def denoise(nblck,filename,mode='sym', wv='sym5' ):
from statsmodels.robust import mad
#noisy_coefs = pywt.wavedec(nblck, 'sym5', level=5, mode='per')
noisy_coefs = pywt.wavedec(nblck, wavelet=wv, mode=mode) #level=5, #dwt is for single level decomposition; wavedecoding is for more levels
sigma = mad(noisy_coefs[-1])
#uthresh=np.std(ca)/2
uthresh = sigma*np.sqrt(2*np.log(len(nblck)))
denoised = noisy_coefs[:]
denoised[1:] = [pywt.threshold(i, value=uthresh,mode='soft') for i in denoised[1:]]
signal = pywt.waverec(denoised, wavelet=wv, mode=mode)
from matplotlib import pyplot as plt
fig, axes = plt.subplots(1, 2, sharey=True, sharex=True,figsize=(8,4))
ax1, ax2 = axes
ax1.plot(signal)
#ax1.set_xlim(0,2**10)
ax1.set_title("Recovered Signal")
ax1.margins(.1)
ax2.plot(nblck)
ax2.set_title("Noisy Signal")
for ax in fig.axes:
ax.tick_params(labelbottom=False, top=False, bottom=False, left=False, right=False)
fig.tight_layout()
fig.savefig(filename+'_'+wv+'.pdf')
plt.clf()
return signal
def wavelet_trasnform(sig):
mode = pywt.Modes.smooth
w = 'coif3'
w = pywt.Wavelet(w)
# hasil=[]
# for n in range(data.shape[0]):
#dd = data[n,1:24]
ca = []
cd = []
for i in range(5):
(a, d) = pywt.dwt(sig, w, mode)
ca.append(a)
cd.append(d)
rec_a = []
rec_d = []
for i, coeff in enumerate(ca):
coeff_list = [coeff, None] + [None] * i
rec_a.append(pywt.waverec(coeff_list, w))
for i, coeff in enumerate(cd):
coeff_list = [None, coeff] + [None] * i
rec_d.append(pywt.waverec(coeff_list, w))
# hasil.append(rec_a[0])
return rec_a[0];
def waverec_lin(x,wavelet,mode="per",sc_lengths=None):
"""Reconstructs the timeseries from the wavelet-coefficients as returned by wavedec_lin."""
assert len(x.shape) in [1,2], "Only 1d and 2d-arrays supported up to now!"
if sc_lengths != None:
assert sum(sc_lengths) == x.shape[0], "The values given for sc_lengths don't make sense!"
else:
sc_lengths = []
l = x.shape[0]
while l>1:
l/=2
sc_lengths.insert(0,l)
sc_lengths.insert(0,l)
assert sum(sc_lengths) == x.shape[0], "The values automatically calculated for sc_lengths don't make sense!"
if len(x.shape) == 1:
wts = []
for j in range(len(sc_lengths)):
offset = sum(sc_lengths[:j])
wts.append(x[offset:offset+sc_lengths[j]])
rv = waverec(wts,wavelet,mode=mode)
else: #len(x.shape)==2
for i in range(x.shape[1]):
wts = []
for j in range(len(sc_lengths)):
offset = sum(sc_lengths[:j])
wts.append(x[offset:offset+sc_lengths[j],i])
if i==0:
ar = waverec(wts,wavelet,mode=mode)
rv = n.zeros((ar.shape[0],x.shape[1]),"d")
rv[:,i] = ar
rv[:,i] = waverec(wts,wavelet,mode=mode)
return rv
def ApproximationsV(data, family, levels):
"""
get approximation reconstrutions at different levels
for a DWT family.
returns levels+1 arrays with A[0]=full reconstruction,
and A[1]=first approx, A[levels] is smoothest
"""
# subtract off mean data
meandata=np.mean(data)
#meandata=0.0
# get DWT coefficients
coeffs = pywt.wavedec(data-meandata, family, mode='sym',level=Nlevels)
lcoeffs=len(coeffs)
for i,l in enumerate(coeffs):
vl=np.var(l)
l[:]=vl
coeffs[i]=l
#print "len coeffs",lcoeffs
#for i in coeffs: print len(i)
# reconstruct approximations
A=[]
c=pywt.waverec(coeffs,family,mode='sym')
A.append(np.array(c)+meandata)
for j in range(Nlevels,0,-1):
coeffs[j][0:]=0.0
c=pywt.waverec(coeffs,family,mode='sym')
A.append(np.array(c)+meandata)
return A
def _wm_reverse(self, wd):
if __debug__:
debug('MAP', "Performing iDWT")
signal = None
wd_offsets = [0] + list(np.cumsum(self.lengths))
nlevels = len(self.lengths)
Ntime_points = self._intimepoints #len(time_points)
# unfortunately sometimes due to padding iDWT would return longer
# sequences, thus we just limit to the right ones
for indexes in _get_indexes(wd.shape, self._dim):
if __debug__:
debug('MAP_', " %s" % (indexes,), lf=False, cr=True)
wd_sample = wd[indexes]
wd_coeffs = [wd_sample[wd_offsets[i]:wd_offsets[i+1]] for i in xrange(nlevels)]
# need to compose original list
time_points = pywt.waverec(
wd_coeffs, wavelet=self._wavelet, mode=self._mode)
if signal is None:
newdim = list(wd.shape)
newdim[self._dim] = Ntime_points
signal = np.empty(newdim)
signal[indexes] = time_points[:Ntime_points]
if __debug__:
debug('MAP_', "")
debug('MAP', "Done iDWT. Total size %s" % (signal.shape, ))
return signal
