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. """
  22. #from akvo.tressel import pca
  23. import akvo.tressel.cpca as pca
  24. if np.shape(x) != np.shape(R[0]): # or np.shape(x) != np.shape(rx1):
  25. print ("Error, non aligned")
  26. exit(1)
  27. if PCA == "Yes":
  28. # PCA decomposition on ref channels so signals are less related
  29. R, K, means = pca.pca( R )
  30. if all(H0) == 0:
  31. H = np.zeros( (len(R)*M))
  32. #print ("resetting filter")
  33. else:
  34. H = H0
  35. Rn = np.ones(len(R)*M) / mu
  36. r_ = np.zeros( (len(R), M) )
  37. e = np.zeros(len(x)) # error, desired output
  38. ilambda = lambda2**-1
  39. cdef int z
  40. cdef int ir
  41. for z in range(0, len(x)):
  42. # Only look forwards, to avoid distorting the lates times
  43. # (run backwards, if opposite and you don't care about distorting very late time.)
  44. for ir in range(len(R)):
  45. if z < M:
  46. r_[ir,0:z] = R[ir][0:z]
  47. r_[ir,z:M] = 0
  48. else:
  49. # TODO, use np.delete and np.append to speed this up
  50. r_[ir,:] = R[ir][z-M:z]
  51. # reshape
  52. r_n = np.reshape(r_, -1) #concatenate((r_v, r_h ))
  53. #K = np.dot( np.diag(Rn,0), r_n) / (lambda2 + np.dot(r_n*Rn, r_n)) # Create/update K
  54. K = (Rn* r_n) / (lambda2 + np.dot(r_n*Rn, r_n)) # Create/update K
  55. e[z] = x[z] - np.dot(r_n.T, H) # e is the filtered signal, input - r(n) * Filter Coefs
  56. H += K*e[z]; # Update Filter Coefficients
  57. Rn = ilambda*Rn - ilambda*np.dot(np.dot(K, r_n.T), Rn) # Update R(n)
  58. return e, H
  59. def transferFunctionFFT(self, D, R, reg=1e-2):
  60. from akvo.tressel import pca
  61. """
  62. Computes the transfer function (H) between a Data channel and
  63. a number of Reference channels. The Matrices D and R are
  64. expected to be in the frequency domain on input.
  65. | R1'R1 R1'R2 R1'R3| |h1| |R1'D|
  66. | R2'R1 R2'R2 R2'R3| * |h2| = |R2'D|
  67. | R3'R1 R3'R2 R3'R3| |h3| |R3'D|
  68. Returns the corrected array
  69. """
  70. # PCA decomposition on ref channels so signals are less related
  71. #transMatrix, K, means = pca.pca( np.array([rx0, rx1]))
  72. #RR = np.zeros(( np.shape(R[0])[0]*np.shape(R[0])[1], len(R)))
  73. # RR = np.zeros(( len(R), np.shape(R[0])[0]*np.shape(R[0])[1] ))
  74. # for ir in range(len(R)):
  75. # RR[ir,:] = np.reshape(R[ir], -1)
  76. # transMatrix, K, means = pca.pca(RR)
  77. # #R rx0 = transMatrix[0,:]
  78. # # rx1 = transMatrix[1,:]
  79. # for ir in range(len(R)):
  80. # R[ir] = transMatrix[ir,0]
  81. import scipy.linalg
  82. import akvo.tressel.pca as pca
  83. # Compute as many transfer functions as len(R)
  84. # A*H = B
  85. nref = len(R)
  86. H = np.zeros( (np.shape(D)[1], len(R)), dtype=complex )
  87. for iw in range(np.shape(D)[1]):
  88. A = np.zeros( (nref, nref), dtype=complex )
  89. B = np.zeros( (nref) , dtype=complex)
  90. for ii in range(nref):
  91. for jj in range(nref):
  92. # build A
  93. A[ii,jj] = np.dot(R[ii][:,iw], R[jj][:,iw])
  94. # build B
  95. B[ii] = np.dot( R[ii][:,iw], D[:,iw] )
  96. # compute H(iw)
  97. #linalg.solve(a,b) if a is square
  98. #print "A", A
  99. #print "B", B
  100. # TODO, regularise this solve step? So as to not fit the spurious noise
  101. #print np.shape(B), np.shape(A)
  102. #H[iw, :] = scipy.linalg.solve(A,B)
  103. H[iw, :] = scipy.linalg.lstsq(A,B,cond=reg)[0]
  104. #print "lstqt", np.shape(scipy.linalg.lstsq(A,B))
  105. #print "solve", scipy.linalg.solve(A,B)
  106. #H[iw,:] = scipy.linalg.lstsq(A,B) # otherwise
  107. #H = np.zeros( (np.shape(D)[1], ) )
  108. #print H #A, B
