Denoising using Marchenko-Pastur Principal Component Analysis
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"MPPCA": 4d image denoising and noise map estimation by exploiting data redundancy in the PCA domain using universal properties of the eigenspectrum of random covariance matrices, i.e. Marchenko Pastur distribution
[Signal, Sigma] = MPdenoising(data, mask, kernel, sampling) output: - Signal: [x, y, z, M] denoised data matrix - Sigma: [x, y, z] noise map input: - data: [x, y, z, M] data matrix - mask: (optional) region-of-interest [boolean] - kernel: (optional) window size, typically in order of [5 x 5 x 5] - sampling: 1. full: sliding window (default for noise map estimation, i.e. [Signal, Sigma] = MPdenoising(...)) 2. fast: block processing (default for denoising, i.e. [Signal] = MPdenoising(...)) Authors: Jelle Veraart (jelle.veraart@nyumc.org) Copyright (c) 2016 New York Universit and University of Antwerp Permission is hereby granted, free of charge, to any non-commercial entity ('Recipient') obtaining a copy of this software and associated documentation files (the 'Software'), to the Software solely for non-commercial research, including the rights to use, copy and modify the Software, subject to the following conditions: 1. The above copyright notice and this permission notice shall be included by Recipient in all copies or substantial portions of the Software. 2. THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIESOF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BELIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF ORIN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 3. In no event shall NYU be liable for direct, indirect, special, incidental or consequential damages in connection with the Software. Recipient will defend, indemnify and hold NYU harmless from any claims or liability resulting from the use of the Software by recipient. 4. Neither anything contained herein nor the delivery of the Software to recipient shall be deemed to grant the Recipient any right or licenses under any patents or patent application owned by NYU. 5. The Software may only be used for non-commercial research and may not be used for clinical care. 6. Any publication by Recipient of research involving the Software shall cite the references listed below.
References
Veraart, J.; Fieremans, E. & Novikov, D.S. Diffusion MRI noise mapping using random matrix theory Magn. Res. Med., 2016, early view, doi: 10.1002/mrm.26059

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