Image Restoration Using Two-Dimensional Variations

摘要

In many applications (consumer and commercial imaging, medical imaging, robotics, space research, and etc.) observed images are often degraded due to atmospheric turbulence, relative motion between a scene and a camera, nonuniform illumination, wrong focus, etc. Image restoration refers to the problem of estimating the ideal image from its observed degraded one. Numerous restoration techniques (linear, nonlinear, deterministic, stochastic, etc.) optimized with respect to different were introduced The amount of a priori information about degradation such as the size and shape of blurs, noise level determines how mathematically ill-posed the problem is. A priori information can be used in a variety of ways in modeling and algorithm development. The information about the nature of blur (e.g., linear or nonlinear and space-variant or space-invariant) and noise (additive or multiplicative) is used in modeling the input-output relation of imaging systems. In blur modeling, when the type of blur is known (e.g., out of focus, motion, turbulence), the blurring operator can be parameterized using only a few parameters. In image modeling, the ideal image can be modeled, for instance, on the basis of a priori Markovian assumption. In algorithm development, a priori information is used in defining constraints on the solution and in defining a criterion or a quantitative description of the solution. The blind and non-blind deconvolutions were extensively studied, and many techniques were proposed for their solution They usually involve some regularization which assures various statistical properties of the image or constrains on the estimated image and restoration filter according to some assumptions. This regularization is required to guarantee a unique solution and stability against noise and some model discrepancies. One of the most popular fundamental techniques is a linear minimum mean square error method. It finds the linear estimate of the ideal image for which the mean square error between the estimate and the ideal image is minimal. This linear operator acting on the observed image to determine the estimate on the base of a priori second-order statistical information about the image and noise processes. For images with sharp changes of intensity, the appropriate regularization is based on variational integrals (Rudin, et al., www.intechopen.com * inf{ ( , ) ( )} Q zZ zA z v z , (3) www.intechopen.com