Comparison of Reconstruction Algorithms for Sparse Signal Recovery from Noisy Measurement
Compressive sensing is a technique that can reconstruct sparse signals under Nyquist rate. This study is about comparison of widely used sparse signal reconstruction algorithms under noisy measurements. Three algorithms, Orthogonal Matching Pursuit, Compressive Sensing Matching Pursuit and Primal Dual Interior Point method are used to reconstruct sparse signal from noisy measurement and performance results are compared. Firstly, a sparse signal is sampled under Nyquist rate and observation vector is obtained. After that, white Gaussian noise is added to this observation vector. Then, sparse reconstruction algorithms are employed to reconstruct the original signal from noisy measurement. These algorithms are tested for various measurement number and sparsity levels. Test conditions are same for all algorithms. Finally some performance metrics results related to reconstructed signal are obtained. These performance metrics are mean squared error, correlation of the reconstructed signal and original signal, reconstruction time of the algorithms and iteration numbers. According to these metrics, when sparsity level is very smaller than measurement number, Orthogonal Matching Pursuit has better results than others. However, when sparsity level is increased and close to measurement number, Primal Dual Interior Point method has better performance than others in terms of reconstruction a sparse signal from noisy measurement.
 E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489–509, 2006.
 E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Math., vol. 346, no. 9–10, pp. 589–592, 2008.
 Y. Arjoune, N. Kaabouch, and H. El Ghazi, “Compressive sensing: Performance comparison of sparse recovery algorithms,” in (Ccwc), 2017.
 E. J. Candes and M. B. Wakin, “An Introduction To Compressive Sampling,” IEEE Signal Process. Mag., vol. 25, no. 2, pp. 21–30, 2008.
 R. Baraniuk, “Compressive Sensing [Lecture Notes],” IEEE Signal Process. Mag., vol. 24, no. 4, pp. 118–121, Jul. 2007.
 S. Çelik, M. Başaran, S. Erküçük, and A. Çırpan, "Seyrek işaret geri oluşturma için sıkıştırılmış algılama tabanlı algoritmaların karşılaştırılması". 2016 24th Signal Processing and Communication Application Conference, 16-19 May 2016, Zonguldak, Turkey. 2016
 K. Hayashi, M. Nagahara, and T. Tanaka, “A User’s Guide to Compressed Sensing for Communications Systems,” IEICE Trans. Commun., vol. E96.B, no. 3, pp. 685–712, 2013.
 E. J. Candes and T. Tao, “Decoding by Linear Programming,” 2005.
 S. Boyd and L. Vandenberghe, Convex Optimization, vol. 25, no. 3. 2010.
 J. a Tropp and A. C. Gilbert, “Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit,” IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4655–4666, Dec. 2007.
 D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal., vol. 26, no. 3, pp. 301–321, 2009.
 M. E. Erkoç, N., Karaboğa, "Comparison of L1 Minimization and Greedy Algorithms for Recovering Sparse Frequency Domain Signals", International Workshop, Mathematical Methods in Engineering, MME-2017, Ankara, Turkey, 27-29 Apr. 2017, pp.67-67.