Singular system analysis of breast tomosynthesis systems for choosing projection angles

Abstract

Optimization of digital breast tomosynthesis (DBT) has been investigated in the medical imaging field for the last several years as DBT has the potential for improved detection of breast cancer. However, a systematic method for choosing the angular range and number of projections of DBT has yet to be developed. Singular system analysis of a linear imaging system1 gives knowledge of how much information about the object being imaged is transferred through the given system, or equivalently how much information about the object is lost through the system. These components of the object to be imaged, which are fully transferrable and nontransferrable through the imaging system in the absence of noise, are respectively called <i>measurable</i> and <i>null</i> components of the object. In this work, given a projection angle, a ray tracing algorithm is used to linearly approximate the nonlinear x-ray imaging process in the 3D object and hence producing a matrix representing for the imaging process. For a DBT system using a combination of different projection angles, the imaging matrices corresponding to the projection angles are combined to form a DBT system matrix, to which the singular system analysis is applied in order to produce singular vectors of the given DBT design. The singular vectors of the DBT system are then used to estimate the null and measurable components of the object and to identify the angular projections of the DBT system that transfer maximum information regarding the object to be imaged. This method facilitates the ability to choose effective projection angles and maximizing information tranfer regarding the object by the system.