def filterData(self, icurr, Fs): """ Denoise an ionic current time-series and store it in self.eventData :Parameters: - `icurr` : ionic current in pA - `Fs` : original sampling frequency in Hz """ # self.eventData=icurr self.Fs=Fs # Set up the wavelet w=pywt.Wavelet(self.waveletType) # Calculate the maximum wavelet level for the data length self.maxWaveletLevel=pywt.dwt_max_level(len(icurr), filter_len=w.dec_len) # Perform a wavelet decomposition to the specified level wcoeff = pywt.wavedec(icurr, w, mode='sym', level=self.waveletLevel) # Perform a simple threshold by setting all the detailed coefficients # up to level n-1 to zero thresh=np.std(wcoeff[-1])*self._thselect(wcoeff, self.waveletThresholdSubType) thrfunc=self.thrtypedict[self.waveletThresholdType] # print thresh, np.std(wcoeff[-1]) wcoeff[1:] = [ thrfunc(wc, thresh) for wc in wcoeff[1:] ] # for i in range(1, self.waveletLevel): # wcoeff[-i]=np.zeros(len(wcoeff[-i])) # Reconstruct the signal with the thresholded wavelet coefficients self.eventData = pywt.waverec(wcoeff, self.waveletType, mode='sym')
def filter(self, mode='soft'):
if self.level > self.max_dec_level():
clevel = self.max_dec_level()
else:
clevel = self.level
# decompose
coeffs = pywt.wavedec(self.sig, pywt.Wavelet(self.wt), \
mode=self.mode, \
level=clevel)
# threshold evaluation
th = sqrt(2 * log(len(self.sig)) * power(self.sigma, 2))
# thresholding
for (i, cAD) in enumerate(coeffs):
if mode == 'soft':
coeffs[i] = pywt.thresholding.soft(cAD, th)
elif mode == 'hard':
coeffs[i] = pywt.thresholding.hard(cAD, th)
# reconstruct
rec_sig = pywt.waverec(coeffs, pywt.Wavelet(self.wt), mode=self.mode)
if len(rec_sig) == (len(self.sig) + 1):
self.sig = rec_sig[:-1]
def wave_stein_filter(y, sigma, tau, w):
coeffs = pywt.wavedec(y, w)
threshold = sigma * tau
hcoeffs = []
for scale, x in enumerate(coeffs):
hcoeffs.append(stein_thresholding(x, threshold))
return pywt.waverec(hcoeffs, w)
def wave_semisoft_filter(y, sigma, tau, w, mu):
coeffs = pywt.wavedec(y, w)
threshold = sigma * tau
hcoeffs = []
for scale, x in enumerate(coeffs):
hcoeffs.append(thresholding_semisoft(x, threshold, mu))
return pywt.waverec(hcoeffs, w)
def soft_threshold(bins, tau, level=1, plot=False):
coeffs = pywt.wavedec(bins, 'haar', level=level)
old_coeffs = copy.deepcopy(coeffs) if plot else None
coeffs[1:] = [sign(a) * np.maximum(0, abs(a)-tau) for a in coeffs[1:] ]
filtered = pywt.waverec(coeffs, 'haar')
if plot:
from matplotlib import pyplot as pl
fig = pl.figure(figsize=(15,8))
fig.suptitle("Level %d Wavelet Decomposition" % level)
fig.subplots_adjust(hspace=0.3, wspace=0.3)
ax = fig.add_subplot(2,1,1)
ax.plot(bins, label='Raw')
ax.plot(filtered, label='Filtered')
ax.legend()
ax = fig.add_subplot(2,level,1+level)
ax.set_title("Approximation coefficients")
ax.plot(coeffs[0])
for l in range(1,level):
ax = fig.add_subplot(2, level, 1+l+level)
ax.plot(old_coeffs[l])
ax.axhline(-tau, color='g'); ax.axhline(+tau, color='g')
ax.set_title("Level %d detail coefficients" % l)
fig.savefig('wavelet-analysis.pdf')
return filtered
def haar(vals, p=80): hC = pywt.wavedec(vals,'haar') cutVal = np.percentile(np.abs(np.concatenate(hC)), p) for A in hC: A[np.abs(A) < cutVal] = 0 tVals = pywt.waverec(hC,'haar') return tVals[:len(vals)]
def _call(self, coeff):
"""Compute the discrete 1D, 2D or 3D inverse wavelet transform.
Parameters
----------
coeff : `DiscreteLpVector`
Returns
-------
arr : `DiscreteLpVector`
"""
if len(self.range.shape) == 1:
coeff_list = array_to_pywt_coeff(coeff, self.size_list)
x = pywt.waverec(coeff_list, self.wbasis, self.mode)
return self.range.element(x)
elif len(self.range.shape) == 2:
coeff_list = array_to_pywt_coeff(coeff, self.size_list)
x = pywt.waverec2(coeff_list, self.wbasis, self.mode)
return self.range.element(x)
elif len(self.range.shape) == 3:
coeff_dict = array_to_pywt_coeff(coeff, self.size_list)
x = wavelet_reconstruction3d(coeff_dict, self.wbasis, self.mode,
self.nscales)
return self.range.element(x)
def generateCompression(cumHist, wavelet, compression): # Do a full multilevel wavelet decomposition until some level/resolution coeffs = pywt.wavedec(cumHist, wavelet) # Reduce trailing equal values from vectors vectors, lengths = reduceVectors(coeffs, 0.01) # Overwrite least significant detail coefficients in coeffs with 0-arrays (simulating removal) if compression < len(vectors): for i in range(compression,len(vectors)): arraySize = len(vectors[i]) vectors[i] = np.zeros(arraySize) # Generate statistics stored = len(lengths) traildel = 0 for i in range(0,min(len(vectors), compression)): stored += len(vectors[i]) traildel += lengths[i] - len(vectors[i]) # Restore trailing equal values restoredCoeffs = restoreVectors(vectors, lengths) # Do a full multilevel wavelet reconstruction from coeffs (zero-padded) recCumHist = pywt.waverec(restoredCoeffs, wavelet) return restoredCoeffs, recCumHist, stored, traildel, coeffs
def filter(self):
if self.level > self.max_dec_level():
clevel = self.max_dec_level()
else:
clevel = self.level
# decompose
coeffs = pywt.wavedec(self.sig, pywt.Wavelet(self.wt), \
