## 7 Conclusions  
For clinical use, the optimization of reconstruction in MRI is an important subject. We evaluated the performance of motion-compensated reconstruction algorithms using the GRICS code as an example, and we determined their main bottlenecks and hotspots. Using the roofline model, we have shown that the memory bandwidth is the main hotspot for this class of advanced MRI reconstruction on CPUs. The thread binding strategy resulted in up to a 17% performance gain when considering only OpenMP parallelization. The architectural efficiency of the program was 28% on Intel Xeon Gold and 52% on AMD EPYC. On the GPU devices, the reconstruction kernel was limited by the computational performance and compute throughput, indicating that the actual implementation does not fully exploit the GPU computational capabilities. Efforts should be directed towards maximizing the workload distribution among threads. However, the roofline analysis of the reconstruction kernel on the A100 GPU, where host-device transfer was not an issue, highlighted that a native C++ GPU implementation of this program, using for example CUDA, could leverage the hardware capabilities more efficiently and achieve a better performance. As a result of the findings, the next step involves implementing a native C++ version of the reconstruction kernel using CUDA, starting with the micro-kernels of Algorithm 2, particularly the sparse matrix vector product, the 1D and 2D FFT, and the element-wise matrix product.  
The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app14219663/s1](https://www.mdpi.com/article/10.3390/app14219663/s1)]([https://www.mdpi.com/article/10.3390/app14219663/s1](https://www.mdpi.com/article/10.3390/app14219663/s1)), Table S1: Performance Benchmarking of 3D FFT on the computing platforms.  
Conceptualization, M.A.Z., P.-A.V. and F.O.; methodology, M.A.Z., K.I., P.-A.V. and F.O.; software, M.A.Z., K.I., P.-A.V. and F.O.; validation, M.A.Z. and F.O.; formal analysis, M.A.Z., P.-A.V. and F.O.; investigation, M.A.Z., K.I., P.-A.V. and F.O.; resources, M.A.Z., K.I., P.-A.V. and F.O.; data curation, M.A.Z., K.I., P.-A.V. and F.O.; writing--original draft preparation, M.A.Z.; writing--review and editing, K.I., P.-A.V. and F.O.; visualization, M.A.Z., K.I., P.-A.V. and F.O.; supervision, P.-A.V. and F.O.; project administration, P.-A.V. and F.O. All authors have read and agreed to the published version of the manuscript.  
MOSAR project (ANR-21-CE19-0028), CPER IT2 MP, FEDER (European Regional Development Fund).  
The study was conducted in accordance with the ethical principles outlined in the Declaration of Helsinki (1975, revised 2013) and was approved by the ethics committee (approval number: [CPP EST-III, 08.10.01]) under the protocol \"METHODO\" (ClinicalTrials.gov Identifier: NCT02887053). All participants provided written informed consent prior to their inclusion in the study.  
Written informed consent has been obtained from the patients involved in this study.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors would like to thank [PERSON], from IonQ company, [PERSON], from Grenoble INP-Ensimag, Universite Grenoble Alpes, and [PERSON], from CIC-IT Nancy, for their valuable advice and suggestions.  
The authors declare