Adaptive regularized image and video restoration

In this thesis, new approaches for adaptive regularized image and video restoration are proposed and applied to various problems. More specifically, nonlinear and high order restoration algorithms are proposed, and applied for error concealment and resolution enhancement.; For the restored image to be locally smooth, the local variance, and the mean and maximum values are utilized to constraint the solution space. These parameters are computed at each iteration step using the partially restored image. A parameter defined by the user determines the degree of local smoothness imposed on the solution, leading to higher convergence rate.; An error concealment algorithm is introduced, which is applicable to a number of multimedia applications. The need of an oriented high pass operator and the requirement of changing the initial condition in iterative regularized recovery algorithms are analyzed. For the recovery of the lost motion vectors, an overlapped region matching algorithm is introduced.; Another application topic addressed in this thesis is the resolution enhancement of video sequence. A weighted multiple input smoothing functional is defined and used to obtain an enhanced video sequence. A spatially invariant point spread function obtained experimently and temporal information are utilized. A mathematical model is developed which uses the point spread function to map the relationship between the original and bilinearly interpolated images in the spatial domain, and motion estimates between frames in the temporal domain. In order to handle the motion estimation error adaptively, we introduce a weighting matrix which is a function of the accuracy of the motion estimates. The properties of the proposed smoothing convex functional are analyzed.; A mixed norm image restoration algorithm combining the LMS and the LMF functionals is proposed. When the two functionals are combined, the main issues which are addressed in this thesis are: (a) how to control the relative contribution of the two terms, and (b) how to estimate the information about the noise distribution, the power of the noise, and the original image. The functional which determines the relative importance between the {dollar}lsb2{dollar} and {dollar}lsb4{dollar} in the mixed norm formulation is automatically adjusted at each iteration based on a measure of the kurtosis of the noise using the partially restored image. When a smoothing functional is incorporated in the problem formulation, the parameter controlling its contribution is also determined by the partially restored image. The parameters are chosen in such a way that the mixed norm smoothing functional is convex, and a local minimizer becomes a global minimizer. This results are extended to the multichannel image case.