Noise is an intrinsic property of every imaging system. For imaging systems using ionizing radiation, such as digital breast tomosynthesis (DBT) or digital mammography (DM), we strive to ensure that x-ray quantum noise is the limiting noise source in images, while using the lowest radiation dose possible to achieve clinically satisfactory images. Therefore, new computer methods are being sought to help reduce the dose of these systems. In the case of DBT, this can be achieved when solving the inverse problem of tomographic reconstruction. In this work, we propose to use a Non-Local Gaussian Markov Random Field (NLGMRF) model to represent a priori knowledge in a Bayesian (Maximum a Posteriori - MAP) reconstruction approach for DBT. The main advantage of the Non-Local Markov Random Field models is that they explicitly consider two important constraints to regularize the solution of this inverse problem - smoothing and redundancy. To evaluate this new method in DBT, a number of experiments were performed to compare these methods to existing reconstruction techniques. Comparable or superior results were achieved when compared with methods in the DBT reconstruction literature in terms of structural similarity index (SSIM), artifact spread function (ASF) and visual analysis, demonstrating that the NLGMRF model is suitable to regularize the MAP solution in DBT reconstruction.
In this work, we investigated and measured the noise in Digital Breast Tomosynthesis (DBT) slices considering the back-projection (BP) algorithm for image reconstruction. First, we presented our open-source DBT reconstruction toolbox and validated with a freely available virtual clinical trials (VCT) software, comparing our results with the reconstruction toolbox available at the Food and Drug Administration's (FDA) repository. A virtual anthropomorphic breast phantom was generated in the VCT environment and noise-free DBT projections were simulated. Slices were reconstructed by both toolboxes and objective metrics were measured to evaluate the performance of our in-house reconstruction software. For the noise analysis, commercial DBT systems from two vendors were used to obtain x-ray projections of a uniform polymethyl methacrylate (PMMA) physical phantom. One system featured an indirect thallium activated cesium iodide (CsI(TI)) scintillator detector and the other a direct amorphous selenium (a-Se) detector. Our in-house software was used to reconstruct raw projections into tomographic slices, and the mean pixel value, noise variance, signal-to-noise ratio (SNR) and the normalized noise power spectrum (NNPS) were measured. In addition, we investigated the adequacy of a heteroskedastic Gaussian model, with an affine variance function, to describe the noise in the reconstruction domain. The measurements show that the variance and SNR from reconstructed slices report similar spatial and signal dependency from previously reported in the projection domain. NNPS showed that the reconstruction process correlates the noise of the DBT slices in the case of projections degraded with almost uncorrelated noise.