Statistical Certainty Models in Image Processing

This paper revisits the fundamental question of how uncertain or unknown signal values should be appropriately dealt with in signal and image processing. It puts the concept of certainty and applicability values proposed by Westin and Knutsson in contrast to a statistical model where the state of knowledge on individual signal values is expressed by expectation values and variances, while the structure of signals is espressed by covariance functions, or covariance matrices, respectively. Using this simple approach, and exploiting the power of the Gauss-Markov-Theorem, a linear signal processing framework is obtained which is both powerful, generally applicable, and encompasses the classical certainty/applicability approach, providing answers to the open issues in that classical theory.