  109. Error = np.zeros(np.shape(D), dtype=complex)
  110. for ir in range(nref):
  111. for q in range( np.shape(D)[0] ):
  112. #print "dimcheck", np.shape(H[:,ir]), np.shape(R[ir][q,:] )
  113. Error[q,:] += H[:,ir]*R[ir][q,:]
  114. return D - Error
  115. def adapt_filt_tworefFreq(self, x, rx0, rx1, M, lambda2=0.95):
  116. """ Frequency domain version of above
  117. """
  118. from akvo.tressel import pca
  119. pylab.figure()
  120. pylab.plot(rx0)
  121. pylab.plot(rx1)
  122. # PCA decomposition on ref channels so signals are less related
  123. transMatrix, K, means = pca.pca( np.array([rx0, rx1]))
  124. rx0 = transMatrix[:,0]
  125. rx1 = transMatrix[:,1]
  126. pylab.plot(rx0)
  127. pylab.plot(rx1)
  128. pylab.show()
  129. exit()
  130. if np.shape(x) != np.shape(rx0) or np.shape(x) != np.shape(rx1):
  131. print ("Error, non aligned")
  132. exit(1)
  133. wx = fft.rfft(x)
  134. wr0 = fft.rfft(rx0)
  135. wr1 = fft.rfft(rx1)
  136. H = np.zeros( (2*M), dtype=complex )
  137. ident_mat = np.eye((2*M))
  138. Rn = ident_mat / 0.1
  139. r_v = np.zeros( (M), dtype=complex )
  140. r_h = np.zeros( (M), dtype=complex )
  141. e = np.zeros(len(x), dtype=complex )
  142. ilambda = lambda2**-1
  143. for z in range(0, len(wx)):
  144. # TODO Padd with Zeros or truncate if M >,< arrays
  145. r_v = wr0[::-1][:M]
  146. r_h = wr1[::-1][:M]
  147. r_n = np.concatenate((r_v, r_h ))
  148. K = np.dot(Rn, r_n) / (lambda2 + np.dot(np.dot(r_n.T, Rn), r_n)) # Create/update K
  149. e[z] = wx[z] - np.dot(r_n,H) # e is the filtered signal, input - r(n) * Filter Coefs
  150. H += K * e[z]; # Update Filter Coefficients
  151. Rn = ilambda*Rn - ilambda*K*r_n.T*Rn # Update R(n)
  152. return fft.irfft(e)
  153. def iter_filt_refFreq(self, x, rx0, Ahat=.05, Bhat=.5, k=0.05):
  154. X = np.fft.rfft(x)
  155. X0 = np.copy(X)
  156. RX0 = np.fft.rfft(rx0)
  157. # step 0
  158. Abs2HW = []
  159. alphai = k * (np.abs(Ahat)**2 / np.abs(Bhat)**2)
  160. betai = k * (1. / (np.abs(Bhat)**2) )
  161. Hw = ((1.+alphai) * np.abs(X)**2 ) / (np.abs(X)**2 + betai*(np.abs(RX0)**2))
  162. H = np.abs(Hw)**2
  163. pylab.ion()
  164. pylab.figure()
  165. for i in range(10):
  166. #print "alphai", alphai
  167. #print "betai", betai
  168. #print "Hw", Hw
  169. alphai = k * (np.abs(Ahat)**2 / np.abs(Bhat)**2) * np.product(H, axis=0)
  170. betai = k * (1. / np.abs(Bhat)**2) * np.product(H, axis=0)
  171. # update signal
  172. Hw = ((1.+alphai) * np.abs(X)**2) / (np.abs(X)**2 + betai*np.abs(RX0)**2)
  173. Hw = np.nan_to_num(Hw)
  174. X *= Hw
  175. H = np.vstack( (H, np.abs(Hw)**2) )
  176. #print "Hw", Hw
  177. pylab.cla()
  178. pylab.plot(Hw)
  179. #pylab.plot(np.abs(X))
  180. #pylab.plot(np.abs(RX0))
  181. pylab.draw()
  182. raw_input("wait")
  183. pylab.cla()
  184. pylab.ioff()
  185. #return np.fft.irfft(X0-X)
  186. return np.fft.irfft(X)
  187. def iter_filt_refFreq(self, x, rx0, rx1, Ahat=.1, Bhat=1., k=0.001):
  188. X = np.fft.rfft(x)
  189. X0 = np.copy(X)
  190. RX0 = np.fft.rfft(rx0)
  191. RX1 = np.fft.rfft(rx1)
  192. # step 0
  193. alphai = k * (np.abs(Ahat)**2 / np.abs(Bhat)**2)
  194. betai = k * (1. / (np.abs(Bhat)**2) )
  195. #Hw = ((1.+alphai) * np.abs(X)**2 ) / (np.abs(X)**2 + betai*(np.abs(RX0)**2))
  196. H = np.ones(len(X)) # abs(Hw)**2
  197. #pylab.ion()
  198. #pylab.figure(334)
  199. for i in range(1000):
  200. #print "alphai", alphai
  201. #print "betai", betai
  202. #print "Hw", Hw
  203. alphai = k * (np.abs(Ahat)**2 / np.abs(Bhat)**2) * np.product(H, axis=0)
