Purpose: The authors develop a practical, iterative algorithm for image-reconstruction in undersampled tomographic systems, such as digital breast tomosynthesis (DBT).
Methods: The algorithm controls image regularity by minimizing the image total p variation (TpV), a function that reduces to the total variation when p = 1.0 or the image roughness when p = 2.0. Constraints on the image, such as image positivity and estimated projection-data tolerance, are enforced by projection onto convex sets. The fact that the tomographic system is undersampled translates to the mathematical property that many widely varied resultant volumes may correspond to a given data tolerance. Thus the application of image regularity serves two purposes: (1) Reduction in the number of resultant volumes out of those allowed by fixing the data tolerance, finding the minimum image TpV for fixed data tolerance, and (2) traditional regularization, sacrificing data fidelity for higher image regularity. The present algorithm allows for this dual role of image regularity in undersampled tomography.
Results: The proposed image-reconstruction algorithm is applied to three clinical DBT data sets. The DBT cases include one with microcalcifications and two with masses.
Conclusions: Results indicate that there may be a substantial advantage in using the present image-reconstruction algorithm for microcalcification imaging.