def test_swt_max_level():
# odd sized signal will warn about no levels of decomposition possible
assert_warns(UserWarning, pywt.swt_max_level, 11)
with warnings.catch_warnings():
warnings.simplefilter('ignore', UserWarning)
assert_equal(pywt.swt_max_level(11), 0)
# no warnings when >= 1 level of decomposition possible
assert_equal(pywt.swt_max_level(2), 1) # divisible by 2**1
assert_equal(pywt.swt_max_level(4*3), 2) # divisible by 2**2
assert_equal(pywt.swt_max_level(16), 4) # divisible by 2**4
assert_equal(pywt.swt_max_level(16*3), 4) # divisible by 2**4
def test_swt_max_level():
# odd sized signal will warn about no levels of decomposition possible
assert_warns(UserWarning, pywt.swt_max_level, 11)
with warnings.catch_warnings():
warnings.simplefilter('ignore', UserWarning)
assert_equal(pywt.swt_max_level(11), 0)
# no warnings when >= 1 level of decomposition possible
assert_equal(pywt.swt_max_level(2), 1) # divisible by 2**1
assert_equal(pywt.swt_max_level(4*3), 2) # divisible by 2**2
assert_equal(pywt.swt_max_level(16), 4) # divisible by 2**4
assert_equal(pywt.swt_max_level(16*3), 4) # divisible by 2**4
def test_swt_decomposition():
x = [3, 7, 1, 3, -2, 6, 4, 6]
db1 = pywt.Wavelet('db1')
(cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=2)
assert_allclose(cA1, [
7.07106781, 5.65685425, 2.82842712, 0.70710678, 2.82842712, 7.07106781,
7.07106781, 6.36396103
])
assert_allclose(cD1, [
-2.82842712, 4.24264069, -1.41421356, 3.53553391, -5.65685425,
1.41421356, -1.41421356, 2.12132034
])
expected_cA2 = [7, 4.5, 4, 5.5, 7, 9.5, 10, 8.5]
assert_allclose(cA2, expected_cA2, rtol=1e-12)
expected_cD2 = [3, 3.5, 0, -4.5, -3, 0.5, 0, 0.5]
assert_allclose(cD2, expected_cD2, rtol=1e-12, atol=1e-14)
# level=1, start_level=1 decomposition should match level=2
res = pywt.swt(cA1, db1, level=1, start_level=1)
cA2, cD2 = res[0]
assert_allclose(cA2, expected_cA2, rtol=1e-12)
assert_allclose(cD2, expected_cD2, rtol=1e-12, atol=1e-14)
coeffs = pywt.swt(x, db1)
assert_(len(coeffs) == 3)
assert_(pywt.swt_max_level(len(x)) == 3)
def c_dists(Y, use_swt=True, level_weights=False):
w = pywt.Wavelet('sym2')
if use_swt:
L = pywt.swt_max_level(Y.shape[0])
C = [pywt.swt(Y[:, i], w, level=L) for i in range(Y.shape[1])]
C = [[list(reshape(l[0], -1)) + list(reshape(l[1], -1)) for l in c]
for c in C]
else:
L = pywt.dwt_max_level(Y.shape[0], w)
C = [pywt.wavedec(Y[:, i], w, level=L) for i in range(Y.shape[1])]
if level_weights:
if use_swt:
raise NameError('No level weights with SWT')
Wc = [1. for x in range(1, L + 1)]
D = zeros((len(C), len(C)))
for i in range(len(C)):
for j in range(i + 1, len(C)):
d = sum([
distance.cosine(C[i][x], C[j][x]) * Wc[x] for x in range(L)
]) / sum(Wc)
D[i, j] = d
D[j, i] = d
return D
else:
Cn = []
for c in C:
cn = []
for l in c:
cn += list(l)
Cn.append(cn)
return abs(pdist(Cn, 'cosine'))
def test_swt_default_level_by_axis():
# make sure default number of levels matches the max level along the axis
wav = 'db2'
x = np.ones((2**3, 2**4, 2**5))
for axis in (0, 1, 2):
sdec = pywt.swt(x, wav, level=None, start_level=0, axis=axis)
assert_equal(len(sdec), pywt.swt_max_level(x.shape[axis]))
def test_swt_decomposition():
x = [3, 7, 1, 3, -2, 6, 4, 6]
db1 = pywt.Wavelet('db1')
