Denoising using Marchenko-Pastur Principal Component Analysis

"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
       
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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