Robust Sparsity Updating Subspace Pursuit with Sparsity Estimation for Compressive Sensing Reconstruction

簡易檢索 / 詳目顯示

回結果列表

研究生：	張力 Chang, Li
論文名稱：	Robust Sparsity Updating Subspace Pursuit with Sparsity Estimation for Compressive Sensing Reconstruction
指導教授：	吳仁銘 Wu, Jen-Ming
口試委員:	蔡育仁 Yuh-Ren Tsai 洪樂文 Yao-Win Peter Hong 吳仁銘 Jen-Ming Wu
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2014
畢業學年度：	103
語文別：	英文
論文頁數：	41
中文關鍵詞：	壓縮感知、稀疏訊號重建、貪婪追蹤、子空間追蹤
外文關鍵詞：	compressive sensing, sparse reconstruction, greedy pursuit, subspace pursuit
相關次數：	點閱：2 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

和傳統取樣技術相比，壓縮感知能利用更少的點數去壓縮訊號。而一個重要的問題便是如何去重建原始的訊號。有許多著名的演算法像是基追蹤、匹配追蹤、正交匹配追蹤、壓縮採樣匹配追蹤。而這些演算法都需要事先知道訊號的稀疏度。這篇論文我們提出一個基於子空間追蹤不斷更新的演算法。我們提出的論文命名為稀疏度更新子空間追蹤。這篇論文主要的貢獻在於處理稀疏度未知的問題。而這個特性讓此演算法可以處理許多實際上稀疏度未知的應用。而此演算法不單處理稀疏度未知的問題，在稀疏度已知的情況下表現也好於許多演算法。

Compared with traditional data acquisition, compressive sensing can reconstruct signal from far fewer samples than the traditional method. One of the critical problem is to reconstruct the original signal from the compressed measurement. There are many popular reconstruction algorithms such as Basis pursuit(BP), Matching Pursuit(MP), Orthogonal Matching Pursuit(OMP), Compressive Sampling Matching Pursuit(CoSaMP); Despite their good performance, these algorithms require the sparse level as a prior information for reconstruction. This thesis demonstrates a recursively updating function based on Subspace Pursuit algorithm, which is a famous algorithm for signal recovery. Our proposed algorithm is called Sparsity Updating Subspace Pursuit(SUSP). The main contribution is that the proposed SUSP can solves the sparse signal problem when the sparsity is not available. This property makes the algorithm to solve many practical compressive sensing problem when the sparse level, the number of non-zero elements of a signal is not given. While SUSP can deal with unknown sparsity problem, results show that it outperforms many existing famous greedy algorithm when the sparsity is pre-known.

Abstract i
Contents ii
Introduction 1
Signal Recovery Algorithms for Reconstruction 5
1 Basis Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Greedy Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Matching Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Orthogonal Matching Pursuit . . . . . . . . . . . . . . . . . . . . . . 8
3 Backtracking Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Subspace Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Compressive Sampling Matching Pursuit . . . . . . . . . . . . . . . . 15
3.3 Sparsity Adaptive Matching Pursuit . . . . . . . . . . . . . . . . . . 16
Proposed Sparsity Updating Subspace Pursuit for Reconstruction 20
1 Proposed Sparsity Updating Subspace Pursuit Algorithm . . . . . . . . . . . 20
1.1 Sparsity Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2 Correlation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3 Stage Change Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.4 Tail Biting Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Procedure of SUSP Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1 SUSP Algorithm for Reconstruction with known Sparsity . . . . . . . 26
2.2 SUSP Algorithm for Reconstruction with Unknown Sparsity . . . . . 28
Simulation 31
1 Performance of SUSP when Sparsity-Preknown . . . . . . . . . . . . . . . . 31
1.1 Comparison of SP, OMP and SUSP vs. the signal sparsity . . . . . . 31
1.2 Comparison of SP, OMP and SUSP vs. the number of measurement . 32
1.3 Simulations for Gaussian Sparse Signals . . . . . . . . . . . . . . . . 33
1.4 Comparison of Compression Ratio . . . . . . . . . . . . . . . . . . . . 34
1.5 Performance of SUSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.6 Robust Signal Recovery from Noisy Data . . . . . . . . . . . . . . . . 37
2 Performance of SUSP when Sparsity-Unknown . . . . . . . . . . . . . . . . . 38
2.1 Performance of Sparsity Estimation . . . . . . . . . . . . . . . . . . . 39
2.2 Performance of SUSP vs. Tail Biting Rules . . . . . . . . . . . . . . . 39
2.3 Comparison of Existing Algorithm Dealing with Unknown Sparsity Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Conclusions 44
                                