atol = tol_double
(cA3, cD3), (cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=3)
expected_cA1 = [7.07106781, 5.65685425, 2.82842712, 0.70710678,
2.82842712, 7.07106781, 7.07106781, 6.36396103]
assert_allclose(cA1, expected_cA1, rtol=1e-8, atol=atol)
expected_cD1 = [-2.82842712, 4.24264069, -1.41421356, 3.53553391,
-5.65685425, 1.41421356, -1.41421356, 2.12132034]
assert_allclose(cD1, expected_cD1, rtol=1e-8, atol=atol)
expected_cA2 = [7, 4.5, 4, 5.5, 7, 9.5, 10, 8.5]
assert_allclose(cA2, expected_cA2, rtol=tol_double, atol=atol)
expected_cD2 = [3, 3.5, 0, -4.5, -3, 0.5, 0, 0.5]
assert_allclose(cD2, expected_cD2, rtol=tol_double, atol=atol)
expected_cA3 = [9.89949494, ] * 8
assert_allclose(cA3, expected_cA3, rtol=1e-8, atol=atol)
expected_cD3 = [0.00000000, -3.53553391, -4.24264069, -2.12132034,
0.00000000, 3.53553391, 4.24264069, 2.12132034]
assert_allclose(cD3, expected_cD3, rtol=1e-8, atol=atol)
# level=1, start_level=1 decomposition should match level=2
res = pywt.swt(cA1, db1, level=1, start_level=1)
cA2, cD2 = res[0]
assert_allclose(cA2, expected_cA2, rtol=tol_double, atol=atol)
assert_allclose(cD2, expected_cD2, rtol=tol_double, atol=atol)
coeffs = pywt.swt(x, db1)
assert_(len(coeffs) == 3)
assert_(pywt.swt_max_level(len(x)), 3)
def __init__(self, signal, wavelet):
super(SWTDistribution, self).__init__()
self.level = pywt.swt_max_level(signal.shape[0])
self.swt = np.asarray(
[D**2 for _, D in pywt.swt(signal, wavelet, level=self.level)])
self.value = np.flip(np.sum(self.swt, axis=1) / np.sum(self.swt),
axis=-1)
def get_swt_coeffs(self, img, wavelet='db1', downsample="True"):
p = self.get_image(img, gray=True)
# downsampling
if downsample:
p = pywt.dwt2(p, wavelet)[0]
# calculate maximum decomposition level
l_max = pywt.swt_max_level(min(np.shape(p)))
self.max_level = l_max
# Multilevel 2D stationary wavelet transform with wavelet filters.
coefs = pywt.swt2(p,
wavelet,
l_max,
start_level=0,
trim_approx=True,
norm=True)
# converting from float64 to uint8 to save memory
coefs[0] = coefs[0].astype(np.uint8)
for level in range(1, l_max):
coefs[level] = list(coefs[level])
for band in range(3):
picture = np.asarray(coefs[level][band])
picture -= np.min(picture)
picture *= 255 / np.max(picture)
picture = picture.astype(np.uint8)
coefs[level][band] = picture
return coefs
def get_wdc(signal):
num_dwt_scales = int(ConfigParams['NUM_WDC_SCALES'])
dwt_segment = pow(2, num_dwt_scales)
dwt_shift = len(signal) % dwt_segment
if dwt_shift != 0:
signal = signal[0:len(signal) - dwt_shift]
max_decomposition_level = pywt.swt_max_level(len(signal))
custom_wavelet = CustomWavelet
# custom_wavelet = pywt.Wavelet('bior1.5')
coeffs = pywt.swt(signal, custom_wavelet, level=num_dwt_scales, start_level=0)
wdc = []
wdc_shifts = [0, 1, 3, 7, 15, 31, 65]
for scale_id in range(0, num_dwt_scales):
wdc_current_scale = coeffs[num_dwt_scales - 1 - scale_id][1]
if scale_id > 0:
list_of_zeros = np.asarray([0] * wdc_shifts[scale_id])
wdc_current_scale = wdc_current_scale[0:-wdc_shifts[scale_id]]
wdc_current_scale = np.concatenate((list_of_zeros, wdc_current_scale))
wdc.append(wdc_current_scale)
return wdc
def get_wavelet_feature(lightcurve):
"""
Returns wavelet coefficients for a given lightcurve object.
