An adaptive Kalman window filter to restore degraded images

A semicausal model for image representation has been described which accounts for the correlated nature of the pixel data. The model is then used to develop a linear imaging system model suitable for Kalman algorithms. Since the blurring PSF is not known in practice, the system model is modified to include the estimation of the pixels while the noise characteristics are assumed to be known. For restoration, an adaptive Kalman filter is developed whose length of the state vector is shown to be a function of the PSF size resulting in significant savings in computational and storage requirements. Through examples, it is demonstrated that by carefully choosing the initial estimates of the PSF and error covariance terms, results comparable to the case when the PSF is fully known can be obtained. Two criteria to select such initial estimates have been described; one is based on the a priori knowledge about the dominant PSF coefficient and the other is based on the law of conservation of light flux.