Improving high frequency image features of deep learning reconstructions via k-space refinement with null-space kernel

Purpose Deep learning (DL) based reconstruction using unrolled neural networks has shown great potential in accelerating MRI. However, one of the major drawbacks is the loss of high-frequency details and textures in the output. The purpose of the study is to propose a novel refinement method that uses null-space kernel to refine k-space and improve blurred image details and textures. Methods The proposed method constrains the output of the DL to comply to the linear neighborhood relationship calibrated in the auto-calibration lines. To demonstrate efficacy, we tested our refinement method on the DL reconstruction under a variety of conditions (i.e., dataset, unrolled neural networks, and under-sampling scheme). Specifically, the method was tested on three large-scale public datasets (knee and brain) from fastMRI's multi-coil track. Results The proposed scheme visually reduces the structural error in the k-space domain, enhance the homogeneity of the k-space intensity. Consequently, reconstructed image shows sharper images with enhanced details and textures. The proposed method is also successful in improving high-frequency image details (SSIM, GMSD) without sacrificing overall image error (PSNR). Conclusion Our findings imply that refining DL output using the proposed method may generally improve DL reconstruction as tested with various large-scale dataset and networks.