# Sinusoidal Sensitivity Calculation for Line Segment Geometries

arXiv: https://arxiv.org/abs/2208.03059 · HTML: https://mlsanity.com/paper/2208.03059/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 8 references that are in the map.
- First posted on arXiv 5 Aug 2022.

## Built on by (most cited first, 1 of 1)

- [LapGM: A Multisequence MR Bias Correction and Normalization Model](https://mlsanity.com/paper/2209.13619/) (2022)

## Abstract (arXiv)

Purpose: Provide a closed-form solution to the sinusoidal coil sensitivity model proposed by Kern et al. Solution allows for the precise computations of varied, simulated bias fields which can be directly applied onto raw intensity datasets. Methods: Fourier distribution theory and standard integration techniques were used to calculate the Fourier transform of measured magnetic field produced from line segment sources. Results: A L1rm loc(ℝ3) function is derived in full generality for arbitrary line segment geometries. Sampling criteria and equivalence to the original sinusoidal model are discussed. Lastly a CUDA accelerated implementation textttbiasgen is provided for on-demand sensitivity and bias generation. Conclusion: Given the modeling flexibility of the simulated procedure, practitioners will now have access to a more diverse ecosystem of simulated datasets which may be used to quantitatively compare prospective debiasing methods.