mode=self.mode, \
level=clevel)
# threshold evaluation
th = sqrt(2 * log(len(self.sig)) * power(self.sigma, 2))
# thresholding
for (i, cAD) in enumerate(coeffs):
if i == 0:
continue
coeffs[i] = sign(cAD) * pywt.thresholding.less(abs(cAD), th)
# reconstruct
rec_sig = pywt.waverec(coeffs, pywt.Wavelet(self.wt), mode=self.mode)
if len(rec_sig) == (len(self.sig) + 1):
self.sig = rec_sig[:-1]
def denoise(self, data, wavelet):
noiseSigma = median(absolute(data - median(data))) / 0.6745
levels = int(floor(log(len(data))))
WC = pywt.wavedec(data, wavelet, level=levels)
threshold = noiseSigma * sqrt(2 * log(len(data)))
NWC = map(lambda x: pywt.thresholding.hard(x, threshold), WC)
return pywt.waverec(NWC, wavelet)
def plot(data, w, title):
print title
w = pywt.Wavelet(w)
a = data
ca = []
cd = []
for i in xrange(5):
(a, d) = pywt.dwt(a, w, mode)
ca.append(a)
cd.append(d)
rec_a = []
rec_d = []
for i, coeff in enumerate(ca):
coeff_list = [coeff, None] + [None] * i
rec_a.append(pywt.waverec(coeff_list, w))
for i, coeff in enumerate(cd):
coeff_list = [None, coeff] + [None] * i
rec_d.append(pywt.waverec(coeff_list, w))
pylab.figure()
ax_main = pylab.subplot(len(rec_a) + 1, 1, 1)
pylab.title(title)
ax_main.plot(data)
pylab.xlim(0, len(data) - 1)
pylab.locator_params(axis = 'y', nbins = 5)
pylab.subplots_adjust(hspace=.5)
for i, y in enumerate(rec_a):
#print len(data), len(x), len(data) / (2**(i+1))
ax = pylab.subplot(len(rec_a) + 1, 2, 3 + i * 2)
ax.plot(y, 'r')
pylab.xlim(0, 65)
pylab.ylabel("Coef%d" % (i + 1))
pylab.locator_params(axis = 'y', nbins = 5)
for i, y in enumerate(rec_d):
ax = pylab.subplot(len(rec_d) + 1, 2, 4 + i * 2)
ax.plot(y, 'g')
pylab.xlim(0, 65)
#pylab.ylim(min(0,1.4*min(x)), max(0,1.4*max(x)))
pylab.ylabel("D%d" % (i + 1))
pylab.locator_params(axis = 'y', nbins = 5)
def sure_shrink_denoise(f, wave, v):
true_coefs = pywt.wavedec(f, wave, level=None)
res = [sure_shrink_fast(coef) for coef in true_coefs[1:]]
den_coefs, thresholds = zip(*res)
den_coefs = list(den_coefs)
den_coefs.insert(0, true_coefs[0])
f_denoised = pywt.waverec(den_coefs, wave)
return f_denoised
def visu_shrink_denoise(f, wave, v):
true_coefs = pywt.wavedec(f, wave, level=2)
res = [visu_shrink(coef) for coef in true_coefs]
den_coefs, thresholds = zip(*res)
den_coefs = list(den_coefs)
#den_coefs.insert(0, true_coefs[0])
f_denoised = pywt.waverec(den_coefs, wave)
return f_denoised
def idwt(E): # print E E_rep=E.tolist()[0:2] for i in range(1,int(pow(len(E),0.5))): E_rep.append(E[pow(2,i):pow(2,i+1)]) E_idwt=pywt.waverec(E_rep,'db1') # print E_idwt return matrix(E_idwt)
def waveletpreprocess(X,threshold=20,threshold2=40): wave_coefs = pywt.wavedec(X,'haar',mode='sym',level=10) for coefs in wave_coefs[1:]: coefs[np.abs(coefs)<=threshold]=0 bcast = [coef>threshold and coef<=threshold2 for coef in np.abs(coefs)] coefs[bcast] = np.sign(coefs[bcast])*(threshold2*(np.abs(coefs[bcast])-threshold)/(threshold2-threshold)) filtered_signal=pywt.waverec(wave_coefs,'haar') return filtered_signal
def rmatvec(x):
x_list = []
count = 0
for el in b:
n_el = np.asarray(el).size
x_list.append(np.array(x[count:count+n_el]))
count += n_el
return pywt.waverec(x_list, wavelet, mode=mode)
def test_waverec_none():
x = [3, 7, 1, 1, -2, 5, 4, 6]
coeffs = pywt.wavedec(x, 'db1')
# set some coefficients to None
coeffs[2] = None
coeffs[0] = None
assert_(pywt.waverec(coeffs, 'db1').size, len(x))
def test_waverec_axis_db2():
# test for fix to issue gh-293
rstate = np.random.RandomState(0)
data = rstate.standard_normal((16, 16))
for axis in [0, 1]:
coefs = pywt.wavedec(data, 'db2', axis=axis)
rec = pywt.waverec(coefs, 'db2', axis=axis)
assert_allclose(rec, data, atol=1e-14)
def waveletDenoise(data, threshold=1, wavelet='haar'):
""" Wavelet denoise test """
# Decompose
wl_dec = pywt.wavedec(data, pywt.Wavelet(wavelet))
# Threshold
wl_thr = map(lambda x: pywt.thresholding.soft(x, threshold), wl_dec)
# Reconstruct
return pywt.waverec(wl_thr, wavelet)
def test_waverec_axes_subsets():
rstate = np.random.RandomState(0)
data = rstate.standard_normal((8, 8, 8))
# test all combinations of 1 out of 3 axes transformed
for axis in [0, 1, 2]:
coefs = pywt.wavedec(data, 'haar', axis=axis)
rec = pywt.waverec(coefs, 'haar', axis=axis)
assert_allclose(rec, data, atol=1e-14)