Param
------
lightcurve: Lightcurve object
An instance of the Lightcurve class
"""
interp_flux = lightcurve.interp_flux
feats = []
for i in range(len(interp_flux)):
flux = interp_flux[i]
mlev = pywt.swt_max_level(len(flux))
coeffs = np.array(pywt.swt(flux, 'sym2', level=mlev))
npoints = len(coeffs[0, 0, :])
c = coeffs.reshape(mlev * 2, npoints).T
wavout = c.flatten('F')
feats.append(wavout)
lc_logger.info(
"Func get_wavelet_feature() extracted features from lightcurve " +
lightcurve.filename)
feats = np.array(feats)
return feats
def test_swt_default_level_by_axis():
# make sure default number of levels matches the max level along the axis
wav = 'db2'
x = np.ones((2**3, 2**4, 2**5))
for axis in (0, 1, 2):
sdec = pywt.swt(x, wav, level=None, start_level=0, axis=axis)
assert_equal(len(sdec), pywt.swt_max_level(x.shape[axis]))
def c_dists(Y,use_swt=True,level_weights=False):
w = pywt.Wavelet('sym2')
if use_swt:
L = pywt.swt_max_level(Y.shape[0])
C = [pywt.swt(Y[:,i],w,level=L) for i in range(Y.shape[1])]
C = [[list(reshape(l[0],-1)) + list(reshape(l[1],-1)) for l in c] for c in C]
else:
L = pywt.dwt_max_level(Y.shape[0],w)
C = [pywt.wavedec(Y[:,i],w,level=L) for i in range(Y.shape[1])]
if level_weights:
if use_swt:
raise NameError('No level weights with SWT')
Wc = [1. for x in range(1,L+1)]
D = zeros((len(C),len(C)))
for i in range(len(C)):
for j in range(i+1,len(C)):
d = sum([distance.cosine(C[i][x],C[j][x])*Wc[x] for x in range(L)])/sum(Wc)
D[i,j] = d
D[j,i] = d
return D
else:
Cn = []
for c in C:
cn = []
for l in c:
cn += list(l)
Cn.append(cn)
return abs(pdist(Cn,'cosine'))
def setup(self, n, wavelet):
try:
from pywt import swt2
except ImportError:
raise NotImplementedError("swt2 not available")
self.data = np.ones((n, n), dtype='float')
self.level = pywt.swt_max_level(n)
def test_swt_decomposition():
x = [3, 7, 1, 3, -2, 6, 4, 6]
db1 = pywt.Wavelet('db1')
(cA3, cD3), (cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=3)
expected_cA1 = [7.07106781, 5.65685425, 2.82842712, 0.70710678,
2.82842712, 7.07106781, 7.07106781, 6.36396103]
assert_allclose(cA1, expected_cA1)
expected_cD1 = [-2.82842712, 4.24264069, -1.41421356, 3.53553391,
-5.65685425, 1.41421356, -1.41421356, 2.12132034]
assert_allclose(cD1, expected_cD1)
expected_cA2 = [7, 4.5, 4, 5.5, 7, 9.5, 10, 8.5]
assert_allclose(cA2, expected_cA2, rtol=tol_double)
expected_cD2 = [3, 3.5, 0, -4.5, -3, 0.5, 0, 0.5]
assert_allclose(cD2, expected_cD2, rtol=tol_double, atol=1e-14)
expected_cA3 = [9.89949494, ] * 8
assert_allclose(cA3, expected_cA3)
expected_cD3 = [0.00000000, -3.53553391, -4.24264069, -2.12132034,
0.00000000, 3.53553391, 4.24264069, 2.12132034]
assert_allclose(cD3, expected_cD3)
# level=1, start_level=1 decomposition should match level=2
res = pywt.swt(cA1, db1, level=1, start_level=1)
cA2, cD2 = res[0]
assert_allclose(cA2, expected_cA2, rtol=tol_double)
assert_allclose(cD2, expected_cD2, rtol=tol_double, atol=1e-14)
coeffs = pywt.swt(x, db1)
assert_(len(coeffs) == 3)
assert_(pywt.swt_max_level(len(x)) == 3)
def multilevel_dwt_decomposition_example():
x = [3, 7, 1, 1, -2, 5, 4, 6]
