Iterative Desensitisation of Image Restoration Filters under Wrong PSF and Noise Estimates

The restoration achieved on the basis of a Wiener scheme is an optimum since the restoration filter is the outcome of a minimisation process. Moreover, the Wiener restoration approach requires the estimation of some parameters related to the original image and the noise, as well as knowledge about the PSF function. However, in a real restoration problem, we may not possess accurate values of these parameters, making results relatively far from the desired optimum. Indeed, a desensitisation process is required to decrease this dependency on the parameter errors of the restoration filter. In this paper, we present an iterative method to reduce the sensitivity of a general restoration scheme (but specified to the Wiener filter) with regards to wrong estimates of the said parameters. Within the Fourier transform domain, a sensitivity analysis is tackled in depth with the purpose of defining a number of iterations for each frequency element, which leads to the aimed desensitisation regardless of the errors on estimates. Experimental computations using meaningful values of parameters are addressed. The proposed technique effectively achieves better results than those obtained when using the same wrong estimates in the Wiener approach, as well as verified on an SAR restoration.