Abstract
In this paper we analyse the non-stationary iterative Tikhonov-Morozov method analytically and numerically for the stable evaluation of differential operators and for denoizing images. A relationship between non-stationary iterative Tikhonov-Morozov regularization and a filtering technique based on a differential equation of third order is established and both methods are shown to be effective for denoizing images and for the stable evaluation of differential operators. The theoretical results are verified numerically on model problems in ultrasound imaging and numerical differentiation.
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