Breast cancer ranks first in female malignant tumors and seriously threatens the life and health of women. However, early diagnosis and treatment can effectively prolong the life of patients. Digital breast tomosynthesis (DBT) is a new three-dimensional imaging technology employed for breast disease diagnosis and scans within a small angle range and reconstructs breast tomography images by collecting a few low-dose projections at equal angle intervals. Compared to computed tomography (CT), it is more suitable for conducting imaging on special human parts such as the breasts that are not easy to scan at large angles and feature low-dose and low-cost imaging. Hologic Selenia Dimensions is a DBT product first certified by the Food and Drug Administration (FDA) in 2011, followed by DBT products from several companies such as GE, Siemens, and Fujifilm. The reconstruction method of DBT plays a vital role in its imaging quality, and currently, the main methods are based on shift and add (SAA) reconstruction, and analytic reconstruction (AR) and iterative reconstruction (IR) methods derived from electronic CT. Among them, SAA calculates the mean of multi-angle projection based on the displacement shift to enhance the information of the focusing plane and weaken the information of the non-focusing plane. However, it is rarely utilized due to the severe out-of-plane interference in the reconstrution slice. Filtered back projection (FBP) is a representative method of the AR class, which makes image details clearer by projection filtering. In particular, the fast reconstruction speed and stable numerical values make it suitable for medical diagnosis. Therefore, it is currently selected as a commercial method. However, FBP can cause serious artifacts and noise in limited-angle scanning DBT, which is unfavorable for breast disease diagnosis. The maximum likelihood expectation maximization (MLEM) method is considered the best reconstruction method in the IR class, providing a good balance between the high- and low-frequency parts of the image. However, the IR method has a longer running time and is difficult to apply in clinical practice before improving the reconstruction speed. Therefore, we seek a DBT reconstruction method that can reduce reconstruction artifacts and improve reconstruction speed. The multi-angle projection is divided into multiple observation vectors, and the BSS technology is adopted to extract the focusing information for reconstructing the focusing plane.

We propose to adopt blind source separation (BSS) to separate any focusing information from multi-angle projections. First, multi-angle projections are collected by DBT imaging machine, and logarithmic transformation is performed on these projections. Then, based on the central projection, the multi-angle projections are focused on the reconstrution slice at depth z via the displacement according to the imaging geometry. Finally, the multi-angle projections after displacement are regarded as a group of linear combinations composed of the focusing information and a lot of outer information. Meanwhile, by selecting a weight-adjusted second order blind identification (WASOBI) that is efficient in separating observation signals with temporal structures, the focusing plane information is extracted from multi-angle projections, and external interference, such as noise and artifacts, is separated. By shifting the multi-angle projection to any depth z, all slices within the thickness range are reconstructed.

The focusing information is separated using BSS to quickly reconstruct any slice within the breast thickness range. By taking central projections as a reference, SAA, FBP, and MLEM are compared with the proposed method. All these four improve the original in reducing noise by 13.4%, 18.8%, 88.5%, and 73.6%, and reduce image contrast (IC) by 83.7%, 81.4%, 74.6%, and 10.7%, respectively. Feature similarity index measure (FSIM) of the reconstrution slice and the central projection is 0.841, 0.866, 0.861, and 0.886, respectively, and the structural similarity index measure (SSIM) is 0.596, 0.594, 0.628, and 0.787, respectively. Additionally, the mean value (MV) of artifact diffusion is 0.571, 0.254, 0.189, and 0.146, respectively. The reconstruction speed of the proposed method is lower than that of SAA and FBP, but it is 56.0% higher than that of MLEM with two iterations. The reconstruction method BSFP is based on BSS, which regards the obtained multi-angle projection as a linear combination of information within a focusing plane and several kinds of information outside the slice at depth z. Then, the focusing information is separated using WASOBI, which is sensitive to temporal observation signals in the BSS, to reconstruct the focusing information. A comparison of the three DBT reconstruction methods, SAA, MLEM, and FBP, shows that BSFP has less residual out-of-plane information, such as artifacts in the reconstrution slice. This is because BSS has a strong separation and filtering effect on out-of-plane interference while separating the reconstruction, which leads to a stronger sense of hierarchy and clearer details in the reconstruction slice. Due to its filtering processing, FBP has higher clarity in its reconstrution slice compared to SAA and MLEM. SAA is equivalent to a simple BP method without filtering. If the filtering processing is added during the reconstruction, the reconstruction results will be similar to SAA, while if filtering is added during the MLEM reconstruction, its contrast will also be improved. The small metal balls which have simple structures are taken as the object to study the artifacts in reconstruction. However, when the object shape is complex, complicated flaky artifacts will be formed, and the artifacts in the SAA, MLEM, and FBP reconstrution slices are more likely to connect into flakes, which can cause severe image blurring. Therefore, it can be concluded that to eliminate external interference in the BSFP reconstrution slice, we can choose effective methods, such as more effective filtering before reconstruction, setting multi-projection weights based on the imaging geometry, correcting the displacement shift formula in the three-dimensional direction based on the imaging geometry irradiated by cone beam rays, and taking into account the small swing angle of the DBT detector.

Our DBT reconstruction method BSFP can improve the original image in reducing noise by 73.6% and improve contrast-to-noise ratio (CNR) by 137.2%. Meanwhile, its reconstruction speed is lower than that of SAA and FBP but is 56.0% higher than that of MLEM with two iterations. This method features sound performance in image noise reduction, detail preservation, artifact suppression, and reconstruction speed. It can continuously improve the separation and reconstruction performance with the rapid development of BSS theory and computer hardware. Therefore, it is a practical and promising DBT reconstruction method. Since the separation accuracy of the focusing information depends on the BSS establishment, the operational efficiency of BSFP depends on the selection and optimization of the BSS method. Additionally, the operational speed of BSFP heavily depends on the hardware environment. Therefore, windowing operations, method optimization, code simplification, and utilization of graphics processing unit (GPU) can all improve the BSFP performance.