A neural net algorithm for multidimensional maximum entropy spectrum estimation

As well known, the maximum entropy (ME) method of spectrum estimation has been shown to provide excellent spectral resolution for both one-dimensional (1D) and multidimensional (mD) signals of short data record length. The maximum entropy spectrum is defined as a solution to a constrained optimization problem, where the constraint being the "correlation-matching" property. The computation of the 1D ME spectrum is efficient because it can be obtained from the linear equations of autoregressive (AR) signal modeling. In the mD case, however, the computation of the ME spectrum appears to require the use of nonlinear optimization techniques. The optimization problem has been attacked by many researchers from the point of views of both the primal problem and the dual problem, where the dual problem has the advantages of being finite dimensional and thus attracts most of the efforts. In this paper, we present a neural net algorithm to solve the general mD ME spectral estimation. The problem is formulated as a primal constrained optimization problem and is reduced to solve a well-defined initial value problem of differential equations of Lyapunov type. This initial value problem comprises the basis of our neural net algorithm. Experiments on simulated data showed convincingly that the algorithm did provide mD spectral estimates with high resolution and correlation matching property as well as computation efficiency. The authors believe that the proposed mD spectral estimator will find a broad scope of applications where the high-resolution spectrum is of importance.