Adaptive image restoration using reduced-order model based Kalman filters

The need for an implementable procedure for identifying spatially varying image models and restoring images has prompted the development of a reduced order model Kalman filter (ROMKF). The ROMKF, presented in this thesis, in conjunction with the maximum likelihood parameter identification technique leads to an adaptive restoration procedure that directly takes into account the spatially varying nature of both the image and degradation models.; Generally, in the past, the original image and the degraded image have been represented with linear, spatially invariant models. For restoration, these models as well as noise statistics must be known prior to filter implementation. One problem that this thesis addresses is the identification of these parameters using a maximum likelihood technique. The likelihood index is optimized using numerical techniques computed with intermediate estimates from a Kalman filter. This involves repetitive restorations of the image as the filter parameters vary. These repetitive restorations require significant computation with established Kalman filtering techniques for image restoration, and motivation for the development of the reduced order model Kalman filter (ROMKF). The reduced state dimension of the ROMKF results in reduced computation when compared with other Kalman filtering techniques. Results show that the ROMKF provides restoration results comparable with established and more complex two-dimensional Kalman filter implementations.; In much of the image restoration literature, the image and the degradation processes have been assumed to be wide-sense stationary resulting in linear shift-invariant models. These are poor assumptions for real world images. In this thesis the incorporation of nonstationary models for use in conjunction with the ROMKF and the maximum likelihood technique is discussed. It is shown that there are improvements in restorations with spatially varying models as compared with spatially invariant models.; The developed restoration and spatially varying parameter identification techniques are then extended to color images represented in the RGB and YIQ domains. The success of restorations with simulated spatially varying degradations should motivate the application of these techniques to real photographs.