Non-stationary iterated Tikhonov-Morozov method and third-order differential equations for the evaluation of unbounded operators

In this paper we analyse the non-stationary iterative Tikhonov-Morozov meth od analytically and numerically for the stable evaluation of differential o perators and for denoizing images. A relationship between non-stationary it erative 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 o n model problems in ultrasound imaging and numerical differentiation. Copyr ight (C) 2000 John Wiley & Sons, Ltd.