Robust iterative image reconstruction for breast CT by use of projection differentiation

Optimization-based image reconstruction with artifact reduction in C-arm CBCT

“…While it is well-known that the condition number can provide a characterization of the ill-conditioning level of a matrix, it is generally challenging numerically to compute the condition number of the matrix of a large size considered. On the other hand, the largest singular value can readily be calculated, and because a condition number is the ratio between the largest and lowest singular values, the largest singular value itself may be used as an index for loosely characterizing the ill-conditioning level of the matrix (Kraemer et al 2015). Therefore, we have calculated the largest singular values of matrices H W c specified with multiple values of [ ] ∈ c 0, 1 as shown in figure 6.…”

“…In particular, a data-derivative fidelity is included in the weighted data fidelity for effectively suppressing dominant, low-frequency components of data truncation, X-ray scatter, and inaccurate estimation of X-ray incident flux [38–40]. The optimization program considered can be solved mathematically by use of the primal-dual algorithms.…”

“…We formulate in the study images to be reconstructed as solutions to a convex optim ization program in which a weighted data divergence is minimized subject to a constraint on the image total variation (TV). In particular, a data-derivative fidelity is included in the weighted data fidelity for effectively suppressing dominant, low-frequency components of data truncation, x-ray scatter, and inaccurate estimation of x-ray incident flux (Frikel and Quinto 2013, Sidky et al 2014b, Kraemer et al 2015. The optimization program considered can be solved mathematically by use of the primal-dual algorithms.…”