Atomic Decomposition by Basis Pursuit
SIAM Review
On the stability of the basis pursuit in the presence of noise
Signal Processing - Sparse approximations in signal and image processing
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Further results on stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Harmonic decomposition of audio signals with matching pursuit
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Matching Pursuit With Block Incoherent Dictionaries
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Designing structured tight frames via an alternating projection method
IEEE Transactions on Information Theory
Recovery of exact sparse representations in the presence of bounded noise
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Improved stability conditions of BOGA for noisy block-sparse signals
Signal Processing
Signal denoising with average sampling
Digital Signal Processing
Block-sparse recovery via redundant block OMP
Signal Processing
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Recently, block-sparse signals, whose nonzero coefficients appearing in blocks, have received much attention. A corresponding block-based orthogonal greedy algorithm (OGA) was proved by Eldar to successfully recover ideal noiseless block-sparse signals under a certain condition on block-coherence. In this paper, the stability problem of block OGA used to recover the noisy block-sparse signals is studied and the corresponding approximation bounds are derived. The theoretical bounds presented in this paper are more general and are proven to include those reported by Donoho and Tseng. Numerical experimental results are presented to support the validity and correctness of theoretical derivation. The simulation results also show that in the noisy case, the block OGA can be proved to achieve better reconstruction performance than the OGA when the conventional sparse signals are represented in block-sparse forms.