On the shape of convolution kernels in MRI reconstruction: Rectangles versus ellipsoids

• Published in: Magnetic resonance in medicine Vol. 87; no. 6; pp. 2989 - 2996
• Main Authors: Lobos, Rodrigo A., Haldar, Justin P.
• Format: Journal Article
• Language: English
• Published: United States Wiley Subscription Services, Inc 01.06.2022
• Subjects: Algorithms; Artificial neural networks; Convolution; Ellipsoids; Image Processing, Computer-Assisted - methods; Image reconstruction; kernel shape; Kernels; Magnetic resonance imaging; Magnetic Resonance Imaging - methods; Mathematical models; MRI reconstruction; Neural networks; Neural Networks, Computer; Parameters; Rectangles; Retrospective Studies; Spatial discrimination; Spatial resolution; kernel shape; convolution; MRI reconstruction
• ISSN: 0740-3194; 1522-2594
• DOI: 10.1002/mrm.29189

Purpose Many MRI reconstruction methods (including GRAPPA, SPIRiT, ESPIRiT, LORAKS, and convolutional neural network [CNN] methods) involve shift‐invariant convolution models. Rectangular convolution kernel shapes are often chosen by default, although ellipsoidal kernel shapes have potentially appealing theoretical characteristics. In this work, we systematically investigate the differences between different kernel shape choices in several contexts. Theory It is well‐understood that a rectangular region of k‐space is associated with anisotropic spatial resolution, while ellipsoidal regions can be associated with more isotropic resolution. Further, for a fixed spatial resolution, ellipsoidal kernels are associated with substantially fewer parameters than rectangular kernels. These characteristics suggest that ellipsoidal kernels may have certain advantages over rectangular kernels. Methods We used real retrospectively undersampled k‐space data to empirically study the characteristics of rectangular and ellipsoidal kernels in the context of seven methods (GRAPPA, SPIRiT, ESPIRiT, SAKE, LORAKS, AC‐LORAKS, and CNN‐based reconstructions). Results Empirical results suggest that both kernel shapes can produce reconstructed images with similar error metrics, although the ellipsoidal shape can often achieve this with reduced computation time and memory usage and/or fewer model parameters. Conclusion Ellipsoidal kernel shapes may offer advantages over rectangular kernel shapes in various MRI applications.