Denoising by sparse approximation: error bounds based on rate-distortion theory
EURASIP Journal on Applied Signal Processing
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Frame Construction and a Universal Distortion Bound for Sparse Representations
IEEE Transactions on Signal Processing
Additive successive refinement
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact characterization of the optimal distortion is given as a function of the dictionary size exponent and the number of reference signals for the linear representation. Roughly speaking, every signal is sparse if the dictionary size is exponentially large, no matter how small the exponent is. Furthermore, an iterative method similar to matching pursuit that successively finds the best reference signal at each stage gives asymptotically optimal representations. This method is essentially equivalent to successive refinement for multiple descriptions and provides a simple alternative proof of the successive refinability of white Gaussian sources.