Stability estimates for the regularized inversion of the truncated Hilbert transform

Rima Alaifari, Michel Defrise, Alexander Katsevich

Onderzoeksoutput: Articlepeer review

5 Citaten (Scopus)


In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection method. Each 1D problem consists of recovering a compactly supported function in F, where F is a finite interval from its partial Hilbert transform data. When the Hilbert transform is measured on a finite interval G that only overlaps but does not cover F , this inversion problem is known to be severely ill-posed (Alaifari et al 2015 SIAM J. Math. Anal. 47 797–824).

In this paper, we study the reconstruction of f restricted to the overlap region between G anf F. We show that with this restriction and by assuming prior knowledge on the L2 norm or on the variation of f, better stability with Hölder continuity (typical for mildly ill-posed problems) can be obtained.
Originele taal-2English
Aantal pagina's17
TijdschriftInverse Problems
Nummer van het tijdschrift6
StatusPublished - apr 2016


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