# Multilevel DWT decomposition.
db1 = pywt.Wavelet('db1')
cA3, cD3, cD2, cD1 = pywt.wavedec(x, db1)
print('Approximation coefficients (level 3) =', cA3)
print('Detail coefficients (level 3) =', cD3)
print('Detail coefficients (level 2) =', cD2)
print('Detail coefficients (level 1) =', cD1)
# Multilevel IDWT reconstruction.
coeffs = pywt.wavedec(x, db1)
print('Signal reconstruction =', pywt.waverec(coeffs, db1))
# Multilevel stationary wavelet transform (SWT) decomposition.
x = [3, 7, 1, 3, -2, 6, 4, 6]
(cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=2)
print('Approximation coefficients (level 1) =', cA1)
print('Detail coefficients (level 1) =', cD1)
print('Approximation coefficients (level 2) =', cA2)
print('Detail coefficients (level 2) =', cD2)
[(cA2, cD2)] = pywt.swt(cA1, db1, level=1, start_level=1)
print('Approximation coefficients (level 2) =', cA2)
print('Detail coefficients (level 2) =', cD2)
coeffs = pywt.swt(x, db1)
print('Coefficients =', coeffs)
print('Length of coefficients =', len(coeffs))
print('Max level =', pywt.swt_max_level(len(x)))
def swt(data, wavelet, level=None):
"""
Stationary Wavelet Transform
This version is 2 orders of magnitude faster than the one in pywt
even though it uses pywt for all the calculations.
Input parameters:
data
One-dimensional data to transform
wavelet
Either the name of a wavelet or a Wavelet object
level
Number of levels
"""
if level is None:
level = pywt.swt_max_level(len(data))
num_levels = level
idata = data.copy()
res = []
for j in range(1,num_levels+1):
step_size = int(math.pow(2, j-1))
last_index = step_size
# allocate
cA = np.empty_like(data)
cD = np.empty_like(data)
for first in xrange(last_index): # 0 to last_index - 1
# Getting the indices that we will transform
indices = np.arange(first, len(cD), step_size)
# select the even indices
even_indices = indices[0::2]
# select the odd indices
odd_indices = indices[1::2]
# get the even
(cA1,cD1) = pywt.dwt(idata[indices], wavelet, 'per')
cA[even_indices] = cA1
cD[even_indices] = cD1
# then the odd
(cA1,cD1) = pywt.dwt(np.roll(idata[indices],-1), wavelet, 'per')
cA[odd_indices] = cA1
cD[odd_indices] = cD1
# set the data for the next loop
idata = cA
# prepend the result
res.insert(0,(cA,cD))
return res
def swt(data, wavelet, level=None):
"""
Stationary Wavelet Transform
This version is 2 orders of magnitude faster than the one in pywt
even though it uses pywt for all the calculations.
