Purpose or Case Report: Convolutional neural networks (CNNs) have proven to be valuable in the fields of image processing and computer vision. Our work applies complex-valued CNNs to magnetic resonance imaging (MRI) to reduce scan times. The reduction of scan times has widespread pediatric benefits. A typical scan requires that patients remain still for up to an hour to produce a clear image, which is difficult for children without inducing anesthesia, which carries risks. A need exists for greatly improved MRI scan times without the loss of diagnostic accuracy. This scan time can be reduced by subsampling in k-space. We use CNNs to reconstruct images from these undersampled acquisitions. Our work investigates complex-valued CNNs for image reconstruction in lieu of two-channel real-valued CNNs.
Methods & Materials: Recent work suggests complex-valued CNNs could be more accurate than real-valued CNNs when dealing with complex-valued data. Typically, complex-valued data is fed into CNNs by using a 2-channel architecture where the channels contain the real and imaginary components of the data. This does not preserve phase information, which is valuable for many MRI applications. Recent work in applying complex-valued CNNs to music transcription and speech prediction tasks demonstrates complex-valued models are highly competitive with their real two-channel counterparts (Trabelsi et al., 2018). Complex-valued neural networks have been applied to MRI fingerprinting with improvements in accuracy in comparison to real models (Virtue et al., 2017).
We apply complex-valued CNNs to subsampled image reconstruction by modifying components of our current CNN within our deep unrolled architecture to be complex-valued. We perform complex convolution and explore various complex-valued activation functions which keep the pre-activated phase intact, as well as activation functions which are based on the phase component. We evaluate the performance in terms of accuracy of this complex model compared to its real counterpart.
Results: We trained two otherwise identical CNNs with real-valued convolution and complex-valued convolution, and approximately 900K trainable parameters each. The validation loss was 0.693 and 0.639, respectively. This shows complex-valued networks have the potential to be much more accurate than their real-valued counterparts.
Conclusions: Our work shows potential for reducing MRI scan times by more accurately reconstructing images from subsampled data acquisitions using complex-valued CNNs.