ESPRIT for Multidimensional General Grids

We present a new method for complex frequency estimation in several variables, extending the classical (1d) ESPRIT-algorithm. We also consider how to work with data sampled on non-standard domains (i.e going beyond multi-rectangles).

[1]  Stéphanie Rouquette-Léveil,et al.  Estimation of frequencies and damping factors by two-dimensional ESPRIT type methods , 2001, IEEE Trans. Signal Process..

[2]  Fredrik Andersson,et al.  On the Structure of Positive Semi-Definite Finite Rank General Domain Hankel and Toeplitz Operators in Several Variables , 2017 .

[3]  Marc Moonen,et al.  An efficient subspace algorithm for 2-D harmonic retrieval , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[4]  Tomas Sauer.  Prony’s method in several variables , 2017, Numerische Mathematik.

[5]  K. Arun,et al.  State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem , 1983 .

[6]  Annie A. M. Cuyt,et al.  Sparse interpolation of multivariate rational functions , 2011, Theor. Comput. Sci..

[7]  Fredrik Andersson,et al.  Nonlinear approximation of functions in two dimensions by sums of exponential functions , 2010 .

[8]  Yi Zhou,et al.  A novel algorithm for two-dimensional frequency estimation , 2007, Signal Process..

[9]  B. Mourrain,et al.  Structured low rank decomposition of multivariate Hankel matrices , 2017, 1701.05805.

[10]  Fredrik Andersson,et al.  On General Domain Truncated Correlation and Convolution Operators with Finite Rank , 2015 .

[11]  Randolph L. Moses,et al.  Two-dimensional Prony modeling and parameter estimation , 1993, IEEE Trans. Signal Process..

[12]  Annie Cuyt,et al.  Multivariate Padé-approximants☆ , 1983 .

[13]  Nina Golyandina,et al.  Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package , 2013, 1309.5050.

[14]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[15]  Ulrich von der Ohe,et al.  A multivariate generalization of Prony's method , 2015, 1506.00450.