  204. betai = k * (1. / np.abs(Bhat)**2) * np.product(H, axis=0)
  205. # update signal
  206. Hw = ((1.+alphai) * np.abs(X)**2) / (np.abs(X)**2 + betai*np.abs(RX0)**2)
  207. Hw = np.nan_to_num(Hw)
  208. X *= Hw #.conjugate
  209. #H = np.vstack((H, np.abs(Hw)**2) )
  210. H = np.vstack((H, np.abs(Hw)) )
  211. #print "Hw", Hw
  212. #pylab.cla()
  213. #pylab.plot(Hw)
  214. #pylab.plot(np.abs(X))
  215. #pylab.plot(np.abs(RX0))
  216. #pylab.draw()
  217. #raw_input("wait")
  218. #pylab.cla()
  219. #pylab.ioff()
  220. return np.fft.irfft(X0-X)
  221. #return np.fft.irfft(X)
  222. def Tdomain_DFT(self, desired, input, S):
  223. """ Lifted from Adaptive filtering toolbox. Modefied to accept more than one input
  224. vector
  225. """
  226. # Initialisation Procedure
  227. nCoefficients = S["filterOrderNo"]/2+1
  228. nIterations = len(desired)
  229. # Pre Allocations
  230. errorVector = np.zeros(nIterations, dtype='complex')
  231. outputVector = np.zeros(nIterations, dtype='complex')
  232. # Initial State
  233. coefficientVectorDFT = np.fft.rfft(S["initialCoefficients"])/np.sqrt(float(nCoefficients))
  234. desiredDFT = np.fft.rfft(desired)
  235. powerVector = S["initialPower"]*np.ones(nCoefficients)
  236. # Improve source code regularity, pad with zeros
  237. # TODO, confirm zeros(nCoeffics) not nCoeffics-1
  238. prefixedInput = np.concatenate([np.zeros(nCoefficients-1), np.array(input)])
  239. # Body
  240. pylab.ion()
  241. pylab.figure(11)
  242. for it in range(nIterations): # = 1:nIterations,
  243. regressorDFT = np.fft.rfft(prefixedInput[it:it+nCoefficients][::-1]) /\
  244. np.sqrt(float(nCoefficients))
  245. # Summing two column vectors
  246. powerVector = S["alpha"] * (regressorDFT*np.conjugate(regressorDFT)) + \
  247. (1.-S["alpha"])*(powerVector)
  248. pylab.cla()
  249. #pylab.plot(prefixedInput[::-1], 'b')
  250. #pylab.plot(prefixedInput[it:it+nCoefficients][::-1], 'g', linewidth=3)
  251. #pylab.plot(regressorDFT.real)
  252. #pylab.plot(regressorDFT.imag)
  253. pylab.plot(powerVector.real)
  254. pylab.plot(powerVector.imag)
  255. #pylab.plot(outputVector)
  256. #pylab.plot(errorVector.real)
  257. #pylab.plot(errorVector.imag)
  258. pylab.draw()
  259. #raw_input("wait")
  260. outputVector[it] = np.dot(coefficientVectorDFT.T, regressorDFT)
  261. #errorVector[it] = desired[it] - outputVector[it]
  262. errorVector[it] = desiredDFT[it] - outputVector[it]
  263. #print errorVector[it], desired[it], outputVector[it]
  264. # Vectorized
  265. coefficientVectorDFT += (S["step"]*np.conjugate(errorVector[it])*regressorDFT) /\
  266. (S['gamma']+powerVector)
  267. return np.real(np.fft.irfft(errorVector))
  268. #coefficientVector = ifft(coefficientVectorDFT)*sqrt(nCoefficients);
  269. def Tdomain_DCT(self, desired, input, S):
  270. """ Lifted from Adaptive filtering toolbox. Modefied to accept more than one input
  271. vector. Uses cosine transform
  272. """
  273. from scipy.fftpack import dct
  274. # Initialisation Procedure
  275. nCoefficients = S["filterOrderNo"]+1
  276. nIterations = len(desired)
  277. # Pre Allocations
  278. errorVector = np.zeros(nIterations)
  279. outputVector = np.zeros(nIterations)
  280. # Initial State
  281. coefficientVectorDCT = dct(S["initialCoefficients"]) #/np.sqrt(float(nCoefficients))
  282. desiredDCT = dct(desired)
  283. powerVector = S["initialPower"]*np.ones(nCoefficients)
  284. # Improve source code regularity, pad with zeros
  285. prefixedInput = np.concatenate([np.zeros(nCoefficients-1), np.array(input)])
  286. # Body