def wavelet_smoother(ts,long_cut=np.inf,short_cut=0,wavelet='db4',preserve_gamma=True): ''' Smooth ts using the wavelet specified. @long_cut is the longest wavelength to keep. @short_cut is the shortest wavelength to keep. @normalize will normalize positive and negative contributions after smoothing. ''' smooth_long=True smooth_short=True if long_cut >= len(ts): smooth_long=False if short_cut < 1: smooth_short=False # No smoothing needed if smooth_long == False and smooth_short == False: return ts # Oversmoothed; Output 0. if long_cut <= short_cut or short_cut >= len(ts): return ts*0 if preserve_gamma==True: avg=np.average(ts) rawts=ts-avg coeffs=pywt.wavedec(rawts,wavelet) #indices of short and long wavelengths. if smooth_short==True: si=np.log2((1.0*len(ts))/short_cut) if si >= len(coeffs): smooth_short=False if smooth_long == True: li=np.log2((1.0*len(ts))/long_cut) if li >= len(coeffs): return ts*0 if smooth_long==True: intpart=int(li) fracpart=li-intpart for i in range(intpart): coeffs[i]*=0 coeffs[intpart]*=1-fracpart if smooth_short==True: intpart=int(si) fracpart=si-intpart for i in range(intpart+1,len(coeffs)): coeffs[i]*=0 coeffs[intpart]*=fracpart smoothts=pywt.waverec(coeffs,wavelet) # Normalization step, ensures the positive and negative # parts of smoothed match those of ts. "Preserves gamma" if preserve_gamma==True: smoothts+=avg return np.array(smoothts)
def test_waverec_accuracies():
rstate = np.random.RandomState(1234)
x0 = rstate.randn(8)
for dt, tol in dtypes_and_tolerances:
x = x0.astype(dt)
if np.iscomplexobj(x):
x += 1j*rstate.randn(8).astype(x.real.dtype)
coeffs = pywt.wavedec(x, 'db1')
assert_allclose(pywt.waverec(coeffs, 'db1'), x, atol=tol, rtol=tol)
def dot(self, m):
d = []
if m.shape[0] != m.size:
for i in xrange(m.shape[1]):
sizes_col = self.sizes[i]
sizes = np.zeros(len(sizes_col) + 1)
sizes[1:] = np.cumsum(sizes_col)
c = [m[:, i][sizes[k]:sizes[k + 1]] for k in xrange(0, len(sizes) - 1)]
d.append(pywt.waverec(c, self.name))
return np.asarray(d).T
else:
sizes_col = self.sizes[0]
sizes = np.zeros(len(sizes_col) + 1)
sizes[1:] = np.cumsum(sizes_col)
m = [m[sizes[k]:sizes[k + 1]] for k in xrange(0, len(sizes) - 1)]
return pywt.waverec(m, self.name)
def test_waverec_all_wavelets_modes():
# test 2D case using all wavelets and modes
rstate = np.random.RandomState(1234)
r = rstate.randn(80)
for wavelet in wavelist:
for mode in pywt.Modes.modes:
coeffs = pywt.wavedec(r, wavelet, mode=mode)
assert_allclose(pywt.waverec(coeffs, wavelet, mode=mode),
r, rtol=tol_single, atol=tol_single)
def Denoise(sig):
"""
Wavelet denoise
"""
coeffs = pywt.wavedec(sig, 'db6', level=9)
coeffs[-1] = np.zeros(len(coeffs[-1]))
coeffs[-2] = np.zeros(len(coeffs[-2]))
coeffs[0] = np.zeros(len(coeffs[0]))
sig_filt = pywt.waverec(coeffs, 'db6')
return sig_filt
def filterOperation(self):
w = pywt.Wavelet('db11')
a = self.sequence
ca, cd = [], []
for i in range(2):
(a, d) = pywt.dwt(a, w)
ca.append(a)
cd.append(d)
rec_a, rec_d = [], []
for i, coeff in enumerate(ca):
coeff_list = [coeff, None] + [None] * i
rec_a.append(pywt.waverec(coeff_list, w))
for i, coeff in enumerate(cd):
coeff_list = [None, coeff] + [None] * i
rec_d.append(pywt.waverec(coeff_list, w))
return rec_a[-1]
def FreqWarp(img, v, wavelet='db4',level=2, mode='constant'):
"Applies warp based on a wavelet decomposition"
if v <= 0: return img
seq_len = img.shape[-1]
level = 1 if level is None else level
new_x = random_cum_noise_generator(img[:img.shape[-1] // 2], magnitude=v)
coeff = pywt.wavedec(img.cpu(), wavelet, mode=mode, level=level)
coeff[1:] = [CubicSpline(np.arange(c.shape[-1]), c, axis=-1)(new_x[:c.shape[-1]]) for c in coeff[1:]]
output = img.new_tensor(pywt.waverec(coeff, wavelet, mode=mode)[..., :seq_len])
return output
def de_noising(x):
wavelet = 'haar'
level = 1
coeff = pywt.wavedec(x, wavelet, mode="per")
sigma = (1 / 0.6745) * maddest(coeff[-level])
uthresh = sigma * np.sqrt(2 * np.log(len(x)))
coeff[1:] = (pywt.threshold(i, value=uthresh, mode='hard')
for i in coeff[1:])
x_dn = pywt.waverec(coeff, wavelet, mode='per')
return x_dn
def doSingleCWTDenoise(x_in, wavelet="db4", level=1):
x = copy.copy(x_in)
coeff = pywt.wavedec(x, wavelet, mode="per")
sigma = mad(coeff[-level])
uthresh = sigma * np.sqrt(2 * np.log(len(x)))
coeff[1:] = (pywt.threshold(i, value=uthresh, mode="soft")
for i in coeff[1:])
y = pywt.waverec(coeff, wavelet, mode="per")
del (x)
return y
def emgdenoise(emgraw):
w = pywt.Wavelet('db8')
maxlev = pywt.dwt_max_level(len(emgraw), w.dec_len)
threshold = 0.06
coeffs = pywt.wavedec(emgraw, 'db8', level=maxlev)
for i in range(1, len(coeffs)):
coeffs[i] = pywt.threshold(coeffs[i], threshold * max(coeffs[i]))
dataout = pywt.waverec(coeffs, 'db8').astype('float32')
# print("denoise emg",dataout)
return dataout
def apply_signal_processing(df):
med = signal.medfilt(df['linear_acceleration.x'], kernel_size=9)
coeffs = pywt.wavedec(df['linear_acceleration.x'], wavelet='haar')
A = pywt.waverec(coeffs[:-3] + [None] * 3, 'haar')
lp = lowpass_filt(df, 75)
