On the stability of the basis pursuit in the presence of noise
Signal Processing - Sparse approximations in signal and image processing
Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution
Signal Processing - Sparse approximations in signal and image processing
Extensions of compressed sensing
Signal Processing - Sparse approximations in signal and image processing
Denoising by sparse approximation: error bounds based on rate-distortion theory
EURASIP Journal on Applied Signal Processing
Sparse representations are most likely to be the sparsest possible
EURASIP Journal on Applied Signal Processing
Hybrid video coding based on bidimensional matching pursuit
EURASIP Journal on Applied Signal Processing
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Online prediction of time series data with kernels
IEEE Transactions on Signal Processing
Dictionary learning for sparse approximations with the majorization method
IEEE Transactions on Signal Processing
High-resolution radar via compressed sensing
IEEE Transactions on Signal Processing
Further results on stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Improved adaptive wavelet threshold for image denoising
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Uncertainty relations for shift-invariant analog signals
IEEE Transactions on Information Theory
Fast sparse representation based on smoothed lo norm
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
Block-sparse signals: uncertainty relations and efficient recovery
IEEE Transactions on Signal Processing
Restricted Eigenvalue Properties for Correlated Gaussian Designs
The Journal of Machine Learning Research
Two conditions for equivalence of 0-norm solution and 1-norm solution in sparse representation
IEEE Transactions on Neural Networks
A Sparse Learning Machine for High-Dimensional Data with Application to Microarray Gene Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Sparse representations and approximation theory
Journal of Approximation Theory
Improved stability conditions of BOGA for noisy block-sparse signals
Signal Processing
A compressed sensing approach for MR tissue contrast synthesis
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
Sparse representations and sphere decoding for array signal processing
Digital Signal Processing
Analysis of performance of palmprint matching with enforced sparsity
Digital Signal Processing
Efficient cross-correlation via sparse representation in sensor networks
Proceedings of the 11th international conference on Information Processing in Sensor Networks
Some uniqueness results in sparse convolutive source separation
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Strengthening hash families and compressive sensing
Journal of Discrete Algorithms
Saliency-guided compressive sensing approach to efficient laser range measurement
Journal of Visual Communication and Image Representation
Multi-resolutive sparse approximations of d-dimensional data
Computer Vision and Image Understanding
Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis
Journal of Mathematical Imaging and Vision
Hi-index | 755.03 |
An elementary proof of a basic uncertainty principle concerning pairs of representations of RN vectors in different orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the improvement of an important result due to Donoho and Huo (2001) concerning the replacement of the l0 optimization problem by a linear programming (LP) minimization when searching for the unique sparse representation.