# Source code for pysptools.noise.dnoise

#
#------------------------------------------------------------------------------
# Copyright (c) 2013-2014, Christian Therien
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
#------------------------------------------------------------------------------
#
# 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)