Iterative Identification and Restoration of Images (The by Reginald L. Lagendijk

By Reginald L. Lagendijk

Some of the most interesting questions in photograph processing is the matter of recuperating the specified or ideal photograph from a degraded model. usually one has the sensation that the degradations within the photo are such that suitable info is just about being recognizable, if in simple terms the picture may be sharpened a little bit. This monograph discusses the 2 crucial steps during which this is completed, particularly the subjects of picture id and recovery. extra particularly the aim of photograph identifi­ cation is to estimate the houses of the imperfect imaging process (blur) from the saw degraded photograph, including a few (statistical) char­ acteristics of the noise and the unique (uncorrupted) picture. at the foundation of those houses the picture recovery method computes an estimate of the unique picture. even though there are numerous textbooks addressing the picture identity and recovery challenge in a basic picture processing atmosphere, there are not often any texts which offer an indepth remedy of the cutting-edge during this box. This monograph discusses iterative methods for picking and restoring photographs that have been degraded via a linear spatially invari­ ant blur and additive white commentary noise. rather than non-iterative tools, iterative schemes may be able to resolve the picture recovery challenge whilst formulated as a limited and spatially variation optimization prob­ during this approach recovery effects may be received which outperform the lem. result of traditional recovery filters.

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2 Image Models Many image identification and restoration methods make use of a priori knowledge about the structure of the original image. In this section we will restrict the discussion to modeling statistical characteristics of discrete images through the use of 2-D autoregressive models. A comprehensive survey of these images models can be found in [9,40,43], including extensive discussions about fitting image models, the model quality and model stability. In Chapter 3 other ways of formulating a priori knowledge about images will be addressed.

25) ~(/) = Ilg - DIll::; Ilwll = E. The bound is related to the uncertainty or noise in the observed image The set of feasible solutions is primarily populated with unacceptable solutions because of the ill-conditioned nature of the restoration problem. Tikhonov defined the regularized solution as the one which minimizes a stabilizing functional n(/) on the set of feasible solutions. Although a wide class of different stabilizing functionals is available, including for example the maximum power [102] and maximum entropy [32] measures, usually a stabilizing functional of the following form is chosen to facilitate the mathematical analysis of the problem [7,74,99]: E g, and can usually be estimated from a smooth image region.

A general criterion for the image model stability is given by the following ztransform of the image model [9,40]: lThis assumption is conflicting with the fact that image intensities are nonnegative. Therefore, the observed noisy blurred image is usually corrected for its mean value in order to satisfy the zero-mean assumption. LJ. -'-+- -I-+-+ -t-r"t ,-r- -rr _Ll. LJ. -I-+-+ -rr"t l -rr _Ll. J. -'-+- -rr _Ll. 5: Model support for various first order image models (a) quarter plane model, (b) nonsymmetric halfplane model, (c) semi-causal model, and (d) noncausal model.

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