Related papers: Improved Algorithms for Adaptive Compressed Sensin…
This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
In the theory of compressed sensing (CS), the sparsity $\|x\|_0$ of the unknown signal $\mathbf{x} \in \mathcal{R}^n$ is of prime importance and the focus of reconstruction algorithms has mainly been either $\|x\|_0$ or its convex…
It is known that certain structures of the signal in addition to the standard notion of sparsity (called structured sparsity) can improve the sample complexity in several compressive sensing applications. Recently, Hegde et al. proposed a…
We introduce a \emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\ldots,A_m' \in \mathbb{R}^n$ that estimate unknown signals $A_1,\ldots,A_m \in \mathbb{R}^n$ using a few linear measurements,…
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h in H? In the sparse recovery literature, where x is…
In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in a given orthonormal basis. The signals are modeled by…
An approximate sparse recovery system in ell_1 norm formally consists of parameters N, k, epsilon an m-by-N measurement matrix, Phi, and a decoding algorithm, D. Given a vector, x, where x_k denotes the optimal k-term approximation to x,…
In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
The central idea of compressed sensing is to exploit the fact that most signals of interest are sparse in some domain and use this to reduce the number of measurements to encode. However, if the sparsity of the input signal is not precisely…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
Based on $\alpha$-stable random projections with small $\alpha$, we develop a simple algorithm for compressed sensing (sparse signal recovery) by utilizing only the signs (i.e., 1-bit) of the measurements. Using only 1-bit information of…
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…
The theory of Compressed Sensing (CS) asserts that an unknown signal $x\in\mathbb{R}^p$ can be accurately recovered from an underdetermined set of $n$ linear measurements with $n\ll p$, provided that $x$ is sufficiently sparse. However, in…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…