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Near Optimal Signal Recovery From Random Projections:Universal Encoding Strategies?
Random matrices singular values of random matrices signal recovery random projections concentration of measure sparsity trigonometric expansions uncertainty principle convex optimization duality in optimization linear programming
2015/6/17
Suppose we are given a vector f in a class F ⊂ RN, e.g. a class of digital signals or digital images. How many linear measurements do we need to make about f to be able to recover f to within pr...
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...
Stable Signal Recovery from Incomplete and Inaccurate Measurements
`1-minimization basis pursuit restricted orthonormality sparsity singular values of random matrices
2015/6/17
Suppose we wish to recover a vector x0 ∈ Rm (e.g. a digital signal or image) from incomplete and contaminated observations y = Ax0 + e; A is a n by m matrix with far fewer rows than columns (n m) an...
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 ...
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...
Signal Recovery in Unions of Subspaces with Applications to Compressive Imaging
Union of Subspaces Group Sparsity Convex Optimization Structured Sparsity Compressed Sensing
2012/11/22
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inac...
Multi-Sparse Signal Recovery for Compressive Sensing
Multi-Sparse Signal Recovery Compressive Sensing Information Theory
2012/6/19
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one do...
Exploiting Correlation in Sparse Signal Recovery Problems: Multiple Measurement Vectors, Block Sparsity, and Time-Varying Sparsity
Multiple Measurement Vectors Block Sparsity Time-Varying Sparsity
2011/6/16
A trend in compressed sensing (CS) is to exploit struc-
ture for improved reconstruction performance. In the
basic CS model (i.e. the single measurement vec-
tor model), exploiting the clustering s...
Sparse Signal Recovery with Temporally Correlated Source Vectors Using Sparse Bayesian Learning
Bayesian Learning Temporally Correlated Signal Recovery
2011/3/23
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorith...
Sparse Signal Recovery with Temporally Correlated Source Vectors Using Sparse Bayesian Learning
Signal Recovery Temporally Correlated Bayesian Learning
2011/3/22
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorith...
Templates for Convex Cone Problems with Applications to Sparse Signal Recovery
Optimal rst-order methods Nesterov's accelerated descent algorithms
2010/12/3
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 elds. The approach works as ...
A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery
compressed sensing best-first search A* search matching pursuit sparse representations sparse signal
2010/11/29
Compressed sensing is a recently developing area which is interested in reconstruction of sparse signals acquired in reduced dimensions. Acquiring the data with a small number of samples makes the rec...
Manifold-Based Signal Recovery and Parameter Estimation from Compressive Measurements
Manifolds dimensionality reduction random projections Compressive Sensing spar-sity signal recovery parameter estimation
2010/3/10
A field known as Compressive Sensing (CS) has recently emerged to help address the growing
challenges of capturing and processing high-dimensional signals and data sets. CS exploits the
surprising f...
Note on sparsity in signal recovery and in matrix identification
Sparse signal recovery compressed sensing Basis Pursuit time-frequency shifts
2008/11/10
We describe a connection between the identi cation problem for matrices with sparse representations in given matrix dictionaries and the problem of sparse signal recovery. This allows the application ...