# Limited-Angle Computer Tomography with Truncated Projection Artifacts Removal
## 1 Introduction  
Digital breast tomosynthesis (DBT) is a medical imaging modality that can provide quasi-three-dimensional (3D) breast structural information. DBT can reduce tissue overlap and improve early breast cancer detection [1; 2; 3; 4; 5]. DBT uses a limited-angle Computed Tomography (CT) technique that obtains low-dose X-ray projections of the breast within a limited range of angles. Currently, there are a variety of image reconstruction methods for DBT, which can be divided into two categories: iterative methods and non-iterative methods. Non-iterative reconstruction methods mainly include the back-projection (BP) algorithm and filtered back-projection (FBP) algorithm. The BP algorithm can only yield low-contrast reconstructed images [6; 7]. The FBP algorithm can attenuate the noise information in the BP algorithm by using spatial filters, but designing these filters strongly depends on the imaging and sampling geometry [8]. Iterative reconstruction algorithms are realized by refining the reconstructed images and improving the image quality through recursive calculations [9; 10; 11; 12; 13; 14]. The simultaneous algebraic reconstruction technique (SART) is one of the commonly used iterative algorithms in limited-angle CT image reconstruction. It enhances the edges of the image by iteration and reconstructs more details in the reconstructed image [10; 13]. The enhancement of image edges by SART depends on the selected reconstruction parameters and the number of iterations. With SART, detailed tissue structures can be revealed in DBT images clearly [11; 12; 13; 14; 15; 16]. When applying SART in the limited-angle DBT system, the field of view (FOV) per projection view (PV) cannot cover the entire object due to the limitations of the X-ray sourceand detector. As shown in Figure 1, ray-B passing through the object cannot be received by the detector. This will exclude part of voxels in each iteration during the update and generate the discontinuous step-like artifacts at boundaries, which are called truncation projection artifacts (TPA). TPA will appear on the left and right sides of the reconstructed images, and will extend to the middle of the image as the distance between the breast slice and the digital detector increases. Through our measurement, the artifact area of the slice at 35 mm from the digital detector accounts for about 24% of the whole reconstructed image area, and the artifact area of the slice at 50 mm accounts for about 42%. Although there may not be images at the left and right sides of the reconstructed area, TPA still has a serious impact on limited angle CT. The influence of TPA can depend upon the sweep-angle, the breast size, the detector area and the acquisition pattern (continuous and step-and-shoot). TPA can seriously affect the quality of the reconstructed images and may impact the diagnoses of radiologists [9]. Methods of reducing TPA can be divided into two categories. The first is to artificially compensate the voxels that are not involved in the update [15; 16]. By this method, [PERSON] proposed a local intensity equalization strategy to compensate for voxel values outside the FOV after each PV updating in SART [15]. However, the local intensity equalization strategy did not retain the structural information from the previous SART iteration. [PERSON] proposed a diffusion-based method to reduce TPA, but the higher breast slices still contain artifacts [16]. The second method is to correct the projection data before reconstruction [17; 18; 19; 20; 21]. To extend the truncated projections, extrapolation methods were employed via polynomial functions [7], symmetric mirroring [17], cylindrical water object fitting [18] and square root function [19]. In this study, for the existing DBT system, the original reconstructed images with TPA are projected to generate a completed projection data set. In this projection process, the detector panel is virtually expanded so that it can receive all the X-rays to avoid the truncation of the projection data.