Frames for compressed sensing using coherence

Subject Areas : Functional analysis

L. Gavruta ¹ , G. Zamani Eskandani ² , P. Gavruta ³

1 - Politehnica University of Timisoara, Department of Mathematics, Piata Victoriei no.2, 300006 Timisoara, Romania
2 - Faculty of Sciences, Department of Mathematics, University of Tabriz, Tabriz, Iran
3 - Politehnica University of Timisoara, Department of Mathematics, Piata Victoriei no.2, 300006 Timisoara, Romania

Received: 2014-12-10 Accepted : 2015-03-20 Published : 2015-04-01

Keywords:

References:

[1] R. Baraniuk, P. Steeghs, Compressive radar imaging, IEEE Radar Conference, Waltham, Massachusetts, April 2007.

[2] T. Cai, L. Wang, and G. Xu, Stable Recovery of Sparse Signals and an Oracle Inequality, IEEE Trans. Inf. Theory, 56(2010) 3516–3522.

[3] E. Candes, The restricted isometry property and its implications for compressed sensing, C. R. Acad. Sci. Paris, Ser. I 346 (2008) 589–592.

[4] E. Candes, M. Wakin, An introduction to Compressive Sampling, IEEE Signal Processing Magazine, 25(2)(2008) 21–30.

[5] E. Candes, T. Tao, Decoding by Linear Programming, IEEE Trans. Inform. Theory, 51(12)(2005) 4203–4215.

[6] E. Candes, J. Romberg, T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math. 59(2006) 1207–1223.

[7] S.S. Chen, D.L. Donoho, M.A. Saunders, Atomic decomposition by basis pursuit, SIAM J. Sci. Comput., 20(1)(1998) 33-61.

[8] O. Christensen, An Introduction to Frames and Riesz bases, Applied and Numerical Harmonic Analysis, Birkhauser, Boston, 2003.

[9] D. L. Donoho, Compressed sensing, IEEE Trans. Inform. Theory, 52(4)(2006) 1289-1306.

[10] D. L. Donoho and M. Elad, Optimally Sparse Representation in General (nonorthogonal) Dictionaries via L1 Minimization, the Proc. Nat. Aca. Sci., 100(2003) 2197–2202.

[11] M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, R. Baraniuk, Single-pixel imaging via compressive sampling, IEEE Signal Processing Magazine, 25(2)(2008) 83–91.

[12] M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer, 2010.

[13] M. Lustig, D.L. Donoho, J.M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging, Magnetic Resonance in Medicine, 58(6)(2007) 1182–1195.

[14] M. Lustig, D.L. Donoho, J.M. Santos, J.M. Pauly, Compressed sensing MRI, IEEE Signal Processing Magazine, 25(2)(2008) 72–82.

[15] S.G. Mallat, Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Trans. Signal Proc., 41(12)(1993) 3397-3415.

[16] L. Potter, P. Schniter, J. Ziniel, Sparse reconstruction for RADAR, SPIE Algorithms for Synthetic Aperture Radar Imagery XV, 2008.

[17] J.A. Tropp, Greed is good: Alogorithmic results for sparse approximation, IEEE Trans. Inform. Theory, 50(10)(2004) 2231–2242.

[18] L.R. Welch, Lower Bounds on the Maximum Cross Correlation of Signals, IEEE Trans. Inform. Theory, 20(1974) 397–399.