return med, A, lp
def dot(self, m):
d = []
if m.shape[0] != m.size:
for i in xrange(m.shape[1]):
sizes_col = self.sizes[i]
sizes = np.zeros(len(sizes_col) + 1)
sizes[1:] = np.cumsum(sizes_col)
c = [m[:, i][sizes[k]:sizes[k + 1]] for k in xrange(0, len(sizes) - 1)]
d.append(pywt.waverec(c, self.name))
return np.asarray(d).T
else:
sizes_col = self.sizes[0]
sizes = np.zeros(len(sizes_col) + 1)
sizes[1:] = np.cumsum(sizes_col)
m = [m[sizes[k]:sizes[k + 1]] for k in xrange(0, len(sizes) - 1)]
return pywt.waverec(m, self.name)
def lowpassfilter(signal, threshold=0.63, wavelet="db4"):
""" Deconstruct the series using a waveform. Apply a threshold filter
then reconstruct
"""
threshold = threshold * np.nanmax(signal)
coeff = pywt.wavedec(signal, wavelet, mode="per")
coeff[1:] = (pywt.threshold(i, value=threshold, mode="soft")
for i in coeff[1:])
reconstructed_signal = pywt.waverec(coeff, wavelet, mode="per")
return reconstructed_signal
def cD3_features(x):
Bands_D3 = np.empty((x.shape[0], x.shape[1], 448))
for i in range(x.shape[0]):
for ii in range(x.shape[1]):
cA3, cD3, cD2, cD1 = Dwt(x[i, ii, :])
cA3 = np.zeros(62)
cD2 = np.zeros(117)
cD1 = np.zeros(227)
Bands_D3[i, ii, :] = pywt.waverec([cA3, cD3, cD2, cD1], db4)
return Bands_D3
def wavelet_decomposition(self, arr, name="..", wvlt='sym9', write=True):
wavelet = pywt.Wavelet(wvlt)
scaler = MinMaxScaler(
feature_range=(0.0,
1.0)) # to normalize the data between 0 and 1.0
mode = pywt.Modes.smooth # unused now
approximations = []
details = []
data = a = arr
for i in range(6):
(a, d) = pywt.dwt(a, wavelet) # removed mode, jde to nahoru pak
approximations.append(a)
details.append(d)
rec_details = []
rec_approx = []
acka = ""
for i, coeff in enumerate(approximations):
coeff_list = [coeff, None] + [None] * i
fitted = scaler.fit_transform(
pywt.waverec(coeff_list, wavelet).reshape(-1, 1)) # scale data
a = []
for b in fitted[0:250]: # bad format, let's adapt it
a.extend(b)
acka += str(len(a)) + ";"
rec_approx.append(a)
for i, coeff in enumerate(details):
coeff_list = [None, coeff] + [None] * i
fitted = scaler.fit_transform(
pywt.waverec(coeff_list, wavelet).reshape(-1, 1))
a = []
for b in fitted[0:250]:
a.extend(b)
acka += str(len(a)) + ";"
rec_details.append(a)
if write:
with open("stats_wavs2.csv", "a") as f:
f.write(wvlt + ";" + name + ";" + acka + '\n')
return (rec_approx, rec_details) # return tuple
def principal_components(num_of_components, pca, shape,coeff_slices,wave):
selfies_output = 'selfie/principal/'
components = pca.components_
for x in range(num_of_components):
img = np.array([components[x, i] for i in range(len(components[0]))])
# coeffs_from_arr = pywt.array_to_coeffs(img, coeff_slices[x])
# cam_recon = pywt.waverecn(coeffs_from_arr, wavelet='db14')
c2a3, c2d3, c2d2, c2d1, cd3, cd2, cd1 = divide(img, coeff_slices[1])
cf = [c2a3, c2d3, c2d2, c2d1]
cd = pywt.waverec(cf, wavelet=wave)
cf2 = [cd, cd3, cd2, cd1]
cam_recon = pywt.waverec(cf2, wavelet=wave)
img = scale(cam_recon, 255)
cv2.imwrite(selfies_output + wave + 'principal' + str(x) + '.jpg',img.reshape(shape))
def denoise(data, family="db4", sigma=None, detrend=False):
coefs = pywt.wavedec(data, family, mode="per")
threshold = sigma * np.sqrt(2 * np.log(len(data)))
new_coefs = coefs.copy()
if detrend:
new_coefs[0] = np.zeros_like(new_coefs[0])
new_coefs[1:] = (pywt.threshold(c, value=threshold, mode="soft")
for c in coefs[1:])
y = pywt.waverec(new_coefs, family, mode="per")
return y
def waveletSmooth(x, wavelet="db4", level=1, title=None):
print("Running waveletSmooth :")
coeff = pywt.wavedec(x, wavelet, mode="per")
sigma = mad(coeff[-level])
uthresh = sigma * np.sqrt(2 * np.log(len(x)))
coeff[1:] = (pywt.threshold(i, value=uthresh, mode="soft")
for i in coeff[1:])
y = pywt.waverec(coeff, wavelet, mode="per")
return y
def wavelet_dec(data):
db4 = pywt.Wavelet('db4')
A5, D5, D4, D3, D2, D1 = pywt.wavedec(data, db4, mode='symmetric', level=5)
D5 = np.zeros(D5.shape[0])
D4 = np.zeros(D4.shape[0])
D3 = np.zeros(D3.shape[0])
D2 = np.zeros(D2.shape[0])
D1 = np.zeros(D1.shape[0])
data_rec = pywt.waverec([A5, D5, D4, D3, D2, D1], db4)
return data_rec
def multiscale_recompose(coeffs_array, split_indices, N=None):
"""
inverse of multiscale_decompose
"""
coeffs_list = np.split(coeffs_array, split_indices)
log_timeseries = pywt.waverec(coeffs_list, 'haar', pywt.MODES.cpd)
timeseries = np.exp(log_timeseries)
if N is not None:
timeseries = timeseries[:N]
return timeseries
def smooth_wavelet2D(indat,
wave='sym8',
nlevel=5,
ncycle=10,
threshtype='hard'):
"""
Compute the wavelet-denoised version of a set of profiles/waveforms.
Required argument:
- 'indat' = (nbins x nchans) data array.
