the algorithm that runs in time $O(n^{k+1}\log n)$, where $k$…

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…

In this paper we consider the following sparse recovery problem. We have query access to a vector $\vx \in \R^N$ such that $\vhx = \vF \vx$ is $k$-sparse (or nearly $k$-sparse) for some orthogonal transform $\vF$. The goal is to output an…

In this paper we study the problem of minimizing a submodular function $f : 2^V \rightarrow \mathbb{R}$ that is guaranteed to have a $k$-sparse minimizer. We give a deterministic algorithm that computes an additive $\epsilon$-approximate…

We study the stable recovery of complex $k$-sparse signals from as few phaseless measurements as possible. The main result is to show that one can employ $\ell_1$ minimization to stably recover complex $k$-sparse signals from $m\geq O(k\log…

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of F with high probability for constraint densities m/n<(1-eps_k)2^k\ln(k)/k,…

We consider the selection problem on a completely connected network of $n$ processors with no shared memory. Each processor initially holds a given numeric item of $b$ bits allowed to send a message of $\max ( b, \lg n )$ bits to another…

We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random…

A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing optimal non Cartesian Fourier sampling patterns is a difficult…

We consider sparse variants of the classical Learning Parities with random Noise (LPN) problem. Our main contribution is a new algorithmic framework that provides learning algorithms against low-noise for both Learning Sparse Parities…

We present the first efficient averaging sampler that achieves asymptotically optimal randomness complexity and near-optimal sample complexity. For any $\delta < \varepsilon$ and any constant $\alpha > 0$, our sampler uses $m + O(\log (1 /…

In the Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into an interval graph, i.e., a graph admitting an intersection model of intervals on a line. Motivated by…