IEEE Transactions on Image Processing
Compressed and privacy-sensitive sparse regression
IEEE Transactions on Information Theory
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
A sparsity detection framework for on-off random access channels
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
A neural network pruning approach based on compressive sampling
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Necessary and sufficient conditions for sparsity pattern recovery
IEEE Transactions on Information Theory
Hash-based identification of sparse image tampering
IEEE Transactions on Image Processing
Relaxed conditions for sparse signal recovery with general concave priors
IEEE Transactions on Signal Processing
Compressed sensing and source separation
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Image representation by compressive sensing for visual sensor networks
Journal of Visual Communication and Image Representation
Dequantizing compressed sensing with non-Gaussian constraints
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
IEEE Transactions on Audio, Speech, and Language Processing
IEEE Transactions on Signal Processing
Average case analysis of multichannel sparse recovery using convex relaxation
IEEE Transactions on Information Theory
Image super-resolution via sparse representation
IEEE Transactions on Image Processing
Randomization of data acquisition and l1-optimization (recognition with compression)
Automation and Remote Control
IEEE Transactions on Signal Processing
Image super-resolution based on multi-space sparse representation
ICIMCS '10 Proceedings of the Second International Conference on Internet Multimedia Computing and Service
Compressive sensing of underground structures using GPR
Digital Signal Processing
Sparse Legendre expansions via l1-minimization
Journal of Approximation Theory
Compressed sampling for heart rate monitoring
Computer Methods and Programs in Biomedicine
Journal of Approximation Theory
Dictionary learning based impulse noise removal via L1-L1 minimization
Signal Processing
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This paper extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants. Thus, signals that are sparse with respect to the dictionary can be recovered via basis pursuit (BP) from a small number of random measurements. Further, thresholding is investigated as recovery algorithm for compressed sensing, and conditions are provided that guarantee reconstruction with high probability. The different schemes are compared by numerical experiments.