基于差值映射的压缩感知MUSIC算法

吕志丰; 雷宏

doi:10.11999/JEIT141542

基于差值映射的压缩感知MUSIC算法

doi: 10.11999/JEIT141542

吕志丰¹,
雷宏²

2.
(中国科学院电子学研究所北京 100190) ②(中国科学院大学北京 100049)

计量
- 文章访问数: 1394
- HTML全文浏览量: 148
- PDF下载量: 683
- 被引次数: 0
出版历程
- 收稿日期: 2014-12-04
- 修回日期: 2015-03-13
- 刊出日期: 2015-08-19

Compressive Sensing MUSIC Algorithm Based on Difference Map

Lü Zhi-feng¹,
Lei Hong²

2.
(Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China)

摘要

摘要: 多快拍(MMV)问题旨在恢复具有相同稀疏结构的多列信号。在传统阵列信号处理中MMV问题的求解通常采用多重信号分类(MUSIC)等确定性方法实现，但当快拍数不足或存在相干源时该类方法失效；而在压缩感知(CS)的概率求解模型下，即使信源相干也能得到恢复结果，但现有算法普遍性能不足。近期Kim等人的研究表明，将CS与MUSIC相结合可得到比二者更加优秀的性能和更为宽泛的使用条件，该方法被称作压缩感知 MUSIC或CS-MUSIC算法。作为一种投影型非凸优化算法，差值映射(DM)最早用于解决X射线晶体学中的相位恢复问题，并逐渐在其他非凸及压缩感知问题的求解中展示出优良性能。该文提出一种基于差值映射的CS-MUSIC算法，仿真结果表明该算法在MMV问题求解中十分有效，相比经典CS-MUSIC具有更高的恢复成功率。
- 压缩感知 /
- 多快拍问题 /
- 联合稀疏 /
- 多重信号分类 /
- 差值映射
Abstract: The Multiple Measurement Vectors (MMV) problem addresses the recovery of unknown input vectors which share the same sparse support. The Compressed Sensing (CS) has the capability of estimating the sparse support even in coherent cases, where the traditional array processing approaches like MUltiple SIgnal Classification (MUSIC) often fail. However, CS guarantees the accurate recovery in a probabilistic manner, and often shows inferior performance in cases where the traditional ways succeed. Recently, a novel compressive MUSIC (or CS-MUSIC) algorithm is proposed by Kim et al., in which both the advantages of CS and traditional MUSIC-like methods are combined together. As an iterative projecting algorithm, Difference Map (DM) is first used to solve the phase retrieval problem in crystallography. Recent results show that it has excellent performance in solving a wide variety of non-convex problems like compressed sensing. In this paper, a DM-based CS-MUSIC algorithm is proposed. Experiments show that the proposed algorithm is very effective in MMV problem solving and the success rate of CS-MUSIC is dramatically improved.
- Compressed Sensing (CS) /
- Multiple Measurement Vectors (MMV) problem /
- Joint sparsity /
- MUltiple SIgnal Classification (MUSIC) /
- Difference Map(DM)

HTML全文

参考文献(34)

Donoho D. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

Cades E, Romberg J, and Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

Fang L Y, Li S T, Ryan P, et al.. Fast acquisition and reconstruction of optical coherence tomography images via sparse representation[J]. IEEE Transactions on Medical Imaging, 2013, 32(11): 2034-2049.

Yang J, Thompson J, Huang X T, et al.. Segmented reconstruction for compressed sensing SAR imaging[J]. IEEE Transactions on Geoscience and Remote Sensing, 2013, 51(7): 4214-4225.

Friedland, S, Li Q, and Schonfeld D. Compressive sensing of sparse tensors[J]. IEEE Transactions on Image Processing, 2014, 23(10): 4438-4447.

Hawes M B and Liu W. Robust sparse antenna array design via compressive sensing[C]. IEEE International Conference on Digital Signal Processing, Nice, France, 2013: 1-5.

Northardt E T, Bilik I, and Abramovich Y I. Spatial compressive sensing for direction-of-arrival estimation with bias mitigation via expected likelihood[J]. IEEE Transactions on Signal Processing, 2013, 61(5): 1183-1195.

Nagahara M, Quevedo D E, and Ostergaard J. Sparse packetized predictive control for networked control over erasure channels[J]. IEEE Transactions on Automatic Control, 2014, 59(7): 1899-1905.

Krim H and Viberg M. Two decades of array signal processing research: the parametric approach[J]. IEEE Signal Processing Magazine, 1996, 13(4): 67-94.

