Quantitative study on exact reconstruction sampling condition by verifying solution uniqueness in limited-view CT

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. Three phantoms are tested to study the sampling condition of limited view exact reconstruction in this paper. 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, the lower bound of the scanning range corresponding to three different phantoms are presented, in which an exact reconstruction cannot be obtained once the projection angular is narrowed to this extent no matter how to increase sampling.