"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

  MATLAB:
  [Signal, Sigma] = MPdenoising(data, mask, kernel, sampling)
       output:
           - Signal: [x, y, z, N] 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(...))
                    
  PYTHON:
  import mpdenoise as mp
  imgdn, sigma, nparameters = mp.denoise(img, kernel='5,5,5)
  
     output:
         - Signal [x, y, z, N] denoised data matrix
         - Sigma [x, y, z] noise map
         - N parameters [x, y, z] significant principal component map
     input:
         - data: [x, y, z, N] data matrix
         - kernel: (optional) window size, typically in order of [5 x 5 x 5]
         
 
  Authors: Jelle Veraart ([email protected]), Ben Ades-Aron ([email protected])
  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