DK1212_C012 - 12 Image Restoration The concept of image...

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539 12 Image Restoration The concept of image restoration differs substantially from the idea of image enhancement. While enhancement aims at improving the appearance of the image or its properties with respect to the follow- ing analysis (by a human operator or even automatic), the goal of restoration is to remove an identified distortion from the observed image g , thus providing (in a defined sense) the best possible esti- mate of the original undistorted image f . The observed image may be distorted by blur, geometrical deformation, nonlinear contrast transfer, etc., and is usually further degraded by additive or other- wise related noise ± . The identification of the properties of distortion (i.e., of the distorting system, the disturbing noise, etc.) therefore forms an essential part of the restoration process. Having described the distortion formally by a mathematical model with measured or estimated parameters, we can try to invert the model and obtain the restored image (estimate of the original) as the result of applying the inverse procedure to the observed (measured, received) image. The schematic representation of the distortion and restoration pro- cess is depicted in Figure 12.1. ± f © 2006 by Taylor & Francis Group, LLC
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540 Jan The images may be distorted in many directions. In this chap- ter, we shall deal primarily with the following types of distortion, which cover most of those met in practice: Intensity distortion, global or space variable Geometrical distortion Blur, e.g., due to defocus or motion Interference by noise of certain properties The methods of identification of distortion models and param- eters are specific to individual types of distortion. Therefore, the identification will be discussed in the individual sections, usually before the actual methods of restoration. Basically, two approaches are used in restoration. The concep- tually simpler of them means formulating distortion models that can be directly inverted (as, e.g., for purely linear distortion); solving the equation systems or using closed formulae obtained by the inversion then provides straightforwardly the estimate of the original. When noise cannot be neglected, the exact inversion is impossible, as the noise represents an unknown stochastic component. In these cases, an approximate inversion minimizing the noise influence must be sought; the commonly used approach is the least mean square (LMS) error approach, which may lead to closed formulae as well (e.g., Wiener type filtering). Often, however, the realistic distortion models are so complex (structurally and/or mathematically) that the direct inversion is not feasible or suffers with too high errors. In such a case, the way that proved successful is gradual optimization aiming at an extreme of a criterion function derived from the distortion model. The rich body of optimization theory and iterative algorithms combined with the signal-theoretical concepts thus provide a powerful tool that often enables the recovering of useful information even from heavily distorted images. Different concepts of this kind will be briefly
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This note was uploaded on 02/27/2008 for the course BME 525 taught by Professor Singh during the Fall '07 term at USC.

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DK1212_C012 - 12 Image Restoration The concept of image...

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