1 Introduction
Digital breast tomosynthesis (DBT) is rapidly replacing digital mammography (DM) as the basic xray technique for evaluation of the breasts. DBT overcomes some of the inherent limitations of DM by adding limited depth information to mammographic images. This prevents inherent information loss caused by tissue superposition, and may even increase specificity by resolving tissue projections that mimick breast lesions. A DBT acquisition consists of several lowdose planar xray projections at equally spaced intervals over a limited angle. These projections are then reconstructed to a threedimensional volume. However, this sparse sampling and limited angular range gives rise to different artifacts, which manufacturers try to solve in several ways. In previous work [6] it was shown that the chosen reconstruction algorithm can greatly influence the reconstruction quality.
In this paper, we are interested in DBT reconstruction with a datadriven approach using deep learning. As we will show, not only does this allow us to easily include complicated (shape) priors into the reconstruction, but it additionally opens opportunities for endtoend learning and predicting lesion locations in CADsystems, or to compute the accumulated xray dose. We propose a datadriven reconstruction algorithm, Deep Breast Tomographic Reconstruction (DBToR) using a deep neural network, which extends the previously proposed Learned PrimalDual algorithm. The neural network consists of several ‘reconstruction blocks’, which take in raw sinogram (i.e., projection) data as the initial input, perform a forward and a backward pass by taking projections and backprojections, and use a convolutional neural network to produce an intermediate reconstruction result which is then improved further by each successive reconstruction block. This neural network is trained by stochastic gradient descent, which minimizes the
loss between the reconstruction computed reconstruction algorithms to determine the reconstruction volume. In contrast to CT imaging, measurements from only a narrow range of sparsely sampled angles are available in breast tomosynthesis. However we also have access to information on the compressed breast thickness, and it is used in the classical reconstruction algorithms to determine the reconstruction volume. We provide these thickness measurements as additional prior information to the Learned PrimalDual algorithm by giving it a mask and allow it to learn how to use this mask efficiently.We have tested the algorithm on virtual breast phantoms. The results indicate that the proposed algorithm outperforms the baseline iterative reconstruction algorithm in terms of reconstruction quality for both breast edges and breast internal structures. Furthermore, the algorithm generalizes well even when trained on a small dataset and is robust to noise.
2 Methods
2.1 Material
To train and evaluate the algorithm, we created a total of 1124 simulated breast phantoms. To limit computational complexity, the phantoms consisted of 2D coronal slices extracted from virtual 3D breast phantoms [2]. These phantoms were indexed with labels for four different materials: skin, adipose tissue, glandular tissue, and Cooper’s ligaments. The elemental compositions of these materials were obtained from the work of Hammerstein et. al.[3], except for the composition of Cooper’s ligaments, which was assumed to be identical to that of glandular tissue. Linear attenuation coefficients at were calculated for each material using the software from Boone and Chavez [4]. The phantoms include compressed breast thicknesses from to and widths from to with an isotropic voxel size of .
Limited angle fanbeam projections were simulated for all phantoms using a geometry with the center of rotation placed at the bottom center of the phantom. The xray source was placed above the center of rotation, and the sourcedetector distance was . A total of 25 equally spaced projections between and were generated, with the detector rotating with the xray source. The detector was a perfect photon counting system consisting of 1280 elements of width. The forward model was used for the simulations, with the simulated projection data, the number of xray photons emitted towards detector pixel , the intersection between voxel and the line between the source and detector pixel , and the linear attenuation in voxel . The noiseless simulated projection data were used to generate a series of data sets at 17 noise levels. This was simulated by setting photon count with . The cases with have a noise level of similar magnitude to clinical DBT projection data. For each noise level, 10 Poisson noiserealizations were generated, resulting in a total of 11240 projection sets at each dose level.
Reference reconstructions were generated for both noiseless and noisy data using 100 iterations of MLTR without any regularization [5].
2.2 Algorithm
The DBToR algorithm, which we propose for the problem is a modification of the Learned PrimalDual Algorithm[1] (LPD), which we extend by taking breast thickness measurements into account in order to improve reconstruction quality. These breast thickness measurements are computed as the distance between the detector cover plate and the compression paddle, and are available during testing. The measurements of breast thickness for breast can be turned into a 2D mask , which is a mask with constant height and fullwidth, which restricts the region in which the breast is located in one axis. Compared to the base LPD algorithm, we have seen that the addition of mask information leads to more stable training and higher reconstruction quality. Complete algorithm training procedure is provided as Algorithm 1, where is the projection operator and is the backprojection. At test time, we compute the reconstruction from the given height mask and the projections as .
Input sinogram data is logtransformed, after which we scale it so that the resulting mean and standard deviation across the training dataset equal
. Forward projection is a linear operator. In all experiments and freq=1. for training on noisy data and for training on noisefree data. for are neural networks with weights respectively, which we call the dual reconstruction block and the primal reconstruction block. Each primal/dual reconstruction block is a ResNettype block consisting of 3 convolutional layers, which is similar to the reconstruction blocks in LPD algorithm [1]. We initialize by zeros. Parameters of the neural network are optimized by performing an iteration of ADAM optimizer (line 16) using cosine annealing as a learning rate schedule starting at a learning rate starting of .