Default arguments:
- 'wave' = mother wavelet (default 'sym8')
- 'nlevel' = number of decomposition levels (default '5')
- 'ncycle' = number of circulant averages to compute (default '10')
- 'threshtype' = type of wavelet thresholding (default 'hard')
"""
nbins = len(indat[:, 0])
nchan = len(indat[0, :])
outdat = np.zeros((nbins, nchan))
# smooth each channel.
for i in range(nchan):
prof = indat[:, i]
data = 0.
# carry out translation-invariant wavelet denoising.
for j in range(ncycle):
m = j - ncycle / 2 - 1
coeffs = pywt.wavedec(np.roll(prof, m), wave, level=nlevel)
# get threshold value.
lopt = np.median(np.fabs(coeffs[1])) / 0.6745 * np.sqrt(
2. * np.log(nbins))
# now do wavelet thresholding.
for k in range(1, nlevel + 1):
# hard threshold.
if (threshtype == 'hard'):
(coeffs[k])[np.where(np.fabs(coeffs[k]) < lopt)] = 0.
# or soft threshold.
else:
(coeffs[k])[np.where(np.fabs(coeffs[k]) < lopt)] = 0.
(coeffs[k])[np.where(
coeffs[k] > lopt)] = (coeffs[k])[np.where(
coeffs[k] > lopt)] + lopt
(coeffs[k])[np.where(
coeffs[k] < -lopt)] = (coeffs[k])[np.where(
coeffs[k] < -lopt)] - lopt
# reconstruct data.
data = data + np.roll(pywt.waverec(coeffs, wave), -m)
# save averaged profile.
outdat[:, i] = data / np.float(ncycle)
# return smoothed portrait.
return outdat
def autoRemoveMuscular(icas):
waveletLevel = 0
if len(icas) > 0:
# getting the level of decomposition for the wavelet transform
# muscular artifacts appear in the Beta band 16-31Hz
frq = icas[0].frequency
while frq >= 16:
frq = frq / 2
waveletLevel += 1
for ica in icas:
maxs = []
s1s = []
s2s = []
wavelets = []
for c in ica.components:
# applying soft thresholding to denoise, removing everything above 50Hz
c = pywt.threshold(c, 50, 'less')
# We use the Haar wavelet since it's the most similar to the muscular artifacts
waveletC = pywt.wavedec(c, 'Haar', level=waveletLevel)
wavelets.append(waveletC)
# wavelet[0] = Ca2 wavelet[waveletLevel-1] = Cd2 wavelet[waveletLevel] = Cd1
# padding Cd2 to make it same length of Cd1
new = []
cd2 = waveletC[waveletLevel - 1]
for i in range(len(waveletC[waveletLevel - 1])):
new.append(cd2[i])
new.append(0.0)
cd2 = np.array(new)
# getting the wavelet power spectral density
# elevating to power 2 the elements of Cd1
cd1 = np.power(waveletC[waveletLevel], 2)
# elevating to power 2 the elements of Cd2
cd2 = np.power(cd2, 2)
s1 = np.sum(cd1)
s1s.append(s1)
s2 = np.sum(cd2)
s2s.append(s2)
if s1 > s2:
maxs.append(s1)
else:
maxs.append(s2)
# getting the mean of all the peaks in the IC
mean = np.mean(maxs)
newComponents = []
for i in range(len(ica.components)):
if s1s[i] > mean:
# making all samples zero since it's an EMG artifact
wavelets[i][waveletLevel][:] = 0.0
if s2s[i] > mean:
# making all samples zero since it's an EMG artifact
wavelets[i][waveletLevel - 1][:] = 0.0
# recreating the component with the inverse wavelet transform
component = pywt.waverec(wavelets[i], 'Haar')
newComponents.append(component)
ica.components = newComponents
def WaveletSmooth(time, flux, threshold=1, wavelet='db6', all=False):
'''
WORK IN PROGRESS - DO NOT USE
Generate a wavelet transform of the data, clip on some noise level,
then do inverse wavelet to generate model.
Requires uniformly sampled data!
If your data has gaps, watch out....
'''
_, dl, dr = FindGaps(time)
if all is True:
dl = [0]
dr = [len(time)]
model = np.zeros_like(flux)
# now loop over every chunk of data and fit wavelet
for i in range(0, len(dl)):
flux_i = flux[dl[i]:dr[i]]
# Do basic wavelet decontruct
WC = pywt.wavedec(flux_i, wavelet)
# now do thresholding
# got some tips here:
# https://blancosilva.wordpress.com/teaching/mathematical-imaging/denoising-wavelet-thresholding/
# and:
# https://pywavelets.readthedocs.org/en/latest/ref/idwt-inverse-discrete-wavelet-transform.html
NWC = map(
lambda x: pywt.thresholding.hard(
x,
threshold * np.sqrt(2. * np.log(len(flux_i))) * np.std(flux_i)
), WC)
model_i = pywt.waverec(NWC, wavelet)
# print(len(flux_i), len(model_i), len(model[dl[i]:dr[i]]))
#
# print(model_i[0:10])
# print(model_i[-10:])
if len(model_i) != len(model[dl[i]:dr[i]]):
print("length error on gap ", i)
print(len(flux_i), len(model_i), len(model[dl[i]:dr[i]]))
model_i = model_i[1:]
model[dl[i]:dr[i]] = model_i
# WC = pywt.wavedec(flux, wavelet)
# NWC = map(lambda x: pywt.thresholding.soft(x,threshold * np.sqrt(2.*np.log(len(flux))) * np.std(flux)), WC)
# model = pywt.waverec(NWC, wavelet)
print(len(model), len(time))
return model
def visualize_reconstructed_signal_bylevel(coef_bank,
signal=None,
wv=None,
wavelet_type='coif4',
mode='symmetric',
plot_approximation_bkgd=True):
"""
Given DWT coefficient bank (list of array of DWT coefficients for each level), plot
