  Compressive sensing (CS) is widely used to reduce the acquisition time of
magnetic resonance imaging (MRI). Although state-of-the-art deep learning based
methods have been able to obtain fast, high-quality reconstruction of CS-MR
images, their main drawback is that they treat complex-valued MRI data as
real-valued entities. Most methods either extract the magnitude from the
complex-valued entities or concatenate them as two real-valued channels. In
both the cases, the phase content, which links the real and imaginary parts of
the complex-valued entities, is discarded. In order to address the fundamental
problem of real-valued deep networks, i.e. their inability to process
complex-valued data, we propose a novel framework based on a complex-valued
generative adversarial network (Co-VeGAN). Our model can process complex-valued
input, which enables it to perform high-quality reconstruction of the CS-MR
images. Further, considering that phase is a crucial component of
complex-valued entities, we propose a novel complex-valued activation function,
which is sensitive to the phase of the input. Extensive evaluation of the
proposed approach on different datasets using various sampling masks
demonstrates that the proposed model significantly outperforms the existing
CS-MRI reconstruction techniques in terms of peak signal-to-noise ratio as well
as structural similarity index. Further, it uses significantly fewer trainable
parameters to do so, as compared to the real-valued deep learning based
methods.
