TY - JOUR

T1 - Almost sure identifiability of multidimensional harmonic retrieval

AU - Jiang, Tao

AU - Sidiropoulos, Nicholas D.

AU - Ten Berge, Jos M.F.

PY - 2001/1/1

Y1 - 2001/1/1

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

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

SN - 0736-7791

ER -