TY - JOUR
T1 - On constant modulus multidimensional harmonic retrieval
AU - Liu, Xiangqian
AU - Sidiropoulos, Nicholas D.
PY - 2002/1/1
Y1 - 2002/1/1
N2 - In a recent paper, it has been shown that up to ⌊K/2⌋ ⌈L/2⌉ two-dimensional (2-D) exponentials are almost surely identifiable from a K × L mixture, assuming regular sampling at or above Nyquist in both dimensions. This holds for damped or undamped exponentials. In this paper, we show that up to ⌈K/2⌉ ⌈L/2⌉ undamped exponentials can be uniquely recovered almost surely. Multidimensional conjugate folding is used to achieve this improvement. The main result is then generalized to N > 2 dimensions. The gain is interesting from a theoretical standpoint, but also for small 2-D sensor arrays or higher dimensions and odd sample sizes. Also important is that the proof implies an algebraic retrieval algorithm, called the MDF algorithm, which outperforms some of the best known algebraic 2-D harmonic retrieval algorithms. We illustrate this by comparing to MEMP, JAFE, and also our own earlier multidimensional embedding (MDE) algorithm.
AB - In a recent paper, it has been shown that up to ⌊K/2⌋ ⌈L/2⌉ two-dimensional (2-D) exponentials are almost surely identifiable from a K × L mixture, assuming regular sampling at or above Nyquist in both dimensions. This holds for damped or undamped exponentials. In this paper, we show that up to ⌈K/2⌉ ⌈L/2⌉ undamped exponentials can be uniquely recovered almost surely. Multidimensional conjugate folding is used to achieve this improvement. The main result is then generalized to N > 2 dimensions. The gain is interesting from a theoretical standpoint, but also for small 2-D sensor arrays or higher dimensions and odd sample sizes. Also important is that the proof implies an algebraic retrieval algorithm, called the MDF algorithm, which outperforms some of the best known algebraic 2-D harmonic retrieval algorithms. We illustrate this by comparing to MEMP, JAFE, and also our own earlier multidimensional embedding (MDE) algorithm.
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U2 - 10.1109/icassp.2002.5745274
DO - 10.1109/icassp.2002.5745274
M3 - Conference article
AN - SCOPUS:0036295134
VL - 3
SP - III/2977-III/2980
JO - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
JF - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
SN - 0736-7791
T2 - 2002 IEEE International Conference on Acoustic, Speech, and Signal Processing
Y2 - 13 May 2002 through 17 May 2002
ER -