Abstract
In order to improve the accuracy and range for application of signal reconstruction, a new measurement matrix optimization method is proposed based on the Gram matrix. The new method can reduce the mutual coherence between the measurement matrix and the sparse transform matrix. Numerical experiments verify the success of the optimized method. Compared with the original Gaussian random matrix and other optimized measurement matrices, the performance and stability of our proposed have a slight increase.
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References
Donoho, D.L., Elad, M., Temlyakov, V.N.: Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theor. 52(1), 6–18 (2006)
Candes, E.J., Romberg, J.K., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theor. 52(2), 489–509 (2006)
Candes, E.J., Romberg, J.K., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)
Candes, E.J.: The restricted isometry property and its implications for compressed sensing. ComptesRendusMatheMatique 346(9), 589–592 (2008)
Baraniuk, R., Davenport, M., Devore, R., et al.: A simple proof of the restricted isometry property for random matrices. Constr. Approximation 28(3), 253–263 (2008)
Xu, J., Pi, Y., Cao, Z.: Optimized projection matrix for compressive sensing. EURASIP J. Adv. Sig. Process. 2010(1), 560349 (2010)
Elad, M.: Optimized projections for compressed sensing. IEEE Trans. Sig. Process. 55(12), 5695–5702 (2007)
Rui-zhen, Z.H.A.O., Zhou, Q.I.N., Shao-hai, Hu: An optimization method for measurement matrix based on eigenvalue decomposition. Sig. Process. 28(5), 653–658 (2012)
Duarte-Carvajalino, J.M., Sapiro, G.: Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization. IEEE Trans. Image Process. 18(7), 1395–1408 (2009)
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© 2016 Springer Science+Business Media Singapore
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Bian, S., Xu, Z., Zhang, S. (2016). A Construction Algorithm of Measurement Matrix with Low Coherence for Compressed Sensing. In: Tan, T., et al. Advances in Image and Graphics Technologies. IGTA 2016. Communications in Computer and Information Science, vol 634. Springer, Singapore. https://doi.org/10.1007/978-981-10-2260-9_18
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DOI: https://doi.org/10.1007/978-981-10-2260-9_18
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