#
#------------------------------------------------------------------------------
# Copyright (c) 2013-2014, Christian Therien
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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#
# dnoise.py - This file is part of the PySptools package.
#
from __future__ import division
import numpy as np
import os.path as osp
import pysptools.util as util
[docs]def whiten(M):
"""
Whitens a HSI cube. Use the noise covariance matrix to decorrelate
and rescale the noise in the data (noise whitening).
Results in transformed data in which the noise has unit variance
and no band-to-band correlations.
Parameters:
M: `numpy array`
2d matrix of HSI data (N x p).
Returns: `numpy array`
Whitened HSI data (N x p).
Reference:
Krizhevsky, Alex, Learning Multiple Layers of Features from
Tiny Images, MSc thesis, University of Toronto, 2009.
See Appendix A.
"""
sigma = util.cov(M)
U,S,V = np.linalg.svd(sigma)
S_1_2 = S**(-0.5)
S = np.diag(S_1_2.T)
Aw = np.dot(V, np.dot(S, V.T))
return np.dot(M, Aw)