Elements of information theory
Elements of information theory
Ten lectures on wavelets
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Nonlinear approximation of random functions
SIAM Journal on Applied Mathematics
Applied numerical linear algebra
Applied numerical linear algebra
Source Coding Theory
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Atomic Decomposition by Basis Pursuit
SIAM Review
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 1)-Volume 1 - Volume 1
A sparse signal reconstruction perspective for source localization with sensor arrays
IEEE Transactions on Signal Processing - Part II
Filtering random noise from deterministic signals via datacompression
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms
IEEE Transactions on Information Theory
Data compression and harmonic analysis
IEEE Transactions on Information Theory
On denoising and best signal representation
IEEE Transactions on Information Theory
A generalized uncertainty principle and sparse representation in pairs of bases
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Designing structured tight frames via an alternating projection method
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Adaptive wavelet thresholding for image denoising and compression
IEEE Transactions on Image Processing
Complexity-regularized image denoising
IEEE Transactions on Image Processing
Very low bit-rate video coding based on matching pursuits
IEEE Transactions on Circuits and Systems for Video Technology
Video compression using matching pursuits
IEEE Transactions on Circuits and Systems for Video Technology
Foundations and Trends in Signal Processing
A plurality of sparse representations is better than the sparsest one alone
IEEE Transactions on Information Theory
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting
IEEE Transactions on Information Theory
Necessary and sufficient conditions for sparsity pattern recovery
IEEE Transactions on Information Theory
Shannon-theoretic limits on noisy compressive sampling
IEEE Transactions on Information Theory
Information-theoretic limits on sparse signal recovery: dense versus sparse measurement matrices
IEEE Transactions on Information Theory
Information theoretic bounds for compressed sensing
IEEE Transactions on Information Theory
Performance analysis for sparse support recovery
IEEE Transactions on Information Theory
SIAM Journal on Scientific Computing
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If a signal x is known to have a sparse representation with respect to a frame, it can be estimated from a noise-corrupted observation y by finding the best sparse approximation to y. Removing noise in this manner depends on the frame efficiently representing the signal while it inefficiently represents the noise. The mean-squared error (MSE) of this denoising scheme and the probability that the estimate has the same sparsity pattern as the original signal are analyzed. First an MSE bound that depends on a new bound on approximating a Gaussian signal as a linear combination of elements of an overcomplete dictionary is given. Further analyses are for dictionaries generated randomly according to a spherically-symmetric distribution and signals expressible with single dictionary elements. Easily-computed approximations for the probability of selecting the correct dictionary element and the MSE are given. Asymptotic expressions reveal a critical input signal-to-noise ratio for signal recovery.