Novel Complex AUTOMAP for Accelerated MRI

Accelerated MR imaging refers to diagnostic-quality image reconstruction using undersampled MR sensor data (k-space). This involves acquiring fewer samples than Nyquist’s criterion for reconstruction, thereby speeding up the MR acquisition process, which is crucial. However undersampled k-space leads to artifact-prone images, which need to be rectified. Data-driven, deep-learning based approaches, such as AUTOMAP (Automated Transform by Manifold Approximation) and other architectures like U-net, have been popular in solving the problem of accelerated MRI. These afore-mentioned architectures have the drawback that they process the complex k-space data as tuples of real data using real arithmetic, processing it differently than it should be according to complex arithmetic. In this paper, we propose a modification of AUTOMAP that explores preservation of the complex-valued structure of the k-space, which we henceforth call Complex AUTOMAP. The objective is to learn the function that reconstructs diagnostic-quality images from undersampled k-space using complex arithmetic. We introduce the novel complex dense layer and use it along with complex convolutional layers, complex transpose-convolutional layers and complex-valued activation functions to create an end-to-end deep neural network adapted for complex-valued data. The novel complex dense layer also helps to reduce the bottleneck w.r.t the memory required in the dense layers in the AUTOMAP architecture, thus accomplishing training using 50% lesser GPU resources. The performance of the Complex AUTOMAP is evaluated on a Shepp Logan phantom and two publicly-available k-space MRI datasets. Comparison of obtained results with those on AUTOMAP are also presented. The proposed Complex AUTOMAP achieves comparable performance as AUTOMAP with respect to standard metrics SSIM, PSNR and NRMSE, with 33% fewer parameters than AUTOMAP.