Uncertainty principles and signal recovery
SIAM Journal on Applied Mathematics
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Generalized gradient adaptive step sizes for stochastic gradient adaptive filters
ICASSP '95 Proceedings of the Acoustics, Speech, and Signal Processing, 1995. on International Conference - Volume 02
IEEE Transactions on Image Processing
Parametric dictionary design for sparse coding
IEEE Transactions on Signal Processing
A stochastic gradient adaptive filter with gradient adaptive stepsize
IEEE Transactions on Signal Processing
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Optimized Projections for Compressed Sensing
IEEE Transactions on Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Designing structured tight frames via an alternating projection method
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Fast Solution of -Norm Minimization Problems When the Solution May Be Sparse
IEEE Transactions on Information Theory
A Robust and Efficient Cross-Layer Optimal Design in Wireless Sensor Networks
Wireless Personal Communications: An International Journal
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In this paper the problem of optimization of the measurement matrix in compressive (also called compressed) sensing framework is addressed. In compressed sensing a measurement matrix that has a small coherence with the sparsifying dictionary (or basis) is of interest. Random measurement matrices have been used so far since they present small coherence with almost any sparsifying dictionary. However, it has been recently shown that optimizing the measurement matrix toward decreasing the coherence is possible and can improve the performance. Based on this conclusion, we propose here an alternating minimization approach for this purpose which is a variant of Grassmannian frame design modified by a gradient-based technique. The objective is to optimize an initially random measurement matrix to a matrix which presents a smaller coherence than the initial one. We established several experiments to measure the performance of the proposed method and compare it with those of the existing approaches. The results are encouraging and indicate improved reconstruction quality, when utilizing the proposed method.