# K2S Challenge: From Undersampled K-Space to Automatic Segmentation
## 1 Introduction  
Magnetic Resonance Imaging (MRI) has emerged as one of the strongest medical imaging modalities for clinical use, offering exquisite soft tissue contrast for visualizing tissues such as ligaments, cartilage, and muscle [1, 2]. Conventional MR sequences see the weighting of images in accordance with intrinsic MR parameters such as T1 and T2 and allow for suppression or saturation of signal from tissue types such as fat or fluid [3, 4]. As such, MR images can be tailored for a given clinical context. Furthering this are recentdevelopments of advanced sequences such as zero echo time (ZTE) and ultrashort echo time (UTE), which allow for high-resolution imaging of additional tissues such as tendons in musculoskeletal imaging [5; 6; 7; 8]. MR has the added advantage of not exposing subjects to ionizing radiation compared to alternatives such as radiographs and computed tomography (CT). Despite these advantages, however, MR faces several challenges, including (1) long acquisition times and (2) the requirement of time-consuming and laborious radiologist annotation and interpretation of images to extract clinical meaning [9; 10]. Fortunately, several tools have been developed to address these concerns. In the case of long MR scan times, acquisitions can be accelerated by sampling fewer points in k-space, the raw frequency-based domain in which MRI signals are obtained. This undersampling induces aliasing artifacts in resulting images that can be removed by image reconstruction algorithms. In recent years, considerable effort has been put into developing several families of reconstruction approaches: (1) compressed sensing (CS) algorithms iteratively reconstruct images by ensuring consistency with acquired k-space and imposing sparsity on the reconstructed image in an alternate domain [11; 12; 13; 14]; (2) parallel imaging (PI) algorithms exploit the redundancy of using multiple coils to acquire the same imaging volume to reduce acquisition times at the expense of signal-to-noise ratio (SNR) [15; 16; 17]; (3) deep learning (DL) approaches use complex, nonlinear models to impute full-length acquisition images from aliased images and/or undersampled k-space [18; 19]. Other approaches growing in popularity include magnetic resonance fingerprinting (MRF) and low-rank and sparse modeling approaches [20; 21; 22]. On the other hand, a host of DL tools have emerged to automate mundane MR image-processing tasks. For instance, the introduction of the U-Net in 2015 seeded major advances in medical image segmentation from limited data, paving the way for more complicated architectures that have been applied for accurate lumbar spine and knee cartilage segmentation, among others [23; 24; 25; 26]. Yet other DL applications include automatic assessments of cartilage thickness, staging of anterior cruciate ligament injury severity, diagnosis of lumbar spine anomalies, and analysis of bone shape [27; 28; 29; 30]. This body of work unquestionably reflects substantial advances made by the MR research community. But it is noteworthy that with extremely few exceptions, the challenges of long acquisition times and image analysis have been treated as separate entities [31]. The long-term vision, however, would be a software package that addresses these challenges simultaneously, raising a niche for optimization. Namely, image analysis algorithms are designed for full-length acquisition of MR image inputs, but there is no guarantee and little investigation that they would perform similarly well on reconstructed images from the accelerated acquisition. On the other hand, image reconstruction algorithms are overwhelmingly optimized for metrics such as normalized root mean square error (nRMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), which correlate to the perceptual quality of a reconstructed image [32; 33; 34].