Multi-Coset Sparse Imaging Arrays

We develop an efficient structured sparse antenna array architecture for coherent imaging of sparse but otherwise unknown scenes. In this architecture, the array elements are configured in a periodic nonuniform pattern that can be viewed as the superposition of multiple sparse uniform subarrays. For such structure, we develop an efficient pattern design procedure using co-array analysis, and we describe robust and efficient algorithms implementing the required associated array processing, which comprise scene support recovery, followed by image reconstruction. In addition, we develop a practical method for detecting reconstruction failures when the scene density exceeds the level for which the array was designed, so that false images are not produced. As a demonstration of its viability, the architecture is used to reconstruct a simulated natural scene.

[1]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[2]  Yoram Bresler,et al.  Subspace-augmented MUSIC for joint sparse recovery with any rank , 2010, 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop.

[3]  Robert J. Mailloux,et al.  Phased Array Antenna Handbook , 1993 .

[4]  Jong Chul Ye,et al.  Compressive MUSIC: Revisiting the Link Between Compressive Sensing and Array Signal Processing , 2012, IEEE Transactions on Information Theory.

[5]  T..  Minimum-Redundancy Linear Arrays , 2022 .

[6]  G. Bienvenu,et al.  Optimality of high resolution array processing using the eigensystem approach , 1983 .

[7]  Geert Leus,et al.  Compressive covariance sampling , 2013, 2013 Information Theory and Applications Workshop (ITA).

[8]  P. P. Vaidyanathan,et al.  Sparse Sensing With Co-Prime Samplers and Arrays , 2011, IEEE Transactions on Signal Processing.

[9]  S. DeGraaf,et al.  Improving the resolution of bearing in passive sonar arrays by eigenvalue analysis , 1981 .

[10]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[11]  P. Vaidyanathan,et al.  Coprime sampling and the music algorithm , 2011, 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE).

[12]  Yonina C. Eldar,et al.  Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals , 2007, IEEE Transactions on Signal Processing.

[13]  Minh N. Do,et al.  A Theory for Sampling Signals from a Union of Subspaces , 2022 .

[14]  Ping Feng,et al.  Spectrum-blind minimum-rate sampling and reconstruction of multiband signals , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[15]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[16]  Harry L. Van Trees,et al.  Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory , 2002 .

[17]  Nuria González Prelcic,et al.  Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[18]  Gregory W. Wornell,et al.  Finite multi-coset sampling and sparse arrays , 2011, 2011 Information Theory and Applications Workshop.

[19]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[20]  P. P. Vaidyanathan,et al.  Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom , 2010, IEEE Transactions on Signal Processing.

[21]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[22]  Yonina C. Eldar,et al.  Rank Awareness in Joint Sparse Recovery , 2010, IEEE Transactions on Information Theory.

[23]  J. Tropp.  Algorithms for simultaneous sparse approximation. Part II: Convex relaxation , 2006, Signal Process..

[24]  S.M. Duffy,et al.  Design considerations and results for an overlapped subarray radar antenna , 2005, 2005 IEEE Aerospace Conference.

[25]  Joel A. Tropp,et al.  Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit , 2006, Signal Process..

[26]  Geert Leus,et al.  Direction of arrival estimation using sparse ruler array design , 2012, 2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).

[27]  Harry L. Van Trees,et al.  Optimum Array Processing , 2002 .

[28]  Scott Kirkpatrick,et al.  Optimization by Simmulated Annealing , 1983, Sci..

[29]  Jie Chen,et al.  Theoretical Results on Sparse Representations of Multiple-Measurement Vectors , 2006, IEEE Transactions on Signal Processing.

[30]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.