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Can we recover a signal f ∈ RN from a small number of linear measurements? A series of recent papers developed a collection of results showing that it is surprisingly possible to reconstruct certain t...
Detecting Highly Oscillatory Signals by Chirplet Path Pursuit
Signal Detection Nonparametric Testing Likelihood Ratios Adaptivity Chirps Chirplets Time-Frequency Analysis Gravitational Waves Graphs Shortest Path in a Graph Dynamic Programming
2015/6/17
This paper considers the problem of detecting nonstationary phenomena, and chirps in particular, from very noisy data. Chirps are waveforms of the very general form A(t) exp(iλ ϕ(t)), where λ is ...
“People Hearing Without Listening”:An Introduction To Compressive Sampling
People Hearing Without Listening Compressive Sampling
2015/6/17
The conventional approach to sampling signals or images follows the celebrated Shannon sampling theorem: the sampling rate must be at least twice the maximum frequency present in the signal (the so-ca...
The Restricted Isometry Property and Its Implications for Compressed Sensing
Restricted Isometry Property Compressed Sensing
2015/6/17
It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with noise. This technique known as “compresse...
We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods f...
In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a highdimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently,...
Compressed Sensing with Coherent and Redundant Dictionaries
Compressed Sensing Coherent and Redundant Dictionaries
2015/6/17
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary...
Templates for Convex Cone Problems with Applications to Sparse Signal Recovery
Optimal first-order methods Nesterov’s accelerated descent algorithms proximal algorithms conic duality smoothing by conjugation the Dantzig selector the LASSO nuclearnorm minimization
2015/6/17
This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as ...
Global Testing under Sparse Alternatives: ANOVA, Multiple Comparisons and the Higher Criticism
Detecting a sparse signal analysis of variance higher criticism minimax detection incoherence random matrices suprema of Gaussian processes compressive sensing
2015/6/17
Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of varianc...
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error...
PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
Exact and Stable Signal Recovery Magnitude Measurements Convex Programming
2015/6/17
Suppose we wish to recover a signal x ∈ Cn from m intensity measurements of the form |hx, zii|2, i = 1, 2, . . . , m; that is, from data in which phase information is missing. We prove that if the vec...
On the Fundamental Limits of Adaptive Sensing
sparse signal estimation adaptive sensing compressed sensing support recovery information bounds hypothesis tests
2015/6/17
Suppose we can sequentially acquire arbitrary linear measurements of an n-dimensional vector x resulting in the linear model y = Ax + z, where z represents measurement noise. If the signal is known to...
Compressive Fluorescence Microscopy for Biological and Hyperspectral Imaging
compressive sensing sparse images fluorescence microscopy biological imaging
2015/6/17
The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed...
A Compressed Sensing Parameter Extraction Platform for Radar Pulse Signal Acquisition
Compressed sensing Indium-Phosphide Parameter Estimation Random-Modulation Pre-Integration
2015/6/17
In this paper we present a complete (hardware/software) sub-Nyquist rate (×13) wideband signal acquisition chain capable of acquiring radar pulse parameters in an instantaneous bandwidth spanning 100 ...
A Non-Uniform Sampler for Wideband Spectrally-Sparse Environments
Non-uniform sampler compressed sensing wideband ADC indium-phosphide HBT sample-and-hold
2015/6/17
We present a wide bandwidth, compressed sensing based non-uniform sampling (NUS) system with a custom sampleand-hold chip designed to take advantage of a low average sampling rate. By sampling signals...