A Novel Task-Based reconstruction approach for digital breast tomosynthesis

•Novel reconstruction method is proposed for Digital Breast Tomosynthesis.•Microcalcifications visibility is enhanced by introducing detectability function.•Novel spatial regularizer preserves the morphological contents of the imaged breast.•Improved optimization algorithm yields faster reconstruction.•Superior image quality is assessed through visual trial session on medical experts. [Display omitted] The reconstruction of a volumetric image from Digital Breast Tomosynthesis (DBT) measurements is an ill-posed inverse problem, for which existing iterative regularized approaches can provide a good solution. However, the clinical task is somehow omitted in the derivation of those techniques, although it plays a primary role in the radiologist diagnosis. In this work, we address this issue by introducing a novel variational formulation for DBT reconstruction, tailored for a specific clinical task, namely the detection of microcalcifications. Our method aims at simultaneously enhancing the detectability performance and enabling a high-quality restoration of the background breast tissues. Our contribution is threefold. First, we introduce an original task-based reconstruction framework through the proposition of a detectability function inspired from mathematical model observers. Second, we propose a novel total-variation regularizer where the gradient field accounts for the different morphological contents of the imaged breast. Third, we integrate the two developed measures into a cost function, minimized thanks to a new form of the Majorize Minimize Memory Gradient (3MG) algorithm. We conduct a numerical comparison of the convergence speed of the proposed method with those of standard convex optimization algorithms. Experimental results show the interest of our DBT reconstruction approach, qualitatively and quantitatively.