## 1 Introduction  
In the last 20 years, the interest on synthetizing pseudo-Computerized Tomography (pseudo-CT) images from Magnetic Resonance (MR) images using computer vision and machine learning techniques has been increasing consistently alongside the adoption of hybrid Positron Emission Tomography/Magnetic Resonance (PET/MR) scanners and the improvement in external radiation therapies [1; 2; 3]. The first approaches used traditional image processing and machine learning strategies, such as segmentation-based methods [4; 5; 6; 7], atlas-based methods [8; 9; 10; 11; 12; 13; 14], or learning based methods [15; 16; 17]. These approaches present several disadvantages, such as the need of an accurate spatial normalization to a template space, the assumption of mostly normal anatomy, or the problem of accommodating a large amount of training data. These problems have been solved in the last few years with the advent of new techniques based on Convolutional Neural Networks (CNNs). The use of CNNs has also improved the quality of the result while reducing the time needed for synthesizing a pseudo-CT. According to our knowledge, the first approach that adopted deep learning to generate a pseudo-CT from an MRI scan was presented by [PERSON] et al. [18]. This work proposed a CNN that used a U-net architecture performing 2D convolutions [19]. The network received axial slices from a T1-weighted volume of the head as input and tried to generate the corresponding slices from a registered CT scan. Their architecture incorporated unpooling layers in the up-sampling steps of the U-net and Mean Absolute Error (MAE) as loss function. Their results were compared to an atlas-based method [20], obtaining favorable results in accuracy and computational time (close to real-time). Later, the work of [PERSON] et al. [21] explored a similar architecture to generate a segmentation of air, bone, and soft tissue instead of generating the continuous pseudo-CT, also using a set of 3D T1-weighted head volumes. In this case, they incorporated a nearest-neighborhood interpolation in the up-sampling steps of the U-net. Additionally, as they were classifying instead of regressing, they employed a multi-class cross-entropy loss metric, which is usually easier to optimize than the L1 or L2 error. Their results were compared with the capability of their segmentation to reconstruct PET images against the reconstruction using Dixon base Attenuation Correction (AC) images. The deep learning approach performed better and took less than 0.5 min to generate the pseudo-CT segmentation. In contrast, our work by [PERSON] et al. [22] proposed a 2D U-net architecture with transposed convolutions as up-sampling layer based only on Dixon images. In this case, we utilized the Dixon-VIBE images from the Pelvis as input to the network to generate their corresponding pseudo-CT. Therefore, the input to the network was composed by four channels corresponding to the four values of the Dixon image. This proposal generated a whole pseudo-CT volume in around 1 min. Other works made use of more sophisticated networks architectures and pipelines for training. The work by [PERSON] [23] proposed a 3D neural network with dilated convolutions to avoid the use of pooling operations. They also explored the advantages of residual connections [24] and auto-context refinement [25]. For training, they employed an adversarial network that tried to differentiate between real CTs and pseudo-CTs [26]. They used 3D patches from T1 volumes of head and pelvis as input and compared their results against traditional methods such as atlas registration, sparse representation, and random forest with auto-context. Their approach outperformed all these methods. On the other hand, a similar approach was proposed by [PERSON] et al. [27] which trained a 2D CNN that incorporated residuals and an adversarial strategy for training. All these recent strategies, including both atlas-based methods and neural networks, relay on databases to generate a dictionary or to train a model.