  287. #pylab.figure(11)
  288. #pylab.ion()
  289. for it in range(0, nIterations): # = 1:nIterations,
  290. regressorDCT = dct(prefixedInput[it:it+nCoefficients][::-1], type=2)
  291. #regressorDCT = dct(prefixedInput[it+nCoefficients:it+nCoefficients*2+1])#[::-1])
  292. # Summing two column vectors
  293. powerVector = S["alpha"]*(regressorDCT) + (1.-S["alpha"])*(powerVector)
  294. #pylab.cla()
  295. #pylab.plot(powerVector)
  296. #pylab.draw()
  297. outputVector[it] = np.dot(coefficientVectorDCT.T, regressorDCT)
  298. #errorVector[it] = desired[it] - outputVector[it]
  299. errorVector[it] = desiredDCT[it] - outputVector[it]
  300. # Vectorized
  301. coefficientVectorDCT += (S["step"]*errorVector[it]*regressorDCT) #/\
  302. #(S['gamma']+powerVector)
  303. #pylab.plot(errorVector)
  304. #pylab.show()
  305. return dct(errorVector, type=3)
  306. #coefficientVector = ifft(coefficientVectorDCT)*sqrt(nCoefficients);
  307. def Tdomain_CORR(self, desired, input, S):
  308. from scipy.linalg import toeplitz
  309. from scipy.signal import correlate
  310. # Autocorrelation
  311. ac = np.correlate(input, input, mode='full')
  312. ac = ac[ac.size/2:]
  313. R = toeplitz(ac)
  314. # cross correllation
  315. r = np.correlate(desired, input, mode='full')
  316. r = r[r.size/2:]
  317. #r = np.correlate(desired, input, mode='valid')
  318. print ("R", np.shape(R))
  319. print ("r", np.shape(r))
  320. print ("solving")
  321. #H = np.linalg.solve(R,r)
  322. H = np.linalg.lstsq(R,r,rcond=.01)[0]
  323. #return desired - np.dot(H,input)
  324. print ("done solving")
  325. pylab.figure()
  326. pylab.plot(H)
  327. pylab.title("H")
  328. #return desired - np.convolve(H, input, mode='valid')
  329. #return desired - np.convolve(H, input, mode='same')
  330. #return np.convolve(H, input, mode='same')
  331. return desired - np.dot(toeplitz(H), input)
  332. #return np.dot(R, H)
  333. # T = toeplitz(input)
  334. # print "shapes", np.shape(T), np.shape(desired)
  335. # h = np.linalg.lstsq(T, desired)[0]
  336. # print "shapes", np.shape(h), np.shape(input)
  337. # #return np.convolve(h, input, mode='same')
  338. # return desired - np.dot(T,h)
  339. def Fdomain_CORR(self, desired, input, dt, freq):
  340. from scipy.linalg import toeplitz
  341. # Fourier domain
  342. Input = np.fft.rfft(input)
  343. Desired = np.fft.rfft(desired)
  344. T = toeplitz(Input)
  345. #H = np.linalg.solve(T, Desired)
  346. H = np.linalg.lstsq(T, Desired)[0]
  347. # ac = np.correlate(Input, Input, mode='full')
  348. # ac = ac[ac.size/2:]
  349. # R = toeplitz(ac)
  350. #
  351. # r = np.correlate(Desired, Input, mode='full')
  352. # r = r[r.size/2:]
  353. #
  354. # #r = np.correlate(desired, input, mode='valid')
  355. # print "R", np.shape(R)
  356. # print "r", np.shape(r)
  357. # print "solving"
  358. # H = np.linalg.solve(R,r)
  359. # #H = np.linalg.lstsq(R,r)
  360. # #return desired - np.dot(H,input)
  361. # print "done solving"
  362. pylab.figure()
  363. pylab.plot(H.real)
  364. pylab.plot(H.imag)
  365. pylab.plot(Input.real)
  366. pylab.plot(Input.imag)
  367. pylab.plot(Desired.real)
  368. pylab.plot(Desired.imag)
  369. pylab.legend(["hr","hi","ir","ii","dr","di"])
  370. pylab.title("H")
  371. #return desired - np.fft.irfft(Input*H)
  372. return np.fft.irfft(H*Input)
  373. def Tdomain_RLS(self, desired, input, S):
  374. """
  375. A DFT is first performed on the data. Than a RLS algorithm is carried out
  376. for noise cancellation. Related to the RLS_Alt Algoritm 5.3 in Diniz book.
