Abstract
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.
Highlights
AND BACKGROUNDLet h be any generic two-dimensional degradation filter mask (PSF, usually invariant low-pass filter)
Our research aims to build an innovative restoration filter G based on G whose sensitivity with respect to the estimates related to the restoration model is smaller than that of G
Thereby, the subsections aim to specify the proposed restoration method by collecting all these possible options in such a way that the main goals of our paper can be clearly evidenced, that is to say, the improvements accomplished by our iterative scheme G on an original restoration filter G when wrong estimates of the parameters are considered
Summary
Let h be any generic two-dimensional degradation filter mask (PSF, usually invariant low-pass filter). Let x be an original image to be degraded. A generic linear shift-invariant degradation process of x using h can be written in a general way as y = h ∗ ∗x + n, (1). Where y is the degraded image (blurred and noisy image), and n is a two-dimensional matrix representing the added noise in the degradation. A restoration procedure will achieve a replica x of the original image x. The inversion of the degradation process cannot be derived directly; fundamentals on image processing [1,2,3] provide further details on this ill-posed problem. A number of approaches have been investigated in the image restoration arena [4]
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