Short communication: Dimensionality reduction of curvelet sparse regularizations in limited angle tomography

• Published in: Proceedings in applied mathematics and mechanics Vol. 11; no. 1; pp. 847 - 848
• Main Author: Frikel, Jürgen
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.12.2011; WILEY‐VCH Verlag
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.201110412

We investigate the reconstruction problem for limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, etc. Since the acquired tomographic data is highly incomplete, the reconstruction problem is severely ill‐posed and the traditional reconstruction methods, such as filtered backprojection (FBP), do not perform well in such situations. To stabilize the inversion we propose the use of a sparse regularization technique in combination with curvelets. We argue that this technique has the ability to preserve edges. As our main result, we present a characterization of the kernel of the limited angle Radon transform in terms of curvelets. Moreover, we characterize reconstructions which are obtained via curvelet sparse regularizations at a limited angular range. As a result, we show that the dimension of the limited angle problem can be significantly reduced in the curvelet domain. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)