# Pocs-Augmented CycleGAN for MR Image Reconstruction
## 1 Introduction  
Magnetic resonance imaging (MRI) has become a standard diagnosis tool in clinic service due to the non-invasiveness, multiple contrasts, and high temporal and spatial resolutions it can provide. However, the speed of MRI is still much slower compared with the other imaging modalities such as computed tomography (CT) because of the sequential encoding paradigm used for acquiring the frequency- or phase-encoded raw data in the so-called k-space (the Fourier transform domain) [1]. Without sacrificing the image resolution and without hardware upgrading, an essential way to shorten the data acquisition time is to acquire a subset of the fully sampled k-space determined by the Nyquist sampling theory. An imperative step is then to reconstruct the MR image from the incomplete k-space data, as it was from a fully sampled k-space dataset. Tremendous MR image reconstruction methods have been developed over the past decades. Among them, parallel imaging is a popular choice which relies on recovering the missing k-space information using the spatially localized sensitivity profiles of the elements within a phase array coil [2; 3; 4; 5; 6]. Compressed sensing (CS) is another widely used reconstruction method which does not depend on the sensitivity encoding as in parallel imaging but rather on suppressing the incoherent or sparse noise caused by random or pseudo-random k-space sampling [7]. Both types of reconstruction methods and other methods often use an iterative process to solve a nonlinear optimization problem, which is time-consuming and sensitive to parameter selections. Outside of the MR research field, the past several years have seen sensational success from a variety of model-free deep neural networks in image classification [8],computer vision, auditory processing, information generation, and medical imaging [9; 10; 11; 12]. Motivated by such superb performance of deep learning (DL) [13], different groups have incorporated various DL networks into MRI reconstructions such as a deep convolutional autoencoder network [14], deep residual learning [15], deep ADMM-net [16], U-Net [17], and Cycle-GAN [18]. While those pioneering studies have shifted MRI reconstruction from a model-based scenario to a new end-to-end learning-based era, most of the machine learning-based methods are still difficult to understand. Trained by limited data, the reconstruction performance may not be generalizable. By contrast, the well-established traditional methods are often guided by physics. Their generalizability is high. Combining the traditional methods and deep learning may provide a better solution that can incorporating merits from both types of image reconstruction algorithms. To assess this possibility, we proposed a hybrid deep learning based image reconstruction method in this study. Our method contains two steps: the first one is a regular DL-based image reconstruction process, and the second is a renewed version of step one but with the output of the DL network trained in step one included as additional training data. This framework is similar to the well-known traditional data reconstruction algorithm: Projection Onto Convex Set (POCS) [19]. From the point of view of DL, our method can be considered as a new data augmentation strategy, and we therefore dubbed the method as a POCS-augmented DL. A related study was reported in [18], where the authors used two sequentially concatenated generative adversarial networks (GANs) [20] to reconstruct the final MR images. Because of the sequential concatenation, the second GAN only sees residual artifacts in the output of the first one. By contrast, the POCS-augmented network sees both the original image artifacts due to the missing data points in the k-space and the residual artifacts due to the imperfect reconstruction of the first round of DL reconstruction, allowing the network to learn the artifact distribution at different noise levels and remove them from the reconstructed images.