The regularized maximum-likelihood solution for boundary-value problems of the heat fields spectral analysis

The estimation problem of the frequency-wavenumber spectral density function of the heat radiation field of the spatially-spread objects is suggested to be considered as a multi-dimensional spectral analysis boundary-value problem for an initial field in the stochastic measurement channel. Defining the regularization constraints, incorporating the boundary conditions, we formulate a generalized maximum-likelihood problem for spectral density function estimation and then apply standard optimization techniques to derive an optimal spectral analysis algorithm.