Distributed Sampling of Signals Linked by Sparse Filtering: Theory and Applications

被引:27
作者
Hormati, Ali [1 ]
Roy, Olivier [1 ]
Lu, Yue M. [1 ]
Vetterli, Martin [1 ,2 ]
机构
[1] Ecole Polytech Fed Lausanne, Sch Comp & Commun Sci, CH-1015 Lausanne, Switzerland
[2] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA
基金
瑞士国家科学基金会;
关键词
Annihilating filter; compressed sensing; compressive sampling; distributed sampling; finite rate of innovation; iterative denoising; sparse reconstruction; Yule-Walker system;
D O I
10.1109/TSP.2009.2034908
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
We study the distributed sampling and centralized reconstruction of two correlated signals, modeled as the input and output of an unknown sparse filtering operation. This is akin to a Slepian-Wolf setup, but in the sampling rather than the lossless compression case. Two different scenarios are considered: In the case of universal reconstruction, we look for a sensing and recovery mechanism that works for all possible signals, whereas in what we call almost sure reconstruction, we allow to have a small set (with measure zero) of unrecoverable signals. We derive achievability bounds on the number of samples needed for both scenarios. Our results show that, only in the almost sure setup can we effectively exploit the signal correlations to achieve effective gains in sampling efficiency. In addition to the above theoretical analysis, we propose an efficient and robust distributed sampling and reconstruction algorithm based on annihilating filters. We evaluate the performance of our method in one synthetic scenario, and two practical applications, including the distributed audio sampling in binaural hearing aids and the efficient estimation of room impulse responses. The numerical results confirm the effectiveness and robustness of the proposed algorithm in both synthetic and practical setups.
引用
收藏
页码:1095 / 1109
页数:15
相关论文
共 33 条
  • [1] ALGAZI VR, 2001, P IEEE WASPAA OCT, V100, P99
  • [2] IMAGE METHOD FOR EFFICIENTLY SIMULATING SMALL-ROOM ACOUSTICS
    ALLEN, JB
    BERKLEY, DA
    [J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1979, 65 (04) : 943 - 950
  • [3] Bajwa W., 2006, Information Processing in Sensor Networks, P134
  • [4] Compressed channel sensing
    Bajwa, Waheed U.
    Haupt, Jarvis
    Raz, Gil
    Nowak, Robert
    [J]. 2008 42ND ANNUAL CONFERENCE ON INFORMATION SCIENCES AND SYSTEMS, VOLS 1-3, 2008, : 5 - +
  • [5] Baron D., 2006, ECE0612 RIC U EL COM
  • [6] BERGER T, 1977, P LECT NOTES PRESENT
  • [7] Blauert J., 1997, Spatial hearing: the psychophysics of human sound localization
  • [8] Sparse sampling of signal innovations
    Blu, Thierry
    Dragotti, Pier-Luigi
    Vetterli, Martin
    Marziliano, Pina
    Coulot, Lionel
    [J]. IEEE SIGNAL PROCESSING MAGAZINE, 2008, 25 (02) : 31 - 40
  • [9] SIGNAL ENHANCEMENT - A COMPOSITE PROPERTY MAPPING ALGORITHM
    CADZOW, JA
    [J]. IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING, 1988, 36 (01): : 49 - 62
  • [10] Robust uncertainty principles:: Exact signal reconstruction from highly incomplete frequency information
    Candès, EJ
    Romberg, J
    Tao, T
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (02) : 489 - 509