An Eigenstructure Approach for the Retrieval of Cylindrical Harmonics

In this paper, we present a high resolution spectral estimation method for 2-D isotropic random fields with covariance functions equal to weighted sums of cylindrical harmonics. Such fields are often used to model some types of background noises in geophysics and in ocean acoustics. The approach that we present differs from previous 2-D spectral estimation techniques by the fact that we take maximal advantage of the symmetries implied by both the isotropy and the special covariance structure of these fields. Note that isotropy is the natural generalization to several dimensions of the 1-D notion of stationarity. Our approach is similar in spirit to 1-D harmonic retrieval techniques, such as the MUSIC method, which rely on an eigenanalysis of the covariance matrix. In the 2-D isotropic context, we begin with a Fourier series representation of an isotropic field with respect to the angle 8 in a polar coordinate representation of the underlying 2-D space. We then obtain a spectral estimate by performing an eigenanalysis of the covariance matrix of samples of the zeroth-order Fourier coefficient process in order to extract the cylindrical harmonics. We also discuss the estimation of this covariance matrix and present examples to illustrate the high resolution and robustness properties of our procedure. *This work was supported by the National Science Foundation under Grant No. ECS-8312921 and by the Army Research Office under Grant No. DAAG-84-K-0005.