High resolution 3D spectral method estimation

In this paper, we investigate the problem of three-dimensional (3D) frequency estimation. We propose a new approach based on the shift invariance property in the data structure. The data are modeled as a sum of 3D complex exponential (SCE) embedded in white noise. In 1 and 2D cases, the approaches based on invariance property have shown efficiency, the purpose of this paper is to take advantage of this feature in the 3D framework. Indeed the special structure of the model permits a decomposition of the autocorrelation matrix into a linear subspace called signal subspace and its orthogonal complement, the noise subspace. The method operates in two steps, firstly one estimates the autocorrelation matrix which is defined and performed from a subset of data. Secondly the estimation of the frequencies is involved by the existence of an invertible matrix mapping between the signal subspace basis and an exact 3D Vandermonde matrix.