"""
lvl = len(coef_bank) - 1
# initialize filtered coefficient bank
coef_bkgd = []
coef_filt = []
for coefs_lvl in coef_bank:
coef_bkgd.append(np.zeros(len(coefs_lvl), ))
if plot_approximation_bkgd:
coef_filt = coef_bkgd.copy()
coef_filt[0] = coef_bank[0]
fig, ax = plt.subplots(int(np.ceil((lvl + 1) / 3)),
3,
sharex='col',
sharey='row',
figsize=(16, 10))
color = ['k', 'm', 'b', 'g', 'orange', 'r']
# plot the various levels of coefficients
for l in range(lvl + 1):
# get plot indices
i = int(np.floor(l / 3))
j = l % 3
if not plot_approximation_bkgd:
coef_filt = coef_bkgd.copy()
coef_filt[l] = coef_bank[l]
if l == 0:
plot_title = 'Signal reconstruction using cA' + str(
lvl) + ' coefficients'
else:
if plot_approximation_bkgd:
plot_title = 'Signal reconstruction using cD' + str(
lvl - l + 1) + ' + cA5 coefficients'
else:
plot_title = 'Signal reconstruction using cD' + str(
lvl - l + 1) + ' coefficients'
sig_rec_partial = pywt.waverec(coef_filt,
wavelet_type,
mode=mode,
axis=-1)
if wv is None:
wv = np.arange(len(sig_rec_partial))
if signal is not None:
ax[i, j].plot(wv, signal, linewidth=0.25, color='grey')
ax[i, j].plot(wv, sig_rec_partial, linewidth=1, color=color[l - 1])
ax[i, j].title.set_text(plot_title)
plt.show()
def cal_cycle(self, data):
if len(data) % 2 == 1:
data = data[1:]
# We will use the Daubechies(4) wavelet
wname = self.wname
data = np.atleast_2d(data)
numwires, datalength = data.shape
# Initialize the container for the filtered data
fdata = np.empty((numwires, datalength))
for i in range(numwires):
# Decompose the signal
c = pywt.wavedec(data[i, :], wname, level=self.maxlevel)
#print c
# Destroy the approximation coefficients
#for j in self.filter_level:
# c[j][:] = 0
# Reconstruct the signal and save it
c[0][:] = pywt.threshold(c[0],
np.percentile(abs(c[0]), 100) + 1, 'soft',
0)
c[1][:] = pywt.threshold(c[1],
np.percentile(abs(c[1]), 100) + 1, 'soft',
0)
#c[2][:] = pywt.threshold(c[2], np.percentile(abs(c[2]), 100) + 1, 'soft', 0)
c[3][:] = pywt.threshold(c[3],
np.percentile(abs(c[3]), 100) + 1, 'soft',
0)
c[4][:] = pywt.threshold(c[4],
np.percentile(abs(c[4]), 100) + 1, 'soft',
0)
c[5][:] = pywt.threshold(c[5],
np.percentile(abs(c[5]), 100) + 1, 'soft',
0)
c[6][:] = pywt.threshold(c[6],
np.percentile(abs(c[6]), 100) + 1, 'soft',
0)
c[7][:] = pywt.threshold(c[7],
np.percentile(abs(c[7]), 100) + 1, 'soft',
0)
fdata[i, :] = pywt.waverec(c, wname)
fdata = fdata.ravel() # If the signal is 1D, return a 1D array
wave = fdata
spectrum = fft.fft(wave)
freq = fft.fftfreq(len(wave))
order = np.argsort(abs(spectrum)[:spectrum.size / 2])[::-1]
cycle = 1 / freq[order[:20]]
max_cycle = cycle[0] / 5
return max_cycle
def plot_signal_decomp(data, w, title):
"""Decompose and plot a signal S.
S = An + Dn + Dn-1 + ... + D1
"""
w = pywt.Wavelet(w)
a = data
ca = []
cd = []
for i in range(5):
(a, d) = pywt.dwt(a, w, mode)
ca.append(a)
cd.append(d)
rec_a = []
rec_d = []
for i, coeff in enumerate(ca):
coeff_list = [coeff, None] + [None] * i
rec_a.append(pywt.waverec(coeff_list, w))
for i, coeff in enumerate(cd):
coeff_list = [None, coeff] + [None] * i
rec_d.append(pywt.waverec(coeff_list, w))
fig = plt.figure()
ax_main = fig.add_subplot(len(rec_a) + 1, 1, 1)
ax_main.set_title(title)
ax_main.plot(data)
ax_main.set_xlim(0, len(data) - 1)
for i, y in enumerate(rec_a):
ax = fig.add_subplot(len(rec_a) + 1, 2, 3 + i * 2)
ax.plot(y, 'r')
ax.set_xlim(0, len(y) - 1)
ax.set_ylabel("A%d" % (i + 1))
for i, y in enumerate(rec_d):
ax = fig.add_subplot(len(rec_d) + 1, 2, 4 + i * 2)
ax.plot(y, 'g')
ax.set_xlim(0, len(y) - 1)
ax.set_ylabel("D%d" % (i + 1))
def wavelet(y, name):
noiseSigma = 0.16
levels = int(np.floor(np.log2(y.shape[0]))) - 3
coeffs = pywt.wavedec(data=y, wavelet=name, level=levels)
threshold = noiseSigma * np.sqrt(2 * np.log2(y.size))
NewWaveletCoeffs = list(
map(lambda x: pywt.threshold(x, threshold, mode='soft'), coeffs))
#print(NewWaveletCoeffs)
#print(levels)
New_y = pywt.waverec(NewWaveletCoeffs, wavelet=name)
return New_y
def cleanEELS_wavelet(data, threshold):
wave = pywt.Wavelet("sym4")
max_level = pywt.dwt_max_level(len(data), wave.dec_len)
coeffs = pywt.wavedec(data, "sym4", level=max_level)
coeffs2 = coeffs
threshold = 0.1
for ii in numba.prange(1, len(coeffs)):
coeffs2[ii] = pywt.threshold(coeffs[ii],
threshold * np.amax(coeffs[ii]))
data2 = pywt.waverec(coeffs2, "sym4")
return data2
def detrend_data(RR_array):
new_coeffs=[];
coeffs=pywt.wavedec(RR_array,'db3',mode='sp1',level=6);
cA6,cD6,cD5,cD4,cD3,cD2,cD1 = coeffs;
#print("cA is: " + str(cA));
#print("cD is: " + str(cD));
for i in range(len(cA6)):
cA6[i]=0;
new_coeffs=cA6,cD6,cD5,cD4,cD3,cD2,cD1;
