A Novel Task-Based reconstruction approach for digital breast tomosynthesis

Abstract

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.

A Local MM Subspace Method for Solving Constrained Variational Problems in Image Recovery

“…Algorithm 1: MMS(x 0 , γ, ε) The penalty function present in Problem (P γ ) may have a large curvature, which can jeopardize the good accuracy of the majorant function inherent to the MM strategy and thus significantly slowdown the convergence of the algorithm [68,23]. This issue had been overcome by the authors of [68], in the particular case of the MM memory gradient (3MG) method, by empirically substituting local majorations for global majorations, in a similar spirit as trust-region approaches [81,73,15]. In what follows, we formalize and generalize such a local approach to accelerate any MM subspace algorithm, and we demonstrate the convergence of the resulting iterative approach to a critical point of Problem (P γ ).…”

“…Consequently, the penalized problem becomes ill-conditioned, hence difficult to solve. This harshly impacts the convergence profile of MMS as observed in [68]. This slowdown is directly related to a large spectral norm of the curvature matrix B k , defined by (40) at each iteration k, which leads to small update steps.…”

SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm

“…(with convention x −1 = x 0 ) brings notably to the so-called MM Memory Gradient (3MG) method whose great performances have been illustrated in [22,23,37,66]. Other choices for the subpace matrix can be found in [53,60,67,74].…”

A nonlinear total variation based computed tomography (CT) image reconstruction method using gradient reinforcement

“…One of the simplest but strongest ideas is using actual image denoiser algorithms as a prior in model fidelity. In the literature, block matching 3D (BM3D) ( Dabov et al, 2007 ), total variation (TV) ( Sidky, Kao & Pan, 2006 ; Velikina, Leng & Chen, 2007 ), non-local denoiser operators, Buades, Coll & Morel (2005) and their modified versions adapted to the specific imaging problems, Sghaier et al (2022) ; Jin et al (2010) ; Kim et al (2016) ; Zhang et al (2021) have been integrated as model fidelity for iterative reconstruction.…”