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In limited-view computed tomography reconstruction, iterative imagereconstruction with sparsity-exploiting methods, such as total variation (TV)minimization, inspired by compressive sensing, potentially claims largereductions in sampling requirements. However, a quantitative notion of thisclaim is non-trivial because of the ill-defined reduction in sampling achievedby the sparsity-exploiting method. In this paper, exact reconstruction samplingcondition for limited-view problem is studied by verifying the uniqueness ofsolution in TV minimization model. Uniqueness is tested by solving a convexoptimization problem derived from the sufficient and necessary condition ofsolution uniqueness. Through this method, the sufficient sampling number ofexact reconstruction is quantified for any fixed phantom and settledgeometrical parameter in the limited-view problem. This paper provides areference to quantify the sampling condition. Using Shepp-Logan phantom as anexample, the experiment results show the quantified sampling number andindicate that an object would be accurately reconstructed as the scanning rangebecomes narrower by increasing sampling number. The increased samplingscompensate for the deficiency of the projection angle. However, a lower boundof the scanning range is presented, in which an exact reconstruction cannot beobtained once the projection angle is narrowed to this extent no matter how toincrease sampling.

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