## 1 Introduction  
Digital tomosynthesis (DT) enables accurate diagnosis compared with traditional 2D radiography due to its superior depth resolution [1]. In addition, the DT can reduce the radiation dose compared to computed tomography (CT) owing to its limited-angle scanning strategy [2]. Despite these benefits, conventional DT systems suffer from mechanical complexity and low efficiency due to the physical movements of the X-ray source and detector. Also, these physical movements introduce motion artifacts in reconstructed images. Thus, there is a need to simplify the geometry of the DT system while maintaining its strengths. In particular, the geometric inversion with a small detector in the DT system allows more efficient diagnosis, image guidance, and radiation dose reduction by minimizing the field-of-view (FOV) relative to the conventional DT systems [3]. Recently, stationary inverse-geometry digital tomosynthesis (s-IGDT) has been proposed by using the geometric inversion with a stationary X-ray source array and a small detector. Several studies demonstrated that the s-IGDT can overcome the drawbacks of the conventional DT and, consequently, improve examination efficiencies [3; 4; 5]. The use of carbon nanotube-based X-ray source arrays within this system further enabled ultra-fast scans for the imaging [5]. In spite of the benefits of the s-IGDT, the stationary-small detector of the s-IGDT system introduces truncation effects in projections due to a limited FOV. This effect leads to the artifacts in reconstructed images, which appear as stepped bands and are parallel to the scan direction. The truncation artifacts are sensitive to scan range and the number of focal spots because truncated areas in projections can be varied by those factors [6; 7; 8]. These drawbacks degrade the quality of the s-IGDT image and reduce diagnostic accuracy. Therefore, developing a method for mitigating the truncation artifacts is essential to fully leverage the clinical potential of the s-IGDT. With the advance of deep learning-based technologies, generative adversarial networks (GANs) have been used for various applications in the field of computer vision [9; 10; 11]. The imaging models based on the GANs are generally generated by the hostile training of the generator and the discriminator, and they showed a remarkable performance in predicting missing data and synthesizing realistic textures. Also, several studies reported that the GAN-based networks can reduce metal artifacts and improve image quality for DT images [12; 13]. In this work, we introduced a deep convolutional GAN (DCGAN)-based out-painting method for alleviating the truncation artifacts in the s-IGDT images. While the GAN-based in-painting methods have been widely utilized for recovering image quality [11; 14; 15], the out-painting based on the GAN is relatively under-researched due to its practical challenge. The GAN-based in-painting model fills in partial image regions with pixel values, which are predicted by using the neighboring pixels located on all sides. In other words, the in-painting model is able to recover an image with sufficient information in a coherent way. The out-painting is conceptually similar to the in-painting. However, the out-painting task is imposed to create new image contents with insufficient information because the neighboring pixels around missing image regions are fewer than those used for the in-painting task. This phenomenon is more noticeable with an increase in missing image regions, and moreover, it may cause the artificiality and inaccuracy of recovered images. In the proposed out-painting method, a dilated convolutional block was added to the DCGAN to provide the contextual information in diverse receptive fields, which is used for restoring the truncated regions of s-IGDT projections, during network training. A generator was designed with an encoder-decoder structure for generating plausible output images and leading to stable network training.