On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
Comparing measures of sparsity
IEEE Transactions on Information Theory
Efficient and robust compressed sensing using optimized expander graphs
IEEE Transactions on Information Theory
Bit precision analysis for compressed sensing
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Shifting inequality and recovery of sparse signals
IEEE Transactions on Signal Processing
An application of compressive sensing for image fusion
Proceedings of the ACM International Conference on Image and Video Retrieval
Shannon-theoretic limits on noisy compressive sampling
IEEE Transactions on Information Theory
| Hi-index | 35.87 |
We consider approximations of signals by the elements of a frame in a complex vector space of dimension N and formulate both the noiseless and the noisy sparse representation problems. The noiseless representation problem is to find sparse representations of a signal r given that such representations exist. In this case, we explicitly construct a frame, referred to as the Vandermonde frame, for which the noiseless sparse representation problem can be solved uniquely using O(N2) operations, as long as the number of non-zero coefficients in the sparse representation of r is isinN for some 0 les isin les 0.5. It is known that isin les 0.5 cannot be relaxed without violating uniqueness. The noisy sparse representation problem is to find sparse representations of a signal r satisfying a distortion criterion. In this case, we establish a lower bound on the tradeoff between the sparsity of the representation, the underlying distortion and the redundancy of any given frame.