Input parameters:
data
One-dimensional data to transform
wavelet
Either the name of a wavelet or a Wavelet object
level
Number of levels
"""
if level is None:
level = pywt.swt_max_level(len(data))
num_levels = level
idata = data.copy()
res = []
for j in range(1,num_levels+1):
step_size = int(math.pow(2, j-1))
last_index = step_size
# allocate
cA = np.empty_like(data)
cD = np.empty_like(data)
for first in xrange(last_index): # 0 to last_index - 1
# Getting the indices that we will transform
indices = np.arange(first, len(cD), step_size)
# select the even indices
even_indices = indices[0::2]
# select the odd indices
odd_indices = indices[1::2]
# get the even
(cA1,cD1) = pywt.dwt(idata[indices], wavelet, 'per')
cA[even_indices] = cA1
cD[even_indices] = cD1
# then the odd
(cA1,cD1) = pywt.dwt(np.roll(idata[indices],-1), wavelet, 'per')
cA[odd_indices] = cA1
cD[odd_indices] = cD1
# set the data for the next loop
idata = cA
# prepend the result
res.insert(0,(cA,cD))
return res
def getSWTcoeflist(self,MaxLevel = 9):
# crop two leads
self.rawsig = self.crop_data_for_swt(self.rawsig)
print '-'*3
print 'len(rawsig)= ',len(self.rawsig)
print 'SWT maximum level =',pywt.swt_max_level(len(self.rawsig))
coeflist = pywt.swt(self.rawsig,'db6',MaxLevel)
cAlist,cDlist = zip(*coeflist)
self.cAlist = cAlist
self.cDlist = cDlist
def main():
noise_sigma = 2
wavelet = 'bior1.3'
images = list(io.load_fits_images_in_folder('./resources'))
with PdfPages('multipage.pdf') as pdf:
for i, (calibrated_image, npe_truth) in tqdm(enumerate(images)):
fig = plt.figure()
plt.text(1, 1, 'Event Number: {}'.format(i))
plt.xlim(0, 2)
plt.ylim(0, 2)
plt.axis('off')
pdf.savefig(fig)
plt.close()
# transform the image
level = pywt.swt_max_level(len(calibrated_image))
# print('maximum level of decomposition: {}'.format(level))
coeff_list = pywt.swt2(calibrated_image, wavelet, level)
fig = plot.coefficients(coeff_list)
pdf.savefig(figure=fig)
plt.close()
levels = [0.889, 0.7, 0.586]
coeff_list = denoise.thresholding(coeff_list,
sigma_d=noise_sigma,
kind='hard',
sigma_levels=levels)
# coeff_list = denoise.wiener(coeff_list)
reconstructed_image = pywt.iswt2(coeff_list, wavelet)
fig = plot.results(calibrated_image, reconstructed_image,
npe_truth)
pdf.savefig(figure=fig)
plt.close()
fig = plot.pixel_histogram(
reconstructed_image,
calibrated_image,
npe_truth,
labels=['reconstructed', 'calibrated', 'npe mc truth'],
bins=60)
pdf.savefig(figure=fig)
plt.close()
def denoise(self):
"""denoise the data using the 2stage kurtosis denoising"""
#make sure the data has a len dividible by 2^2
self.len_swt = self.len
while not (self.len_swt / 4).is_integer():
self.len_swt -= 1
inp = self.input_nobase[:self.len_swt]
self.wave = pywt.Wavelet(self.wave_type)
nLevel = pywt.swt_max_level(self.len_swt)
self.coeffs = pywt.swt(inp, self.wave, level=2)
print(" \t Denoise STW coefficients \t %1.2f %1.2f" %
(self.TK, self.TT))
(cA2, cD2), (cA1, cD1) = self.coeffs
# rolling kurtosis
k2 = self._rolling_kts(cD2, self.nwin)
k1 = self._rolling_kts(cD1, self.nwin)
# thresholding
cD2[k2 < self.TK] = 0
cD1[k1 < self.TK] = 0
cA2[k2 < self.TK] = 0
cA1[k1 < self.TK] = 0
