Sinusoidal Sensitivity Calculation for Line Segment Geometries

• URL: http://arxiv.org/abs/2208.03059v1
• Date: Fri, 5 Aug 2022 09:30:55 GMT
• Title: Sinusoidal Sensitivity Calculation for Line Segment Geometries
• Authors: Luciano Vinas and Atchar Sudyadhom
• Abstract summary: This paper presents a closed-form solution to the sinusoidal coil sensitivity model proposed by Kern et al. It allows for precise computations of varied, simulated bias fields for ground-truth debias datasets.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Purpose: Provide a closed-form solution to the sinusoidal coil sensitivity model proposed by Kern et al. This closed-form allows for precise computations of varied, simulated bias fields for ground-truth debias datasets. Methods: Fourier distribution theory and standard integration techniques were used to calculate the Fourier transform for line segment magnetic fields. Results: A $L^1_{\rm loc}(\mathbb{R}^3)$ function is derived in full generality for arbitrary line segment geometries. Sampling criteria and equivalence to the original sinusoidal model are also discussed. Lastly a CUDA accelerated implementation $\texttt{biasgen}$ is provided by authors. Conclusion: As the derived result is influenced by coil positioning and geometry, practitioners will have access to a more diverse ecosystem of simulated datasets which may be used to compare prospective debiasing methods.

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