Ensuring convergence in total-variation-based reconstruction for accurate microcalcification imaging in breast X-ray CT

Breast X-ray CT imaging is being considered in screening as an extension to mammography. As a large fraction of the population will be exposed to radiation, low-dose imaging is essential. Iterative image reconstruction based on solving an optimization problem, such as Total-Variation minimization, shows potential for reconstruction from sparse-view data. For iterative methods it is important to ensure convergence to an accurate solution, since important image features, such as presence of microcalcifications indicating breast cancer, may not be visible in a non-converged reconstruction, and this can have clinical significance. To prevent excessively long computational times, which is a practical concern for the large image arrays in CT, it is desirable to keep the number of iterations low, while still ensuring a sufficiently accurate reconstruction for the specific imaging task. This motivates the study of accurate convergence criteria for iterative image reconstruction. In simulation studies with a realistic breast phantom with microcalcifications we compare different convergence criteria for reliable reconstruction. Our results show that it can be challenging to ensure a sufficiently accurate microcalcification reconstruction, when using standard convergence criteria. In particular, the gray level of the small microcalcifications may not have converged long after the background tissue is reconstructed uniformly. We propose the use of the individual objective function gradient components to better monitor possible regions of non-converged variables. For microcalcifications we find empirically a large correlation between nonzero gradient components and non-converged variables, which occur precisely within the microcalcifications. This supports our claim that gradient components can be used to ensure convergence to a sufficiently accurate reconstruction.