Image reconstruction by array modeling

A variety of factors cause image distortion. One type of distortion is blurring where the lines of sight are altered. The objective of this paper is to create mathematical models that simulate blurring and restoration processes of images. Blurring is modeled by a matrix product, and noise is represented by a random number generator; for simple images the true image is modeled by a one dimensional array so that the distorted image is expressed by a matrix times the true image augmented by a random column vector. More complex images are modeled by two dimensional arrays. To preserve computational uniformity, the reconstruction procedure follows the one for the one dimensional case. This was attained by converting the two dimensional array for the true image to a one dimensional column vector. For both dimensional models, the goal is to approximate the true image given the distorted image so that the residual (error) is small and the approximate image has the a minimum number of erroneous surface oscillations. Analysis of results indicate that the convergence criteria of the various computational processes range from a judgmental visual inspection of the "restored" image to monitoring the step error