[1] E. Candes and M. Wakin, "An introduction to compressive sampling," IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21-30, 2008.
[2] D. Donoho, "Compressed sensing," IEEE Trans. on Information Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
[3] S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Journal on Scientic Computing, vol. 20, pp. 33-61, Jan. 1998.
[4] S. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries.," IEEE Trans. Sign. Process., vol. 41, no. 12, pp. 3397-3415, 1993.
[5] J. Tropp and A. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. on Information Theory, vol. 53, no. 12, pp. 4655-4666, 2007.
[6] D. Needell and J. Tropp, "Cosamp: Iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, vol. 26, no. 3, pp. 301-321, 2009.
[7] W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. on Information Theory, vol. 55, no. 5, pp. 2230-2249, 2009.
[8] J. Kahn, J. Komls, and E. Szemerdi, "On the probability that a random 1-matrix is
singular," Journal of the American Mathematical Society, vol. 8, no. 1, pp. pp. 223-240, 1995.
[9] E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: exact signal reconstruction
from highly incomplete frequency information," Information Theory, IEEE Transactions on, vol. 52, pp. 489-509, Feb 2006.
[10] R. Baraniuk, M. Davenport, R. Devore, and M. Wakin, "A simple proof of the restricted isometry property for random matrices," Constr. Approx, vol. 2008, 2007.
[11] B. Rao and K. Kreutz-Delgado, "An ane scaling methodology for best basis selection," Signal Processing, IEEE Transactions on, vol. 47, pp. 187-200, Jan 1999.
[12] R. A. DeVore, "Nonlinear approximation," ACTA NUMERICA, vol. 7, pp. 51-150, 1998.
[13] E. Candes and T. Tao, "Decoding by linear programming," Information Theory, IEEE Transactions on, vol. 51, pp. 4203-4215, Dec 2005.
[14] M. Rudelson and R. Vershynin, "Sparse reconstruction by convex relaxation: Fourier and gaussian measurements," in Information Sciences and Systems, 2006 40th Annual
Conference on, pp. 207-212, March 2006.
[15] Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming. Society for Industrial and Applied Mathematics, 1994.
[16] E. Candes and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies," IEEE Transactions on Information Theory, vol. 52, no. 12,
pp. 5406-5425, 2006.
[17] Y. Pati, R. Rezaiifar, and P. S. Krishnaprasad, "Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition," in Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers, 1993., pp. 40-44 vol.1, 1993.
[18] J. Tropp, "Greed is good: algorithmic results for sparse approximation," Information Theory, IEEE Transactions on, vol. 50, pp. 2231-2242, Oct 2004.
[19] M. Davenport and M. Wakin, "Analysis of orthogonal matching pursuit using the restricted isometry property," Information Theory, IEEE Transactions on, vol. 56,
pp. 4395-4401, Sept 2010.
[20] D. Donoho, Y. Tsaig, I. Drori, and J.-L. Starck, "Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit," IEEE Trans. on Information Theory, vol. 58, no. 2, pp. 1094-1121, 2012.
[21] Z. Tian, "Compressed wideband sensing in cooperative cognitive radio networks," in IEEE Global Telecommunications Conference, 2008., pp. 1-5, 2008.
[22] D. Baby and S. Pillai, "Ordered orthogonal matching pursuit," in 2012 National Conference on Communications (NCC), pp. 1-5, 2012.
[23] T. Do, L. Gan, N. Nguyen, and T. Tran, "Sparsity adaptive matching pursuit algorithm for practical compressed sensing," in Signals, Systems and Computers, 2008 42nd Asilomar Conference on, pp. 581-587, Oct 2008.
[24] H. Huang and A. Makur, "Backtracking-based matching pursuit method for sparse signal reconstruction," Signal Processing Letters, IEEE, vol. 18, pp. 391-394, July 2011.
[25] M. Figueiredo, R. Nowak, and S. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," Selected Topics in Signal Processing, IEEE Journal of, vol. 1, pp. 586-597, Dec 2007.
[26] D. L. Donoho, "For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution," Comm. Pure Appl. Math, vol. 59, pp. 797-829, 2004.
[27] P. Gill, W. Murray, and M. Saunders, "Snopt: An sqp algorithm for large-scale constrained optimization," SIAM Review, vol. 47, no. 1, pp. 99-131, 2005.

全文公開日期本全文未授權公開 (校內網路)
全文公開日期本全文未授權公開 (校外網路)

簡易檢索 / 詳目顯示

相關論文