RR_detrended=pywt.waverec(new_coeffs,'db3',mode='sp1');
return RR_detrended
def test_waverec_all_wavelets_modes():
# test 2D case using all wavelets and modes
rstate = np.random.RandomState(1234)
r = rstate.randn(80)
for wavelet in wavelist:
for mode in pywt.Modes.modes:
coeffs = pywt.wavedec(r, wavelet, mode=mode)
assert_allclose(pywt.waverec(coeffs, wavelet, mode=mode),
r,
rtol=tol_single,
atol=tol_single)
def WT(index_list, wavefunc='db4', lv=4, m=1, n=4, plot=False):
'''
WT: Wavelet Transformation Function
index_list: Input Sequence;
lv: Decomposing Level；
wavefunc: Function of Wavelet, 'db4' default；
m, n: Level of Threshold Processing
'''
# Decomposing
coeff = pywt.wavedec(
index_list, wavefunc, mode='sym',
level=lv) # Decomposing by levels，cD is the details coefficient
sgn = lambda x: 1 if x > 0 else -1 if x < 0 else 0 # sgn function
# Denoising
# Soft Threshold Processing Method
for i in range(
m, n + 1
): # Select m~n Levels of the wavelet coefficients，and no need to dispose the cA coefficients(approximation coefficients)
cD = coeff[i]
Tr = np.sqrt(2 * np.log2(len(cD))) # Compute Threshold
for j in range(len(cD)):
if cD[j] >= Tr:
coeff[i][j] = sgn(cD[j]) * (np.abs(cD[j]) - Tr
) # Shrink to zero
else:
coeff[i][j] = 0 # Set to zero if smaller than threshold
# Reconstructing
coeffs = {}
for i in range(len(coeff)):
coeffs[i] = copy.deepcopy(coeff)
for j in range(len(coeff)):
if j != i:
coeffs[i][j] = np.zeros_like(coeff[j])
for i in range(len(coeff)):
coeff[i] = pywt.waverec(coeffs[i], wavefunc)
if len(coeff[i]) > len(index_list):
coeff[i] = coeff[i][:-1]
if plot:
denoised_index = np.sum(coeff, axis=0)
data = pd.DataFrame({'CLOSE': index_list, 'denoised': denoised_index})
data.plot(figsize=(10, 10), subplots=(2, 1))
data.plot(figsize=(10, 5))
return coeff
def GetSignalList(filepath,pre_mode='no',lvbo_mode='no',lvbo1=8,low=0,high=0,wave1='sym5',wave2=3):
# this function just for test
print(filepath)
filepathaa1=os.path.abspath(filepath)
print('lalaal')
print(filepathaa1)
volt_data2 = sio.loadmat(filepath) # r'E:\huihuang_mat\4/4-11.mat'
volt_data2 = volt_data2['signal']
volt_data2 = volt_data2.reshape(volt_data2.shape[0],)
if pre_mode=="Min-Max Normalization":
volt_min=volt_data2.min()
volt_max=volt_data2.max()
volt_data2=(volt_data2-volt_min)/(volt_max-volt_min)
volt_data2=volt_data2*2-1
if pre_mode=="Mean Normaliztion":
volt_data2=(volt_data2 - volt_data2.mean())/volt_data2.std()
if lvbo_mode=="High filter":
high=float((2*high)/5000)
b, a = signal.butter(lvbo1, high, 'highpass')
volt_data2 = signal.filtfilt(b, a, volt_data2)
if lvbo_mode=="Low filter":
low=float((2*low)/5000)
b, a = signal.butter(lvbo1, 0.02, 'lowpass')
volt_data2 = signal.filtfilt(b, a, volt_data2)
if lvbo_mode=="Brand filter":
low=float((2*low)/5000)
high=float((2*high)/5000)
b, a = signal.butter(lvbo1, [low,high], 'bandpass')
volt_data2 = signal.filtfilt(b, a, volt_data2)
if lvbo_mode=="Wave filter": # 此处需要修改，只返回一个值，因为数据量太大，不支持有多个
w = pywt.Wavelet(wave1)#选取小波函数
a = volt_data2
ca = []#近似分量
cd = []#细节分量
mode = pywt.Modes.smooth
for i in range(5):
(a, d) = pywt.dwt(a, w, mode)#进行5阶离散小波变换
ca.append(a)
cd.append(d)
#选择特定的层数进行小波变换
coeff_list = [None,cd[wave2]] + [None] * wave2
volt_data2=pywt.waverec(coeff_list, w)
model_parfile='E:\\huihuang_mat\\4'
#sio.savemat(model_parfile+'\\signal_wyk2.mat', {'signal':volt_data2})
ecg = pywt.data.ecg()
data2=volt_data2.tolist()
return data2
def denoise1D(data, noiseSigma, wavelet='db3'):
"""performed the 1D denoising
data : a 1D numpy array
wavelet : the wavelet basis used,
"""
levels = ilog2(data.shape[0])
WC = pywt.wavedec(data, wavelet, level=levels)
threshold = noiseSigma * np.sqrt(2 * ilog2(data.size))
NWC = map(lambda x: pywt.thresholding.soft(x, threshold), WC)
return pywt.waverec(NWC, wavelet)
def wavelet_denoising(data):
db4 = pywt.Wavelet('db4')
coeffs = pywt.wavedec(data, db4,level=3)
for i in range(1,len(coeffs)):
coeffs[i]=pywt.threshold(coeffs[i],0.05*max(coeffs[i]))
meta = pywt.waverec(coeffs, db4)
return meta
def DWT_synthesize(self, coefs, slices, wavelet_name="db10"):
"""
Returns the original array from a numpy array that contains the
wavelet coefficients.
"""
wavelet = pywt.Wavelet(wavelet_name)
samples = np.empty(coefs.shape, dtype=np.int32)
decomposition_0 = pywt.array_to_coeffs(coefs[:, 0],
slices,
output_format="wavedec")
decomposition_1 = pywt.array_to_coeffs(coefs[:, 1],
slices,
output_format="wavedec")
samples[:, 0] = np.rint(
pywt.waverec(decomposition_0, wavelet=wavelet,
mode="per")).astype(np.int32)
samples[:, 1] = np.rint(
pywt.waverec(decomposition_1, wavelet=wavelet,
mode="per")).astype(np.int32)
return samples