A fast Total Variation-based iterative algorithm for digital breast tomosynthesis image reconstruction

Abstract

In this work, we propose a fast iterative algorithm for the reconstruction of digital breast tomosynthesis images. The algorithm solves a regularization problem, expressed as the minimization of the sum of a least-squares term and a weighted smoothed version of the Total Variation regularization function. We use a Fixed Point method for the solution of the minimization problem, requiring the solution of a linear system at each iteration, whose coefficient matrix is a positive definite approximation of the Hessian of the objective function. We propose an efficient implementation of the algorithm, where the linear system is solved by a truncated Conjugate Gradient method. We compare the Fixed Point implementation with a fast first order method such as the Scaled Gradient Projection method, that does not require any linear system solution. Numerical experiments on a breast phantom widely used in tomographic simulations show that both the methods recover microcalcifications very fast while the Fixed Point is more efficient in detecting masses, when more time is available for the algorithm execution.