Reconstruction of multidimensional signals from irregular noisy samples

被引:10
作者
Nordio, Alessandro [1 ]
Chiasserini, Carla-Fabiana [1 ]
Viterbo, Emanuele [2 ]
机构
[1] Politecn Torino, Dept Elect Engn, I-10129 Turin, Italy
[2] Univ Calabria, DEIS, I-87036 Arcavacata Di Rende, CS, Italy
关键词
field reconstruction; irregular sampling; random matrix theory; wireless sensor networks;
D O I
10.1109/TSP.2008.925953
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 focus on a multidimensional field with uncorrelated spectrum and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More specifically, we apply linear reconstruction techniques and take the mean-square error (MSE) of the field estimate as a metric to evaluate the signal reconstruction quality. We find that the MSE analysis could be carried out by using the closed-form expression of the eigenvalue distribution of the matrix representing the sampling system. Unfortunately, such distribution is still unknown. Thus, we first derive a closed-form expression of the distribution moments, and we find that the eigenvalue distribution tends to the Marcnko-Pastur distribution as the field dimension goes to infinity. Finally, by using our approach, we derive a tight approximation to the MSE of the reconstructed field.
引用
收藏
页码:4274 / 4285
页数:12
相关论文
共 40 条
  • [1] Nonuniform sampling and reconstruction in shift-invariant spaces
    Aldroubi, A
    Gröchenig, K
    [J]. SIAM REVIEW, 2001, 43 (04) : 585 - 620
  • [2] [Anonymous], 2000, INTRO SPECTRAL ANAL
  • [3] [Anonymous], The Online Encyclopedia of Integer Sequences, Number of graphs on n unlabeled nodes
  • [4] Bellman R., 1970, INTRO MATRIX ANAL
  • [5] Billingsley P., 1995, PROBABILITY MEASURE
  • [6] Brookes M, 2005, MATRIX REFERENCE MAN
  • [7] CANDES EJ, DANTZIG SELECTOR STA
  • [8] On data acquisition and field reconstruction in wireless sensor networks
    Chiasserini, Carla-Fabiana
    Nordio, Alessandro
    Viterbo, Emanuele
    [J]. DISTRIBUTED COOPERATIVE LABORATORIES: NETWORKING, INSTRUMENTATION, AND MEASUREMENTS, 2006, : 161 - +
  • [9] CRISTESCU R, 2005, P INT C INF PROC SEN
  • [10] ORDERED TREES AND NON-CROSSING PARTITIONS
    DERSHOWITZ, N
    ZAKS, S
    [J]. DISCRETE MATHEMATICS, 1986, 62 (02) : 215 - 218