Quantitative Study on Exact Reconstruction Sampling Condition in Limited-view CT

TL;DR

This paper quantitatively analyzes the sampling conditions necessary for exact image reconstruction in limited-view CT using TV minimization, providing a benchmark for sampling requirements based on solution uniqueness.

Contribution

It introduces a method to verify the uniqueness of TV minimization solutions, quantifies the necessary sampling number for exact reconstruction, and establishes bounds on the scanning range.

Findings

Quantified the sufficient sampling number for exact reconstruction.

Showed increased sampling compensates for narrower scanning angles.

Identified a lower bound of scanning range for guaranteed reconstruction.

Abstract

In limited-view computed tomography reconstruction, iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, inspired by compressive sensing, potentially claims large reductions in sampling requirements. However, a quantitative notion of this claim is non-trivial because of the ill-defined reduction in sampling achieved by the sparsity-exploiting method. In this paper, exact reconstruction sampling condition for limited-view problem is studied by verifying the uniqueness of solution in TV minimization model. Uniqueness is tested by solving a convex optimization problem derived from the sufficient and necessary condition of solution uniqueness. Through this method, the sufficient sampling number of exact reconstruction is quantified for any fixed phantom and settled geometrical parameter in the limited-view problem. This paper provides a reference to quantify the sampling condition. Using Shepp-Logan phantom as an example, the experiment results show the quantified sampling number and indicate that an object would be accurately reconstructed as the scanning range becomes narrower by increasing sampling number. The increased samplings compensate for the deficiency of the projection angle. However, a lower bound of the scanning range is presented, in which an exact reconstruction cannot be obtained once the projection angle is narrowed to this extent no matter how to increase sampling.