Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Image Denoising Via Learned Dictionaries and Sparse representation
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Exploiting Prior Knowledge in The Recovery of Signals from Noisy Random Projections
DCC '07 Proceedings of the 2007 Data Compression Conference
An affine scaling methodology for best basis selection
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Compressive sensing method for improved reconstruction of gradient-sparse magnetic resonance images
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Modified-CS: modifying compressive sensing for problems with partially known support
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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Iteratively reweighted least-squares (IRLS) algorithms have been successfully used in compressive sensing to reconstruct sparse signals from incomplete linear measurements taken in nonsparse domains. The underlying optimization problem corresponds to finding the vector that solves the lp minimization while explaining the measurements, and IRLS allows to easily control the used value of p, with effect on the number of required measurements. In this paper, we propose a weighting strategy in the reconstruction method based on IRLS in order to add prior information on the support of the sparse domain. Our simulation results show that the use of prior knowledge about positions of at least some of the nonzero coefficients in the sparse domain leads to a reduction in the number of linear measurements required for unambiguous reconstruction. This reduction occurs for all values of p, so that a further reduction can be achieved by decreasing p and using prior information. The proposed weighting scheme also reduces the computational complexity with respect to the IRLS with no prior information, both in terms of number of iterations and computation time.