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{{documentation/{{documentation/version}}/module-section|Introduction and Acknowledgements}}
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This work was partially funded by CAPES and CNPq, a Brazillian Agencies. Information on CAPES can be obtained on the [http://www.capes.gov.br/ CAPES website] and [http://www.cnpq.br/ CNPq website].<br>
Author: Antonio Carlos da S. Senra Filho, CSIM Laboratory (University of Sao Paulo, Department of Computing and Mathematics)<br>
Contact: Antonio Carlos da S. Senra Filho <email>acsenrafilho@usp.br</email><br>
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|Image:CSIM-logo.png|CSIM Laboratory
|Image:USP-logo.png|University of Sao Paulo
|Image:CNPq-logo.png|CNPq Brazil
|Image:CAPES-logo.png|CAPES Brazil
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{{documentation/{{documentation/version}}/module-section|Extension Description}}
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[[Image:AnomalousDiffusionExtension-logo.png|left]]

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 adopted the so-called porous media equation, allowing the super-diffusive and the sub-diffusive processes <ref>Tsallis, C. (2009). Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World. Springer.</ref>. In porous media, channels are created promoting or blocking the flow of the density function, which has been proved to provide a suitable application for MRI noise attenuation <ref>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</ref>.

Basically, there are two different filters already implementing the anomalous diffusion process: the isotropic anomalous diffusion and anisotropic anomalous diffusion filters <ref>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</ref>. These filters were already applied on different imaging MR modalities, such as structural T1 and T2 images <ref>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</ref>, diffusion-weighted images (DWI and DTI)<ref>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</ref><ref>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.</ref>, MRI relaxation T1 and T2 relaxometry<ref>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</ref> and to fMRI<ref>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</ref> as an initial study.


{{documentation/{{documentation/version}}/extension-section|Modules}}
* '''Structural image denoising with tissues border preservation function''': [[Documentation/{{documentation/version}}/Modules/AADImageFilter|AAD Image Filter]]
* '''Structural image denoising without tissues border preservation function''': [[Documentation/{{documentation/version}}/Modules/IADImageFilter|IAD Image Filter]]
* '''Diffusion-weighted MR image denoising with tissues border preservation''': [[Documentation/{{documentation/version}}/Modules/AADDiffusionWeightedData|AAD on DWI Image]]
* '''Echo-planar imaging denoising with tissues border preservation (fMRI and ASL)''': [[Documentation/{{documentation/version}}/Modules/AADEPIData|AAD on EPI Image]]


{{documentation/{{documentation/version}}/module-section|Use Cases}}
Most frequently used for these scenarios:
* Use Case 1: Noise reduction as a pre-processing step for tissue segmentation
**When dealing with single voxel classification schemes, a noise reduction pre-processing step is usually helpful to reduce data fluctuation due to acquisition artifacts (e.g. reducing the number of misclassified voxels).
* Use Case 2: Volume rendering
**Noise reduction will result in nicer looking volume renderings
* Use Case 3: Noise reduction as part of image processing pipeline
**Could offer a better segmentation and classification on specific brain image analysis such as in Multiple Sclerosis lesion segmentation
<gallery widths="400px" heights="400px" perrow="3">
Image:MRI_raw.png|Raw T1 weighted MRI Image
Image:MRI_AAD.png|T1 weighted MRI Image with AAD filter (q=1.2)
Image:MRI_IAD.png|T1 weighted MRI Image with IAD filter (q=1.2)
Image:DTI_FA_raw.png|DTI-FA map without image filtering process
Image:DTI_FA_AAD.png|DTI-FA map with AAD image filtering (q=0.4)
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{{documentation/{{documentation/version}}/extension-section|Similar Extensions}}
*[[Documentation/{{documentation/version}}/Modules/GradientAnisotropicDiffusion|Gradient Anisotropic Diffusion]]


{{documentation/{{documentation/version}}/extension-section|References}}
* 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), pp.2355–2373. DOI: 10.1088/0031-9155/60/6/2355
* Filho, A.C. da S.S. et al., 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. IEEE, pp. 3893–3896.
* Filho, A.C. da S.S., Barizon, G.C. & Junior, L.O.M., 2014. Myocardium Segmentation Improvement with Anisotropic Anomalous Diffusion Filter Applied to Cardiac Magnetic Resonance Imaging. In Annual Meeting of Computing in Cardiology.
* Filho, A.C. da S.S. et al., 2014. Brain Activation Inhomogeneity Highlighted by the Isotropic Anomalous Diffusion Filter. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Chicago: IEEE, pp. 3313–3316.
* Senra Filho, A.C. da S., Duque, J.J. & Murta, L.O., 2013. Isotropic anomalous filtering in Diffusion-Weighted Magnetic Resonance Imaging. I. E. in M. and B. Society, ed. Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference, 2013, pp.4022–5.


{{documentation/{{documentation/version}}/extension-section|Information for Developers}}
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Repositories:
* Source code: [https://github.com/CSIM-Toolkits/AnomalousFiltersExtension GitHub repository]
* Issue tracker: [https://github.com/CSIM-Toolkits/AnomalousFiltersExtension/issues open issues and enhancement requests]


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Documentation/4.10/Extensions/AnomalousFilters - Revision history

UpdateBot: Nightly -> 4.10