Identification and restoration of images based on overall modeling of the imaging process

This thesis addresses the identification and restoration of noisy and blurred images recorded by possibly nonlinear sensors. Comprehensive mathematical models of the imaging process, that accurately describe the characteristics of different image sensors and blur formation, are incorporated into the identification and restoration procedures. A new parametric maximum likelihood blur identification method, a minimum mean square error restoration filter for multiplicative observation noise, and a multichannel Kalman filter for restoration of multispectral images are developed. Both simulated and real, as well as monochromatic and color images are considered.; We first review models of blur formation for some commonly encountered blurs such as the out-of-focus and linear motion blur. We compare the models for the out-of-focus blur obtained using the principles of geometrical and physical optics. We discuss the importance of incorporating the models for nonlinear image recording media, such as photographic film and photographic paper, into image restoration algorithms.; Based on the above models the identification of unknown blur and image model parameters is discussed. For images recorded on photographic film and paper, we identify the blur after transforming the image into the exposure domain where a linear convolutional relationship between the observed and ideal image can be established. We can use the well known log-spectrum method for the identification of linear motion blurs and out of focus blurs represented by the uniform disc model. In order to identify out of focus blurs modeled based on the theory of physical optics, we extend the blur identification algorithm that uses sharp edges in the ideal image into 2-D. A new maximum likelihood (ML) blur identification algorithm that is based on a parametric model of the blur in the continuous spatial coordinates is also developed for the identification of a more general class of blurs, including the atmospheric turbulence blur.; We next study the restoration of images that are obtained by various image sensors, such as photographic film, photographic paper and CCD cameras. As a consequence of transforming the image into the exposure domain the observation noise becomes multiplicative. The derivation of the optimal linear minimum mean square error deconvolution filter in the presence of multiplicative noise is provided. The restoration of color images is addressed as well. We first analyze the independent restoration of each image channel in the RGB and YIQ domains. Then, we present a new multichannel Kalman filter that incorporates the spectral correlations between the channels of a color image.; The experiments for the blur identification and image restoration methods are performed on both simulated and real images. The improvement in results obtained by using our methods compared to results generated by existing methods is significant.