A spectral 2-D Wold decomposition algorithm for homogeneous random fields

The theory of the 2-D Wold decomposition of homogeneous random fields is effective in image and video analysis, synthesis, and modeling. However, a robust and computationally efficient decomposition algorithm is needed for use of the theory in practical applications. This paper presents a spectral 3-D Wold decomposition algorithm for homogeneous and near homogeneous random fields. The algorithm relies on the intrinsic fundamental-harmonic relationship among Fourier spectral peaks to identify harmonic frequencies, and uses a Hough transformation to detect spectral evanescent components. A local variance based procedure is developed to determine the spectral peak support. Compared to the two other existing methods for Wold decompositions, global thresholding and maximum-likelihood parameter estimation, this algorithm is more robust and flexible for the large variety of natural images, as well as computationally more efficient than the maximum-likelihood method.