Pattern theoretic image restoration

Pattern theory is a combination of pattern recognition, machine learning, switching theory, and computational complexity technologies with the central theme that the pattern in a function can be found by minimizing the complexity of a particular generalized representation. The sense of `pattern' used in pattern theory has been demonstrated to be very robust. This paper develops a pattern theoretic approach to image restoration. We assume that an original, patterned, binary image has been corrupted by additive noise and is given as a gray-scale image. The decision theoretic approach to restoration would be simply to threshold the gray- scale image to regain a binary image. The pattern theoretic approach is to use two thresholds. These thresholds separate the pixels into three classes: pixels that were very probably white, pixels that were very probably black, and pixels that we are less certain about. We then use only those pixels that we are confident about and find the pattern based on those pixels. Finally, we use this pattern to extrapolate through the pixels that are uncertain. The amount of noise that can be abated depends on the strength of the underlying pattern. This relationship is developed for uniform and normal noise distributions.