## 1 Introduction  
Chest X-ray radiography (CXR) is usually the first imaging technique employed to perform the early diagnosis of cardiopulmonary diseases. Typical pathologies detected in CXRs include pneumonia, atelectasis, consolidation, pneumothorax, and pleural and pericardial effusion [1]. Since the COVID-19 pandemic started in 2020, it has also been used as a tool to detect and assess the evolution of pneumonia caused by this condition [2]. CXR is used worldwide thanks to the simplicity with which it can be completed, the low cost, low radiation dose, and its sensitivity [3, 4]. Regarding the position and orientation of the patient in relation to the X-ray source, the desired and most frequently used setup is posteroanterior (PA) projection [5] since it provides better visualization of the lungs [6]. However, this configuration requires the patient to be standing erect, which is not possible for critically ill patients, intrubated patients, or some elderly people [6, 7]. In these situations, it is more convenient to carry out anteroposterior (AP) projection, in which the patient can be sitting up in bed or lying in a supine position. Thus, AP images can also be acquired with a portable X-ray unit outside the radiology department when, due to the patient's condition, it is advised not to shift him/her [6]. X-ray imaging is based on the attenuation that photons suffer when they traverse the human body so that photons that cross the body and reach the detector without interacting with the media, i.e., primary photons, form the image [8]. However, some photons interact with the media and are not absorbed but scattered. This secondary radiation can also reach the detector, representing background noise and causing a blurring in the primary image and considerable loss in the contrast-to-noise ratio (CNR) [9]. This effect is especially relevant in CXR due to the requirement of large detectors (at least 35 cm wide) to be able to cover the whole region of interest (ROI) [10]. To overcome this problem, several techniques have been proposed, which can be split into two types: scatter suppression and scatter estimation [11]. Scatter suppression methods aim to remove, or at least reduce, the scattered photons that arrive at the detector, while scatter estimation methods try to obtain only the signal of the secondary photons and then subtract it from the total projection. The most widely used scatter correction method is the anti-scatter grid, where a grid is interposed between the patient and the detector so that scattered photons are absorbed, while primary photons are allowed to pass [7; 12]. This technique is successfully implemented in clinical practice [10] since many clinical systems incorporate this grid [13], although it has some disadvantages. First, an anti-scatter grid can also attenuate primary radiation, leading to noisy images [9; 10]. Additionally, it can generate grid line artifacts in the image [14], and it can increase the radiation exposure between two and five times [5; 15]. Finally, in AP acquisitions, it is difficult to accurately align the grid with respect to the beam, so the use of anti-scatter grids in combination with portable X-ray units used in intensive care units or with patients who cannot stand up is more time-consuming and does not guarantee a good result [7; 13]. Another method studied to physically remove scattered X-rays consists of increasing the air gap between the patient and the detector, which enlarges the probability that secondary photons miss the detector due to large scatter angles [16; 17]. This approach causes a smaller increase in the radiation dose than the anti-scatter grid, but it can magnify the acquired image [5]. Other alternatives to the use of an anti-scatter grid are slit scanning, with the drawback of an increase in acquisition time, or strict collimation, which compromises the adaptability of imaging equipment [10; 11; 13].