  377. The desired and input signals are assummed to be real time series data.
  378. """
  379. # Transform data into frequency domain
  380. Input = np.fft.rfft(input)
  381. Desired = np.fft.rfft(desired)
  382. # Initialisation Procedure
  383. nCoefficients = S["filterOrderNo"]+1
  384. nIterations = len(Desired)
  385. # Pre Allocations
  386. errorVector = np.zeros(nIterations, dtype="complex")
  387. outputVector = np.zeros(nIterations, dtype="complex")
  388. errorVectorPost = np.zeros(nIterations, dtype="complex")
  389. outputVectorPost = np.zeros(nIterations, dtype="complex")
  390. coefficientVector = np.zeros( (nCoefficients, nIterations+1), dtype="complex" )
  391. # Initial State
  392. coefficientVector[:,1] = S["initialCoefficients"]
  393. S_d = S["delta"]*np.eye(nCoefficients)
  394. # Improve source code regularity, pad with zeros
  395. prefixedInput = np.concatenate([np.zeros(nCoefficients-1, dtype="complex"),
  396. np.array(Input)])
  397. invLambda = 1./S["lambda"]
  398. # Body
  399. pylab.ion()
  400. pylab.figure(11)
  401. for it in range(nIterations):
  402. regressor = prefixedInput[it:it+nCoefficients][::-1]
  403. # a priori estimated output
  404. outputVector[it] = np.dot(coefficientVector[:,it].T, regressor)
  405. # a priori error
  406. errorVector[it] = Desired[it] - outputVector[it]
  407. psi = np.dot(S_d, regressor)
  408. if np.isnan(psi).any():
  409. print ("psi", psi)
  410. exit(1)
  411. pylab.cla()
  412. #pylab.plot(psi)
  413. pylab.plot(regressor.real)
  414. pylab.plot(regressor.imag)
  415. pylab.plot(coefficientVector[:,it].real)
  416. pylab.plot(coefficientVector[:,it].imag)
  417. pylab.legend(["rr","ri", "cr", "ci"])
  418. pylab.draw()
  419. raw_input("paws")
  420. S_d = invLambda * (S_d - np.dot(psi, psi.T) /\
  421. S["lambda"] + np.dot(psi.T, regressor))
  422. coefficientVector[:,it+1] = coefficientVector[:,it] + \
  423. np.conjugate(errorVector[it])*np.dot(S_d, regressor)
  424. # A posteriori estimated output
  425. outputVectorPost[it] = np.dot(coefficientVector[:,it+1].T, regressor)
  426. # A posteriori error
  427. errorVectorPost[it] = Desired[it] - outputVectorPost[it]
  428. errorVectorPost = np.nan_to_num(errorVectorPost)
  429. pylab.figure(11)
  430. print (np.shape(errorVectorPost))
  431. pylab.plot(errorVectorPost.real)
  432. pylab.plot(errorVectorPost.imag)
  433. pylab.show()
  434. print(errorVectorPost)
  435. #return np.fft.irfft(Desired)
  436. return np.fft.irfft(errorVectorPost)
  437. if __name__ == "__main__":
  438. def noise(nu, t, phi):
  439. return np.sin(nu*2.*np.pi*t + phi)
  440. import matplotlib.pyplot as plt
  441. print("Test driver for adaptive filtering")
  442. Filt = AdaptiveFilter(.1)
  443. t = np.arange(0, .5, 1e-4)
  444. omega = 2000 * 2.*np.pi
  445. T2 = .100
  446. n1 = noise(60, t, .2 )
  447. n2 = noise(61, t, .514 )
  448. x = np.sin(omega*t)* np.exp(-t/T2) + 2.3*noise(60, t, .34) + 1.783*noise(31, t, 2.1)
  449. e = Filt.adapt_filt_tworef(x, n1, n2, 200, .98)
  450. plt.plot(t, x)
  451. plt.plot(t, n1)
  452. plt.plot(t, n2)
  453. plt.plot(t, e)
  454. plt.show()