Rodrigo A Lobos1, Justin P Haldar1. 1. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California, USA.
Abstract
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.
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.
Authors: Florian Knoll; Kerstin Hammernik; Chi Zhang; Steen Moeller; Thomas Pock; Daniel K Sodickson; Mehmet Akçakaya Journal: IEEE Signal Process Mag Date: 2020-01-20 Impact factor: 12.551
Authors: Martin Uecker; Peng Lai; Mark J Murphy; Patrick Virtue; Michael Elad; John M Pauly; Shreyas S Vasanawala; Michael Lustig Journal: Magn Reson Med Date: 2014-03 Impact factor: 4.668