Documentation/Nightly/Modules/AnomalousFilters
Introduction
Anomalous diffusion processes (ADP) are mathematically denoted by a power law in the Fokker-Planck equation, leading to the generalized form. There are several generalizations of the Fokker-Plank equation, which should give many different partial differential equations (PDEs). Here we adopt only the so-called porous media form, allowing the super-diffusive and the subdiffusive processes. [1] In porous media, channels are created promoting or blocking the flow of the density function, which has been proved to provide a suitable application on MRI filtering.[2]
Basically, there are two different filters already implementing the anomalous diffusion process: the isotropic anomalous diffusion and anisotropic anomalous diffusion filters.[3] Each of these filters were already applied on different imaging MR modalities, such as structural T1 and T2 images[4], diffusion weighted images (DWI and DTI)[5][6], MRI relaxation T1 and T2 relaxometry[7] and in fMRI[8] as an initial study.
References
- ↑ Tsallis, C. (2009). Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World. Springer.
- ↑ Da S Senra Filho, A. C., Garrido Salmon, C. E., & Murta Junior, L. O. (2015). Anomalous diffusion process applied to magnetic resonance image enhancement. Physics in Medicine and Biology, 60(6), 2355–2373. doi:10.1088/0031-9155/60/6/2355
- ↑ Da S Senra Filho, A. C., Garrido Salmon, C. E., & Murta Junior, L. O. (2015). Anomalous diffusion process applied to magnetic resonance image enhancement. Physics in Medicine and Biology, 60(6), 2355–2373. doi:10.1088/0031-9155/60/6/2355
- ↑ Da S Senra Filho, A. C., Garrido Salmon, C. E., & Murta Junior, L. O. (2015). Anomalous diffusion process applied to magnetic resonance image enhancement. Physics in Medicine and Biology, 60(6), 2355–2373. doi:10.1088/0031-9155/60/6/2355
- ↑ Senra Filho, A. C. da S., Duque, J. J., & Murta, L. O. (2013). Isotropic anomalous filtering in Diffusion-Weighted Magnetic Resonance Imaging. Conference Proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference, 2013, 4022–5. doi:10.1109/EMBC.2013.6610427
- ↑ Senra Filho, A. C. da S., Simozo, F. H., Salmon, C. E. G., & Murta Junior, L. O. (2014). Anisotropic anomalous filter as a tool for decreasing patient exam time in diffusion-weighted MRI protocols. In XXIV Brazilian Congress on Biomedical Engineering (pp. 0–3). Uberlandia.
- ↑ Filho, A. C. da S. S., Barbosa, J. H. O., Salmon, C. E. G. S., & Junior, L. O. M. (2014). Anisotropic Anomalous Diffusion Filtering Applied to Relaxation Time Estimation in Magnetic Resonance Imaging. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 3893–3896). IEEE. doi:10.1109/EMBC.2014.6944474
- ↑ Filho, A. C. da S. S., Rondinoni, C., Santos, A. C. dos, & Junior, L. O. M. (2014). Brain Activation Inhomogeneity Highlighted by the Isotropic Anomalous Diffusion Filter. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 3313–3316). Chicago: IEEE. doi:10.1109/EMBC.2014.6944331
