Reconstruction of sparse-view tomography via preconditioned Radon sensing matrix

Computed Tomography (CT) is one of the significant research areas in the field of medical image analysis. As X-rays used in CT image reconstruction are harmful to the human body, it is necessary to reduce the X-ray dosage while also maintaining good quality of CT images. Since medical images have a...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied mathematics & computing 2019-02, Vol.59 (1-2), p.285-303
Main Authors: Theeda, Prasad, Kumar, P. U. Praveen, Sastry, C. S., Jampana, P. V.
Format: Article
Language:English
Subjects:
Applied mathematics
Coherence
Computational geometry
Computational Mathematics and Numerical Analysis
Computed tomography
Convexity
Correlation analysis
Detection
Image analysis
Image quality
Image reconstruction
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Medical imaging
Medical research
Optimization
Optimization techniques
Original Research
Radon
Signal reconstruction
Theory of Computation
Tomography
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Computed Tomography (CT) is one of the significant research areas in the field of medical image analysis. As X-rays used in CT image reconstruction are harmful to the human body, it is necessary to reduce the X-ray dosage while also maintaining good quality of CT images. Since medical images have a natural sparsity, one can directly employ compressive sensing (CS) techniques to reconstruct the CT images. In CS, sensing matrices having low coherence (a measure providing correlation among columns) provide better image reconstruction. However, the sensing matrix constructed through the incomplete angular set of Radon projections typically possesses large coherence. In this paper, we attempt to reduce the coherence of the sensing matrix via a square and invertible preconditioner possessing a small condition number, which is obtained through a convex optimization technique. The stated properties of our preconditioner imply that it can be used effectively even in noisy cases. We demonstrate empirically that the preconditioned sensing matrix yields better signal recovery than the original sensing matrix.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-018-1180-1