3 Results
In this section we provide a summary of the results and compare the proposed DBToR algorithm to the baseline iterative reconstruction algorithm and the Learned PrimalDual algorithm. We trained two versions of the DBToR algorithm: one on noisefree projections and one on noisy projections at noise level . For DBToR trained on noisefree data we report the corresponding loss, Structural Similarity Index (SSIM) and Peak SignaltoNoise Ratio (PSNR) on noisefree test data in Table 1, while for DBToR trained on noisy projections we report these metrics for noise levels in Table 2. These results were obtained by making 3 random crossvalidation splits with approximately 50% for training and 50% for testing at the ‘patient’ level, thus we ensured that all breast slices for any specific patient belong to either the train or to the test set for each split. For noisefree projections, we trained the basic LPD algorithm in addition to DBToR in order to compare the performance (Table 1). Since LPD performed poorly on noisefree projections, we excluded it from further training on noisy projections.
The proposed DBToR algorithm outperforms the baseline iterative reconstruction algorithm at all noise levels and for all metrics being considered, while yielding visually more accurate reconstructions as well (see ground truth in Figure 1 and reconstructions in Figure 2). The LPD algorithm is significantly outperformed in the noisefree case. It is also interesting to note from Table 2 that the performance of DBToR at noise level is comparable to the baseline iterative reconstruction algorithm at noise level , which corresponds to a 4 times higher photon count. Further performance gains are to be expected when training on a larger dataset.
Model  loss  SSIM  PSNR 

Baseline (noisefree)  
LPD algorithm (noisefree)  
DBToR algorithm (noisefree) 
Model  loss  SSIM  PSNR 

Baseline ()  
DBToR ()  
Baseline ()  
DBToR ()  
Baseline ()  
DBToR () 
4 Discussion and conclusions
We have presented DBToR, a modification of the Learned PrimalDual reconstruction algorithm, which is specifically suited for digital breast tomosynthesis. We showed that adding priors such as the breast thickness improves learning stability, generalization and reconstruction quality. Furthermore, we have shown that the DBToR algorithm outperforms the baseline iterative reconstruction algorithm and is robust to noise.
This paper has not been submitted for consideration elsewhere.
References
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 [3] G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, and J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology, vol. 130, no. 2, pp. 485–491, 1979.
 [4] J. M. Boone and A. E. Chavez, “Comparison of xray cross sections for diagnostic and therapeutic medical physics,” Med. Phys., vol. 23, no. 12, pp. 1997–2005, 1996.
 [5] J. Nuyts, B. De Man, P. Dupont, M. Defrise, P. Suetens, and L. Mortelmans, “Iterative reconstruction for helical CT: a simulation study,” Phys. Med. Biol., vol. 43, no. 4, pp. 729–737, 1998.
 [6] A. RodriguezRuiz, J. Teuwen, S. Vreeman, R.W. Bouwman, R.E. van Engen, N. Karssemeijer, R.M. Mann, A. GubernMerida, I. Sechopoulos, “New reconstruction algorithm for digital breast tomosynthesis: better image quality for humans and computers,” Acta Radiologica, 2017.
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