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

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.

Iterative Restoration Methods to Loose Estimations Dependency of Regularized Solutions

“…In Santiago et al, 2007 we verified that the higher the regularization is, the lower the product ˆĜ H becomes with a dynamic range ˆ0 1 GH  .…”

“…After differentiating the filter G of (24) with respect to G we come up with an expression for the relative sensitivity function (see Santiago et al, 2007 for further details)…”

Joint Wavelet Video Denoising and Motion Activity Detection in Multimodal Human Activity Analysis: Application to Video-Assisted Bioacoustic/Psychophysiological Monitoring

“…Video denoising, as it happens with all single-sided signal restoration techniques [14,30,31], try to estimate the noise statistical attributes from the available noise-contaminated signal, in order to apply spatiotemporal filtering. In addition, autonoise estimation methods have been proposed to facilitate unsupervised image and video denoising [14][15][16][17][18][31][32][33][34][35]. Wiener filter, which minimizes the mean-square error between the original clean signal and the estimated one obtained during the reconstruction procedure, is the basis for the current denoising approach.…”

“…Wiener filter, which minimizes the mean-square error between the original clean signal and the estimated one obtained during the reconstruction procedure, is the basis for the current denoising approach. Thus, extending the 1D processing case [30], the Wiener filtering operation in the frequency-space domain is described by the following equation [14,31,35]:…”

“…The appearance of motion artefacts in the case of moving pixels is a common disadvantage of these techniques, already discussed. There have been researchers in past works that have evaluated the order of operations (spatial and temporal filtering) that provides optimal de-noising [14,18], while various motion compensation strategies have been proposed to reduce motion artefacts during temporal smoothing [14,16,18,35]. Taking these facts into account, 1D and 2D wavelet domain Wiener filtering algorithms can be effectively combined to provide improved video denoising solutions.…”