A Development toward Matching Pursuit Algorithm Aims To Reduce Calculation Mass in the Process of the Compessed Sampling and Errors in the Signal Recovery Process
Main Article Content
Abstract
Many works related to the signal restoration from discrete samples that are unsatisfactory requirements of Nyquist's criteria has been deployed and published recently. There were many algorithms to solve this issue, such as CoSaMP and the matching pursuit. This article presents a developed algorithm which is based on the matching pursuit algorithm to recover multi-dimensional architectures. This development is permissible to reduce the calculation mass in several cases along with a number of dedicated conditions when sampling signal compression. Simultaneously, the article will demonstrate this algorithm also makes reduce the occurred error at each step in the signal recovery process by using the mathematical method.
Keywords
Signal restoration, Matching pursuit, Compressed sampling
Article Details
References
[1] S. Mallat and Z. Zhang. Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process., 41(12):3397-3415, (1993).
[2] D. Needell and J. A. Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied Comput. Harmon. Anal., 26:301-321, (2008).
[3] C. C. Johnson, A. Jalali, and P. Ravikumar. High-dimensional sparse inverse covariance estimation using greedy methods. In Proc. 15th Inter Conf. Artic. Intell. Statist. (AISTAT), La Palma, Canary Islands, (2012).
[4] Ngoc Minh Nguyen, Nam Nguyen, An Iterative Greedy Algorithm for Sparsity-Constrained Optimization, Tạp chí nghiên cứu KH&CN quân sự, số 40 (2015), tr. 109-117.
[5] M. A. Davenport, D. Needell, and M. B. Wakin. Signal space cosamp for sparse recovery with redundant dictionaries. Preprint at http://arxiv.org/abs/1208.0353, (2012).
[6] S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu. A unied framework for high- dimensional analysis of M-estimators with decomposable regularizers. Stat. Scien., 27(4):, (2012) 538-557.
[7] K. Lee and Y. Bresler. ADMIRA: Atomic decomposition for minimum rank approximation. IEEE Trans. Inf. Theory, 56(9), (2010) 4402-4416.
[8] A. Agarwal, S. Negahban, and M. J. Wainwright. Fast global convergence of gradient methods for high-dimensional statistical recovery. Ann. Statist., 40(5):, (2012) 2452-2482
[2] D. Needell and J. A. Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied Comput. Harmon. Anal., 26:301-321, (2008).
[3] C. C. Johnson, A. Jalali, and P. Ravikumar. High-dimensional sparse inverse covariance estimation using greedy methods. In Proc. 15th Inter Conf. Artic. Intell. Statist. (AISTAT), La Palma, Canary Islands, (2012).
[4] Ngoc Minh Nguyen, Nam Nguyen, An Iterative Greedy Algorithm for Sparsity-Constrained Optimization, Tạp chí nghiên cứu KH&CN quân sự, số 40 (2015), tr. 109-117.
[5] M. A. Davenport, D. Needell, and M. B. Wakin. Signal space cosamp for sparse recovery with redundant dictionaries. Preprint at http://arxiv.org/abs/1208.0353, (2012).
[6] S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu. A unied framework for high- dimensional analysis of M-estimators with decomposable regularizers. Stat. Scien., 27(4):, (2012) 538-557.
[7] K. Lee and Y. Bresler. ADMIRA: Atomic decomposition for minimum rank approximation. IEEE Trans. Inf. Theory, 56(9), (2010) 4402-4416.
[8] A. Agarwal, S. Negahban, and M. J. Wainwright. Fast global convergence of gradient methods for high-dimensional statistical recovery. Ann. Statist., 40(5):, (2012) 2452-2482