Surface NMR processing and inversion GUI
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  1. import numpy as np
  2. from numpy.linalg import lstsq
  3. from numpy.linalg import norm
  4. from numpy import fft
  5. import pylab
  6. from scipy.signal import correlate
  7. def autocorr(x):
  8. #result = np.correlate(x, x, mode='full')
  9. result = correlate(x, x, mode='full')
  10. return result[result.size/2:]
  11. class AdaptiveFilter:
  12. def __init__(self, mu):
  13. self.mu = mu
  14. def adapt_filt_Ref(self, x, R, M, mu, PCA, lambda2=0.95, H0=0):
  15. """ Taken from .m file
  16. This function is written to allow the user to filter a input signal
  17. with an adaptive filter that utilizes 2 reference signals instead of
  18. the standard method which allows for only 1 reference signal.
  19. Author: Rob Clemens Date: 3/16/06
  20. Modified and ported to Python, now takes arbitray number of reference points
  21. Original public domain source
  22. https://www.mathworks.com/matlabcentral/fileexchange/10447-noise-canceling-adaptive-filter
  23. x = data array
  24. R = reference array
  25. M = number of taps
  26. mu = forgetting factor
  27. PCA = Perform PCA
  28. """
  29. #from akvo.tressel import pca
  30. import akvo.tressel.pca as pca
  31. if np.shape(x) != np.shape(R[0]): # or np.shape(x) != np.shape(rx1):
  32. print ("Error, non aligned")
  33. exit(1)
  34. if PCA == "Yes":
  35. #print("Performing PCA calculation in noise cancellation")
  36. # PCA decomposition on ref channels so signals are less related
  37. R, K, means = pca.pca( R )
  38. # test for in loop reference
  39. #print("Cull nearly zero terms?", np.shape(x), np.shape(R))
  40. #R = R[0:3,:]
  41. #R = R[2:4,:]
  42. #print(" removed zero terms?", np.shape(x), np.shape(R))
  43. #H0 = H0[0:3*np.shape(x)[0]]
  44. #H0 = H0[0:2*np.shape(x)[0]]
  45. if all(H0) == 0:
  46. # corrects for dimensionality issues if a simple 0 is passed
  47. H = np.zeros( (len(R)*M))
  48. else:
  49. H = H0
  50. Rn = np.ones(len(R)*M) / mu
  51. r_ = np.zeros( (len(R), M) )
  52. e = np.zeros(len(x)) # error, in our case the desired output
  53. ilambda = lambda2**-1
  54. for ix in range(0, len(x)):
  55. # Only look forwards, to avoid distorting the lates times
  56. # (run backwards, if opposite and you don't care about distorting very late time.)
  57. for ir in range(len(R)): # number of reference channels
  58. if ix < M:
  59. r_[ir,0:ix] = R[ir][0:ix]
  60. r_[ir,ix:M] = 0
  61. else:
  62. r_[ir,:] = R[ir][ix-M:ix]
  63. # reshape
  64. r_n = np.reshape(r_, -1) # concatenate the ref channels in to a 1D array
  65. K = (Rn* r_n) / (lambda2 + np.dot(r_n*Rn, r_n)) # Create/update K
  66. e[ix] = x[ix] - np.dot(r_n.T, H) # e is the filtered signal, input - r(n) * Filter Coefs
  67. H += K*e[ix]; # Update Filter Coefficients
  68. Rn = ilambda*Rn - ilambda*np.dot(np.dot(K, r_n.T), Rn) # Update R(n)
  69. return e, H
  70. def transferFunctionFFT(self, D, R, reg=1e-2):
  71. from akvo.tressel import pca
  72. """
  73. Computes the transfer function (H) between a Data channel and
  74. a number of Reference channels. The Matrices D and R are
  75. expected to be in the frequency domain on input.
  76. | R1'R1 R1'R2 R1'R3| |h1| |R1'D|
  77. | R2'R1 R2'R2 R2'R3| * |h2| = |R2'D|
  78. | R3'R1 R3'R2 R3'R3| |h3| |R3'D|
  79. Returns the corrected array
  80. """
  81. # PCA decomposition on ref channels so signals are less related
  82. #transMatrix, K, means = pca.pca( np.array([rx0, rx1]))
  83. #RR = np.zeros(( np.shape(R[0])[0]*np.shape(R[0])[1], len(R)))
  84. # RR = np.zeros(( len(R), np.shape(R[0])[0]*np.shape(R[0])[1] ))
  85. # for ir in range(len(R)):
  86. # RR[ir,:] = np.reshape(R[ir], -1)
  87. # transMatrix, K, means = pca.pca(RR)
  88. # #R rx0 = transMatrix[0,:]
  89. # # rx1 = transMatrix[1,:]
  90. # for ir in range(len(R)):
  91. # R[ir] = transMatrix[ir,0]
  92. import scipy.linalg
  93. import akvo.tressel.pca as pca
  94. # Compute as many transfer functions as len(R)
  95. # A*H = B
  96. nref = len(R)
  97. H = np.zeros( (np.shape(D)[1], len(R)), dtype=complex )
  98. for iw in range(np.shape(D)[1]):
  99. A = np.zeros( (nref, nref), dtype=complex )
  100. B = np.zeros( (nref) , dtype=complex)
  101. for ii in range(nref):
  102. for jj in range(nref):
  103. # build A
  104. A[ii,jj] = np.dot(R[ii][:,iw], R[jj][:,iw])
  105. # build B
  106. B[ii] = np.dot( R[ii][:,iw], D[:,iw] )
  107. # compute H(iw)
  108. #linalg.solve(a,b) if a is square
  109. #print "A", A
  110. #print "B", B
  111. # TODO, regularise this solve step? So as to not fit the spurious noise
  112. #print np.shape(B), np.shape(A)
  113. #H[iw, :] = scipy.linalg.solve(A,B)
  114. H[iw, :] = scipy.linalg.lstsq(A,B,cond=reg)[0]
  115. #print "lstqt", np.shape(scipy.linalg.lstsq(A,B))
  116. #print "solve", scipy.linalg.solve(A,B)
  117. #H[iw,:] = scipy.linalg.lstsq(A,B) # otherwise
  118. #H = np.zeros( (np.shape(D)[1], ) )
  119. #print H #A, B
  120. Error = np.zeros(np.shape(D), dtype=complex)
  121. for ir in range(nref):
  122. for q in range( np.shape(D)[0] ):
  123. #print "dimcheck", np.shape(H[:,ir]), np.shape(R[ir][q,:] )
  124. Error[q,:] += H[:,ir]*R[ir][q,:]
  125. return D - Error