## TR#482: A Spectral 2-D Wold Decomposition Algorithm for Homogeneous Random Fields

### Fang Liu and Rosalind W. Picard

Proceedings of ICASSP'99

Phoenix, Arizona

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 2-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.

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