Affiliations: National Digital Switching System Engineering and
Technological Research Center, Zhengzhou, Henan, China | He Nan Province People's Hospital, Zhengzhou, Henan,
China
Note: [] Corresponding author: Bin Yan, National Digital Switching System
Engineering and Technological Research Center, Zhengzhou 450002, Henan, China.
E-mail: tom.yan@gmail.com
Abstract: Iterative image reconstruction (IIR) with sparsity-exploiting
methods, such as total variation (TV) minimization, used for investigations in
compressive sensing (CS) claim potentially large reductions in sampling
requirements. Quantifying this claim for computed tomography (CT) is
non-trivial, as both the singularity of undersampled reconstruction and the
sufficient view number for sparse-view reconstruction are ill-defined. In this
paper, the singular value decomposition method is used to study the condition
number and singularity of the system matrix and the regularized matrix. An
estimation method of the empirical lower bound is proposed, which is helpful
for estimating the number of projection views required for exact
reconstruction. Simulation studies show that the singularity of the system
matrices for different projection views is effectively reduced by
regularization. Computing the condition number of a regularized matrix is
necessary to provide a reference for evaluating the singularity and recovery
potential of reconstruction algorithms using regularization. The empirical
lower bound is helpful for estimating the projections view number with a sparse
reconstruction algorithm.
Keywords: System matrix analysis, sparse-view reconstruction, singularity, condition number, projection views number, total variation regularization
