#### Technical Report USC-IPI-580

“An Algorithmic Image Estimation Method Applicable to Nonlinear Observations”

by Manouher Naraghi

June 1975

The principle of image estimation in the presence of linear and nonlinear observations is considered in this dissertation and a recursive estimation algorithm in this dissertation and a recursive estimation algorithm is developed. The development proceeds from the assumptions that the image is statistically characterized by its first two moments namely the mean and the autocorrelation while the observation is allowed to be a general function of the signal and noise. A two step recursive estimation procedure, compatible with the logical structure of the optimal minimum square estimator, is developed. The procedure consists of a linear one step prediction and a filtering operation.

In order to derive the linear predictor, the a priori mean and autocorrelation information is employed to obtain a linear finite order model of the two dimensional random process. This model is of an autoagressive form whose derivation requires only the numerical values of the mean and the correlation functions. At each step of the estimation, the autoagressive model is used in finding the best linear predicted value and its error variance as a function of past estimates and their error variances. Following the prediction process, the filtering operation proceeds to evaluate the estimate and its error variance as a function of the predicted value and the observation.

The estimation method is applied to a number of one and two dimensional problems and the appropriate estimators are developed for the cases where the observation contains additive and/or multiplicative noise term(s). The performance of the method is evaluated by applying the estimation procedure to two dimensional pictorial data corrupted by additive-Gaussian and multiplicative uniform noise.

The value of the method has been analyzed and discussed as to its application to practical problems and its optimality as an estimation technique.

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