Multidimensional harmonic inversion by filter-diagonalization

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Abstract
We present a new method for harmonic inversion in multi-dimensions, i.e., extracting the wave vectors ω k and amplitudes d k from a signal c n =∑ k d k e −i nω k , where n defines the multi-index. The method is an extension of the filter-diagonalization method for 1D signals. As such it enables the harmonic inversion in any small wavevector domain D ω by solving a small generalized eigenvalue problem. The computed ω k and d k can then be used to create a high resolution image F( ω ) for ω ∈ D ω . The method greatly overperforms the conventional Fourier analysis for a model 2D signal containing as many as 10 000 damped sinusoids with moderate amount of noise.