GpU acceleration of a model-based iterative method for Digital Breast tomosynthesis

Digital Breast Tomosynthesis (DBT) is a modern 3D Computed Tomography X-ray technique for the early detection of breast tumors, which is receiving growing interest in the medical and scientific community. Since DBT performs incomplete sampling of data, the image reconstruction approaches based on iterative methods are preferable to the classical analytic techniques, such as the Filtered Back Projection algorithm, providing fewer artifacts. In this work, we consider a Model-Based Iterative Reconstruction (MBIR) method well suited to describe the DBT data acquisition process and to include prior information on the reconstructed image. We propose a gradient-based solver named Scaled Gradient Projection (SGP) for the solution of the constrained optimization problem arising in the considered MBIR method. Even if the SGP algorithm exhibits fast convergence, the time required on a serial computer for the reconstruction of a real DBT data set is too long for the clinical needs. In this paper we propose a parallel SGP version designed to perform the most expensive computations of each iteration on Graphics Processing Unit (GPU). We apply the proposed parallel approach on three different GPU boards, with computational performance comparable with that of the boards usually installed in commercial DBT systems. The numerical results show that the proposed GPU-based MBIR method provides accurate reconstructions in a time suitable for clinical trials. Digital Breast Tomosynthesis (DBT) is a quite recent 3D Computed Tomography (CT) technique providing a vol- umetric breast reconstruction as a stack of 2D images, each representing a cross-sectional slice of the breast itself1. When compared with traditional 2D mammography, DBT has the advantage of separating the breast anatomical tissues, which can be overlapped in a mammography, and this generally reduces false negative diagnosis. At the same time, since the DBT source emits X-rays only from a small number of angles in an arc trajectory, DBT pro- vides a low radiation dose comparable to the radiation dose used in a standard mammography. For this reason, DBT is appealing to the medical and scientific community as a breast screening routine2,3. Until a few years ago, the introduction of DBT in a clinical setting has been slowed down by the absence of effi- cient algorithms for image reconstruction from a limited number of projections. It is well known that the tradi- tional Filtered Back Projection (FBP)4 analytic algorithm amplifies noise and artifacts in the case of low-sampled data3. Iterative algorithms are known to perform better than FBP in the case of tomosynthesis data, but they require computational times incompatible with a clinical use3,5, since in clinical DBT examinations the breast reconstruction must be provided in 40 to 60 seconds. Nevertheless, the recent advent of low cost parallel architec- tures, such as Graphics Processing Units (GPUs), has provided the chance for a remarkable reduction of the image reconstruction time, making iterative methods a realistic alternative to analytic algorithms. Among the different iterative approaches in X-ray CT (see5 for a detailed classification of iterative meth- ods in CT), the so called Model-Based Iterative Reconstruction (MBIR) methods are now getting growing attention. In general, they try to model the acquisition process as accurately as possible, since they take into account system geometry, physical interactions of photons in the projections and prior information about the acquired volume. This approach produces better results than the traditional FBP in terms of quality of the reconstructed image and artifacts reduction, especially for low-dose or limited data X-ray CT. The MBIR methods can be described in a unifying framework as constrained or unconstrained minimization problems5–7, involving a fit-to-data function and a regularizing function, acting as a prior on the solution. A widely used regularization term, proposed in sparse tomography by8 and then used by many authors9–14,