A Novel Dictionaries Preconditioning Algorithm for Compressive Sensing

Abstract:

A Novel dictionaries preconditioning algorithm for compressive sensing is proposed in this paper. This algorithm uses alternating projection method to construct sensing and measurement dictionaries with low mutual and cumulative cross coherence. The coherence property of the constructed dictionaries is superior to those constructed by Schnass’ method and by Dictionaries Construction algorithm. The complexity and computation amount is lower than Dictionaries Construction algorithm. The constructed dictionaries improve the performance of OMP and SP algorithms.

• Periodical: Applied Mechanics and Materials (Volumes 130-134)
• Pages: 183-187
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.130-134.183
• Online since: October 2011
• Authors: Chao Zhang, Yi He, Bo Li
• Keywords: Alternating Projection, Compressive Sensing (CS), Sensing Dictionary

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[10] B. Li, J. Li, Y. Shen. Dictionaries Construction using Alternating Projection Method in Compressive Sensing. Submitted to IEEE Signal Proceeding Letters. Fig. 2. (a) Comparison of mutual cross coherence of dictionaries constructed via DC algorithm and DP algorithm. The number of rows is 128 and the number of columns ranges from 132 to 256; (b) Frobenius distance of type Gram matrix and the set of ideal Gram matrix at each iteration. The size of dictionaries is 128×256. Fig. 3. Comparison of OMP performance using Gaussian dictionaries, dictionaries constructed via Schnass' method, DC algorithm and DP algorithm. The size of dictionaries is 128×256. (a) The non-zeros components of signal are of unite magnitude; (b) The non-zeros components of signal follow standard Gaussian distribution. Fig. 4. Comparison of running time of DC algorithm and DP algorithm. The number of rows of dictionaries is 128 and the number of columns ranges from 132 to 256. (a) DP algorithm; (b) DC algorithm.