Parametric estimation algorithms for the modeling and restoration of geometrically deformed images

This work deals with the problem of reconstructing an image viewed from perspective. The viewing angles are assumed to be unknown. A model for the deformed image is built, based on the harmonic components in the original image. The original image contains 2-D harmonic components with linear phases. After being viewed from perspective, these components cease to be harmonic, and no longer have linear phases. The phases can be approximated by polynomials in the space variables. This has resulted in the building of a model for the deformed image, of a sum of complex-modulus, 2-D polynomial-phase signals, with special relationships among the parameters of the various components. Those relationships are used to develop a simple non-iterative algorithm for estimating the model parameters. The algorithm is based on the recently-developed high-order ambiguity function. The estimated parameters can be optionally supplied as initial conditions to a maximum likelihood algorithm, thereby reducing the biases of the estimates and improving their statistical accuracy. Performance of the maximum likelihood algorithm is derived, in the sense of the variances of the parameters in the presence of additive white complex Gaussian noise. Possible applications of the algorithms developed in the paper include interpretation and reconstruction of aerial and satellite images.