A new approach to image processing by nonlinear estimation

Alireza Bemanian, Marquette University


The inherent nonlinear aspect of many practical systems and observation models is explicitly suggestive of the importance and necessity of considering the nonlinear behavior of such a system. The theoretical part of nonlinear systems and in particular nonlinear estimation and filtering has been developed through the decades of sixties and beginning part of seventies. The main obstacles in exact practical implementation of the theoretical results still remain unchallenged. But based on the possibility of realizing an adequate approximation criterion to feasibly utilize the scattered theory, this work has concentrated on least square approximation techniques as well as the Gauss-Hermite numerical integration method. The chosen trend to the estimation process in this work is a stochastic approach. In which by using a nonlinear state and observation equation and based on the Bayes law the conditional probability density is calculated. The derived recursive density equations are the pillar of the later calculations and have been used extensively thereafter. Primarily, this dissertation has been evolved around two prime purposes: (1) Considering the nonlinear aspects of image processing and detection in particular. (2) Developing a practical scheme to restore an observed image (scanned), by not ignoring the nonlinearities sustained in the system. The first intent has been fulfilled by the point that essentially main sources of nonlinearity in image processing are the scanning or recording mechanisms. The chosen observation models express the relationship between the input stimuli and the output response, and well indicate the nonlinear behaviour of the image detectors. Regarding the second goal, state of scanned image is calculated by a stochastic approach, where calculation of its conditional probability density is the prime objective of the task. One of the main difficulties in dealing with these equations is caused by their integral terms and lack of existence of an analytical approach to calculate them. This problem has been overcome by deployment of numerical integration formulas. Stochastic nonlinear filtering mechanisms being implemented in image processing, are a versatile and more general class of image processors which offer potential promise for image restoration and enhancement tasks. Particularly when the image processor is accounted for as a nonlinear entity. In such a case linear estimation methods are not likely to produce good results. However, stochastic restoration methods have been presented relatively on a limited scale, mainly due to the problems imposed by lack of proper statistical modeling techniques, as well as analytic manipulation, and implementation complexity.

Recommended Citation

Bemanian, Alireza, "A new approach to image processing by nonlinear estimation" (1992). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. AAI9318921.