Restoration of spatially varying images using multiple model extended Kalman filters

This thesis addresses the problem of identifying spatially varying image parameters and image restoration. The new proposed algorithm identifies image model parameters using an Extended Kalman filter, and estimates a single blur model parameter using a multiple model approach.; We proved that the Extended Kalman filter cannot estimate the blur parameters. We demonstrated that for the problem of image restoration with non-homogeneous parameters, there are inherent restrictions which limit the use of the Extended Kalman filter for blur identification. We therefore use an alternative approach to solve the problem. We implement the Extended Kalman filter in order to identify image parameters, and apply a multiple model approach in order to identify the blur parameter.; In addition, we use the Extended Kalman filter to estimate the parameters of the non-linear degradation encountered when recording the image on photographic films. The algorithm identifies the parameters of the non-linear transformation, and restores the image, taking into account the non linear degradation. We combine previously developed methods to solve the problem of image restoration in the presence of spatially varying parameters and non-linear degradation.; The emphasis of the thesis is on processing images with spatially varying parameters. In much of the literature, image and degradation processes have been assumed to be spatially invariant, resulting in linear invariant models. These are poor assumptions for real life images. Unlike previous methods that are based on invariant models, we develop a new algorithm to restore images with non-homogeneous parameters. Image model parameters and blur model parameters are identified on-line, using an Extended Kalman filter based multiple model algorithm. Based on this identification, the blurred image is subsequently restored.; The degraded image is represented with state space equations. The image is modeled as a plant process, and the degradation is modeled as a measurement process. Varying parameters are identified using the Extended Kalman filter (EKF) and a multiple model approach. The Extended Kalman filter has been used with systems described by state space equations, and it can handle varying parameters and non-linear equations.; The state vector that represents a 2-D image is of the order of {dollar}{lcub}cal O{rcub}(M{lcub}cal N{rcub}sb{lcub}h{rcub}),{dollar} where M = max {dollar}{lcub}{dollar}image support, blur support{dollar}{rcub}{dollar} and {dollar}{lcub}cal N{rcub}sb{lcub}h{rcub}{dollar} is the width of the image. To reduce the computational load involved with 2-D Kalman filtering, we used a previously developed model reduction procedure for the image model. The reduced support substantially reduces the number of pixels in the state vector. The low dimension of this support makes on-line parameter identification a feasible task. Unlike Kalman filtering algorithms for homogeneous parameters, which frequently use the steady state solution, the Extended Kalman filter for non-homogeneous parameters has to compute the gain vector and the covariance matrix at each pixel.