U Schmitt and A K Louis 2002 Inverse Problems 18 645 doi:10.1088/0266-5611/18/3/308
U Schmitt and A K Louis
Show affiliationsIn this paper dynamic inverse problems are studied, where the investigated object is allowed to change during the measurement procedure. In order to achieve reasonable results, temporal a priori information will be considered. Here, 'temporal smoothness' is used as a quite general, but for many applications sufficient, a priori information. This is justified in the case of slight movements during an x-ray scan in computerized tomography, or in the field of current density reconstruction, where one wants to conclude from electrical measurements on the surface of the head, the locations of brain activity.
First, the notion of a dynamic inverse problem is introduced, then we describe how temporal smoothness can be incorporated in the regularization of the problem, and finally an efficient solver and some regularization properties of this solver are presented.
This theory will be exploited in three practically relevant applications in a following paper.
65K05 Mathematical programming algorithms (For theory see 90Cxx)
65F22 Ill-posedness, regularization
92C55 Biomedical imaging and signal processing (See also 44A12, 65R10)
Issue 3 (June 2002)
Received 11 September 2001, in final form 14 February 2002
Published 24 April 2002
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