Chebyshev-polynomial-based deformable registration of magnetic resonance images with a specific application in adaptive gantry-less proton therapy

<i>Objective.</i>Efficient image guidance and online adaptive treatment are essential for the success of gantry-less proton therapy (PT). Low-field magnetic resonance imaging (MRI) is a viable option for image guidance, but scan time can limit the quality of low-field MRI images. This study aims to investigate the impact of MRI image quality on deformable image registration (DIR) performance.<i>Approach.</i>We propose a Chebyshev-polynomial-based DIR method, which calculates a mapping between the voxels of a high-quality source image and a lower-quality target image. We prepared a longitudinal breast MRI dataset and synthesized lower-quality target images with four image resolutions and noise levels. For evaluation, we assumed the registration between a pair of high-quality images as the reference registration. We calculated the root-mean-square error (RMSE) between the warped image and the reference target image, as well as between the warped images aligned with high- and lower-quality target images. Deformable vector field (DVF) errors were calculated based on the reference DVF. We obtained binary masks for glandular tissue and calculated Dice coefficients after DIR. The method was further validated with a volunteer breast MRI study with intentional movements between two scan sets and a longitudinal pelvic MRI dataset that includes two contours. Comparison studies with commercial software and open-source software were performed.<i>Main results.</i>Although the quantitative metrics worsened with higher levels of undersampling or increased noise, the RMSE between the warped and target images was substantially reduced compared to the RMSE between the source and target images before registration, even when the target images were severely degraded. Dice coefficients were also considerably increased under various image degradation scenarios.<i>Significance.</i>We have developed a Chebyshev-polynomial-based DIR method and demonstrated its performance with high-quality source and lower-quality target images. This study could help optimize MRI for adaptive gantry-less PT.