Cascaded systems analysis of shift‐variant image quality in slit‐scanning breast tomosynthesis
Authors: Berggren Karl , Cederström Björn , Lundqvist Mats , Fredenberg Erik 
Published: August 2018

PurposeDigital breast tomosynthesis (DBT) is becoming an important part of breast cancer screening and diagnosis. Compared to two‐dimensional mammography, tomosynthesis introduces limited three‐dimensional (3D) resolution, but maintains high in‐plane resolution, low dose, and allows for similar clinical protocols. The scanning motion and oblique projections of tomosynthesis acquisitions introduce shift‐variance to the image quality, in addition to effects such as source blurring and geometric magnification. Shift‐variant detector response caused by oblique incidence has been extensively studied previously and is most easily mitigated by letting the source and detector move in sync. In addition, conical reconstruction grids, that is, a grid aligned with the central tomosynthesis projection, have been proposed to compensate for magnification effects. This paper introduces a shift‐variant cascaded systems model for tomosynthesis and validates it against measurements. As an example, the model was used to investigate the shift‐variance of a tomosynthesis system.MethodsThe shift‐variant cascaded systems model was validated on a slit‐scanning photon‐counting DBT system, with synchronous source–detector movement, using simple back‐projection in a conical reconstruction volume. The modulation transfer function (MTF), normalized noise‐power spectrum (NNPS), and detective quantum efficiency (DQE) were used as figures of merit. Simulations were performed for single points while measurements were done over a finite volume, assuming local shift invariance. To investigate the full extent of shift‐variance, 80 locations across the volume were simulated, and the MTF and DQE at 2.5 lp/mm were calculated as a function of position.ResultsThe simulated metrics generally agreed well with their corresponding measurements. The frequency at 50% MTF along the scan direction showed a relatively small variation, ranging from 2.1 to 2.4 lp/mm for the different locations. The frequency at 50% MTF along the chest‐mammilla direction showed a larger variation, ranging from 2.9 to 3.8 lp/mm. All points exhibited a similarly shaped NNPS but the noise magnitude varied with slice height. The zero‐frequency DQE in reconstructed slices was lower than that of the projections, an effect likely caused by noise‐aliasing increasing the zero‐frequency noise.ConclusionsA shift‐variant cascaded systems model has been developed for slit‐scanning tomosynthesis using simple back‐projection. The model was successfully validated against measurements. Even though the study was performed on a slit‐scanning system, several parts of the framework can be applied and extended to other tomosynthesis geometries. The conical reconstruction grid has low variation in image quality in the scan direction where the 3D information is acquired, but source and geometric magnification still dominate in the slit direction, causing a larger variation in image quality. We conclude that image quality is close to shift‐invariant in the scan direction, but not in the height and chest‐mammilla directions, and we recommend that small measurement volumes are used when measuring image quality in these directions to minimize the effects of shift variance.