Interior Tomography With Curvelet-Based Regularization

Keywords

Computed tomography (CT); curvelet transform; interior tomography; local reconstruction; radon transform; regularization method

Abstract

The interior problem, i.e. reconstruction from local truncated projections in computed tomography (CT), is common in practical applications. However, its solution is non-unique in a general unconstrained setting. To solve the interior problem uniquely and stably, in recent years both the prior knowledge- and compressive sensing (CS)-based methods have been developed. Those theoretically exact solutions for the interior problem are called interior tomography. Along this direction, we propose here a new CS-based method for the interior problem based on the curvelet transform. A curvelet is localized in both radial and angular directions in the frequency domain. A two-dimensional (2D) image can be represented in a curvelet frame. We employ the curvelet transform coefficients to regularize the interior problem and obtain a curvelet frame based regularization method (CFRM) for interior tomography. The curvelet coefficients of the reconstructed image are split into two sets according to their visibility from the interior data, and different regularization parameters are used for these two sets. We also presents the results of numerical experiments, which demonstrate the feasibility of the proposed approach.

Publication Date

1-1-2017

Publication Title

Journal of X-Ray Science and Technology

Volume

25

Issue

1

Number of Pages

1-13

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.3233/XST-160602

Socpus ID

85011556659 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85011556659

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