Schmidt R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas ?and Propagation, 1986, 34(3): 276-280.

Kim J M, Lee O K, and Ye J C. Compressive MUSIC: revisiting the link between compressive sensing and array signal processing[J]. IEEE Transactions on Information Theory, 2012, 58(1): 278-301.

Lee K and Bresler Y. Subspace-augmented MUSIC for joint sparse recovery with any rank[C]. Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop, Jerusalem, Israel, 2010: 205-208.

Elser V. Phase retrieval by iterated projections[J]. Journal of the Optical Society of America A, 2003, 20(1): 40-55.

Elser V, Rankenburg I, and Thibault P. Searching with iterated maps[J]. Proceedings of the National Academy of Sciences, 2007, 104(2): 418-423.

Eldar Y C, Sidorenko P, Mixon D G, et al.. Sparse phase retrieval from short-time Fourier measurements[J]. IEEE Signal Processing Letters, 2015, 22(5): 638-642.

Shechtman Y, Beck A, and Eldar Y C. GESPAR: efficient phase retrieval of sparse signals[J]. IEEE Transactions on Signal Processing, 2014, 62(4): 928-938.

Qiu K and Dogandzic A. Nonnegative signal reconstruction from compressive samples via a difference map ECME algorithm[C]. Proceedings of the IEEE Statistical Signal Processing Workshop, Nice, France, 2011: 561-564.

Landecker W, Chartrand R, and DeDeo S. Robust compressed sensing and sparse coding with the difference map[C]. IEEE European Conference on Computer Vision, Zurich, Switzerland, 2014: 315-329.

Feng P. Universal minimum-rate sampling and spectrum-blind reconstruction for multiband signals[D]. [Ph.D. dissertation], University of Illinois, Urbana-Champaign, 1997.

Chen J and Huo X. Theoretical results on sparse representations of multiple measurement vectors[J]. IEEE Transactions on Signal Processing, 2006, 54(12): 4634-4643.

Tropp J A, Gilbert A C, and Strauss M J. Algorithms for simultaneous sparse approximation, Part I: Greedy pursuit[J]. Signal Processing, 2006, 86(3): 572-588.

Malioutov D, Cetin M, and Willsky A S. A sparse signal reconstruction perspective for source localization with sensor arrays[J]. IEEE Transactions on Signal Processing, 2005, 53(8): 3010-3022.

Tropp J A. Algorithms for simultaneous sparse approximation. Part II: Convex relaxation[J]. Signal Processing, 2006, 86(3): 589-602.

Wipf D P. Bayesian methods for finding sparse representations[D]. [Ph.D. dissertation], University of California, San Diego, 2006.

Mishali M and Eldar Y C. Reduce and boost: recovering arbitrary sets of jointly sparse vectors[J]. IEEE Transactions on Signal Processing, 2008, 56(10): 4692-4702.

Eldar Y C, Kuppinger P, and Bolcskei H. Compressed sensing of block-sparse signals: uncertainty relations and efficient recovery[J]. IEEE Transactions on Signal Processing, 2010, 58(6): 3042-3054.

Baraniuk R G, Cevher V, Duarte M F, et al.. Model-based compressive sensing[J]. IEEE Transactions on Information Theory, 2010, 56(4): 1982-2001.

Capon J. High-resolution frequency-wavenumber spectrum analysis[J]. Proceedings of the IEEE, 1969, 57(8): 1408-1418.

Roy R and Kailath T. ESPRIT-estimation of signal parameters via rotational invariance techniques[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1989, 37(7): 984-995.

Fienup J R. Phase retrieval algorithms: a comparison[J]. Applied Optics, 1982, 21(15): 2758-2769.

Bauschke H and Borwein J. On projection algorithms for solving convex feasibility problems[J]. SIAM Review, 1996, 38(3): 367-426.

Adiga A and Seelamantula C S. An alternating Lp-L2 projections algorithm (ALPA) for speech modeling using sparsity constraints[C]. IEEE International Conference on Digital Signal Processing, Hong Kong, China, 2014: 291-296.

Yan W, Wang Q, and Shen Y. Shrinkage-based alternating projection algorithm for efficient measurement matrix construction in compressive sensing[J]. IEEE Transactions on Instrumentation and Measurement, 2014, 63(5): 1073-1084.

Hesse R, Luke D R, and Neumann P. Alternating projections and Douglas-Rachford for sparse affine feasibility[J]. IEEE Transactions on Signal Processing, 2014, 62(18): 4868-4881.

施引文献

资源附件(0)

访问统计