TY - JOUR
T1 - Almost sure identifiability of multidimensional harmonic retrieval
AU - Jiang, Tao
AU - Sidiropoulos, Nicholas D.
AU - Ten Berge, Jos M.F.
PY - 2001
Y1 - 2001
N2 - Two-dimensional (2-D) and more generally multi-dimensional harmonic retrieval is of interest in a variety of applications. The associated identifiability problem is key in understanding the fundamental limitations of parametric high-resolution methods. In the 2-D case, existing identifiability results indicate that, assuming sampling at Nyquist or above, the number of resolvable exponentials is proportional to I + J, where I is the number of (equispaced) samples along one dimension, and J likewise for the other dimension. We prove in this paper that the number of resolvable exponentials is roughly I J/4, almost surely. This is not far from the equations-versus-unknowns bound of I J/3. We then generalize the result to the N-D case for any N > 2, showing that, under quite general conditions, the number of resolvable exponentials is proportional to total sample size, hence grows exponentially with the number of dimensions.
AB - Two-dimensional (2-D) and more generally multi-dimensional harmonic retrieval is of interest in a variety of applications. The associated identifiability problem is key in understanding the fundamental limitations of parametric high-resolution methods. In the 2-D case, existing identifiability results indicate that, assuming sampling at Nyquist or above, the number of resolvable exponentials is proportional to I + J, where I is the number of (equispaced) samples along one dimension, and J likewise for the other dimension. We prove in this paper that the number of resolvable exponentials is roughly I J/4, almost surely. This is not far from the equations-versus-unknowns bound of I J/3. We then generalize the result to the N-D case for any N > 2, showing that, under quite general conditions, the number of resolvable exponentials is proportional to total sample size, hence grows exponentially with the number of dimensions.
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U2 - 10.1109/ICASSP.2001.940312
DO - 10.1109/ICASSP.2001.940312
M3 - Article
AN - SCOPUS:0034848860
SN - 0736-7791
VL - 5
SP - 3093
EP - 3096
JO - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
JF - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
ER -