Statistical estimation with 1/f-type prior models: robustness to mismatch and efficient model determination

One common problem in signal and image processing is the determination of a discrete representation of a signal given data corresponding to a noisy and blurred version of the unknown. We examine the performance degradation associated with the use of a two-parameter family of fractal-type statistical models in a linear least squares estimator (LLSE) when the model parameters do not match those of the actual process. These models are shown to perform well under various circumstances for estimating noisy and blurred 1/f type fractals and first order Gauss-Markov (FOGM) signals. In addition we demonstrate an effective means of bounding one of the model parameters as a function of the other so as to reduce the model to a single parameter.