A K Louis 1996 Inverse Problems 12 175 doi:10.1088/0266-5611/12/2/005
A K Louis
Show affiliationsThe version of this paper that was published in Inverse Problems 1995 1211-33 was an earlier draft of the paper and did not include the many refinements that had been made. The correct version of this paper is published in full below.
In this paper we present a method for solving problems such as Af = g by constructing an approximate inverse which maps the data g to a regularized solution of this equation of the first kind. No discretization for f is needed. The solution operator can be precomputed independently of the data. This works for linear problems and for nonlinear problems with a special structure. The regularization is achieved by computing mollified versions of the (minimum-norm) solution. It is shown that this class of regularization operators contains, as special cases, the classical methods such as Tikhonov - Phillips, iteration methods and also discretization methods. In the case where the operator has some invariance properties the storage needs are dramatically reduced.
Issue 2 (April 1996)
Received 14 March 1995, in final form 7 August 1995
A K Louis 1996 Inverse Problems 12 175
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