Linear Least-Squares Filtering of Distorted Images

Abstract

In the model studied here, the illuminance f of a distorted image is assumed to be the sum of a spatially stationary noise process and the result of a convolution of the illuminance g of the undistorted image with an optical point spread function k. The illuminance ĝ of a restored image is obtained by a linear filtering operation on f. We determine the filter that minimizes the mean squared error between ĝ and g. The case in which k is stochastic (e.g., observations made through a turbulent atmosphere) is our main concern.