Blur identification by statistical analysis

The topics of modeling and identification of the point spread function (PSF) for the restoration of degraded images are investigated.; Out-of-focus blur models based on both geometrical and physical optics are presented, and the estimation of their parameters is discussed. Comparisons of the restorations which employ both types of PSF models illustrate that the more accurate physical PSF models do not always result in significantly better restorations. The restoration improvement due to the use of the physical PSF is related to the sampling resolution and signal-to-noise ratio.; A new method for the PSF identification based on residual spectral matching is developed and tested. The PSF estimate is chosen from a collection of candidate PSFs which may be constructed via a parametric model or by experimental measurements. The PSF estimate is selected to provide the best match between the periodogram of the restoration residual and its expected value, derived under the assumption that the restoration PSF is the true PSF. The a priori knowledge required is the noise variance and the original image power spectrum. Methods for the estimation of these quantities are discussed, and the sensitivity of the method to errors in the estimates is examined both theoretically and by simulations. The results illustrate that the method can be successful in estimating the PSFs in both synthetically and optically blurred images.