# universal threshold
sigma_roll_1 = mad(cD1[cD1 != 0]) * np.ones(self.len_swt)
uthresh_roll_1 = self.TT * sigma_roll_1 * np.sqrt(
2 * np.log(self.len_swt))
cD1[abs(cD1) < uthresh_roll_1] = 0
# universal threshold
sigma_roll_2 = mad(cD2[cD2 != 0]) * np.ones(self.len_swt)
uthresh_roll_2 = self.TT * sigma_roll_2 * np.sqrt(
2 * np.log(self.len_swt))
cD2[abs(cD2) < uthresh_roll_2] = 0
# final threshold
cA1[cD1 == 0] = 0
cA2[cD2 == 0] = 0
self.denoised_coeffs = [(cA1, cD1), (cA2, cD2)]
# denoise the data
#self.input_denoised = self._iswt(self.denoised_coeffs,self.wave)
self.input_denoised = pywt.iswt(self.denoised_coeffs, self.wave)
def _swt(self, sequence):
""" Use stationary wavelet transform method. """
details_filename = self.options.out_filename + '_details.txt'
details_handle = open(details_filename, 'w')
padded_sequence = self._pad_sequence(sequence)
sequence_encoding = self.encode_sequence(padded_sequence)
level = pywt.swt_max_level(len(sequence_encoding))
coeffs = pywt.swt(sequence_encoding, 'haar', level)
for (cA, cD) in coeffs:
approx_handle.write('\t'.join(str(a) for a in cA) + '\n')
details_handle.write('\t'.join(str(d) for d in cD) + '\n')
details_handle.close()
return details_filename
def _swt(self, sequence):
""" Use stationary wavelet transform method. """
details_filename = self.options.out_filename + '_details.txt'
details_handle = open(details_filename, 'w')
padded_sequence = self._pad_sequence(sequence)
sequence_encoding = self.encode_sequence(padded_sequence)
level = pywt.swt_max_level(len(sequence_encoding))
coeffs = pywt.swt(sequence_encoding, 'haar', level)
for (cA, cD) in coeffs:
approx_handle.write('\t'.join(str(a) for a in cA) + '\n')
details_handle.write('\t'.join(str(d) for d in cD) + '\n')
details_handle.close()
return details_filename
def w2decomp(img, mode='bior3.5', _compute=True):
# Run all available wavelet decomp
# return an image cube
imArray = fits.getdata(img)
# DataPrep conversions
imArray[imArray < 0.1] = 0.1
imArray = np.float32(np.sqrt(imArray))
normal = imArray.max()
imArray /= imArray.max();
max_lvl = pywt.swt_max_level(len(imArray))
out_imgs = np.zeros((imArray.shape[0], imArray.shape[1], max_lvl - 1))
for level in range(1, max_lvl):
if _compute:
lw = pywt.swt2(imArray, mode, level=level)[0][0]
out_imgs[:, :, level - 1] = lw
return out_imgs
def calculate_suitable_lvl(data, wv, r, swt=True):
# stationary
if swt:
max_lvl = pywt.swt_max_level(len(data))
lvl = 1
ent = []
pre_e = entropy(pywt.swt(data, wv, lvl), r)
ent.append(pre_e)
lvl += 1
while True:
new_e = entropy(pywt.swt(data, wv, lvl), r)
ent.append(new_e)
if lvl < max_lvl:
lvl += 1
else:
break
e_sorted = sorted(ent[:])
median = e_sorted[len(e_sorted) / 2]
lvl = ent.index(median) + 1
# discrete
else:
lvl = 1
data_e = entropy(data, r, True)
max_lvl = pywt.dwt_max_level(len(data), wv)
while True:
new_e = entropy(pywt.dwt(data, wv, lvl)[lvl - 1], r, True)
if new_e > data_e:
break
elif lvl == max_lvl:
break
else:
lvl += 1
if lvl == max_lvl:
pass
return lvl
def test_swt_decomposition():
x = [3, 7, 1, 3, -2, 6, 4, 6]
db1 = pywt.Wavelet("db1")
(cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=2)
assert_allclose(
cA1, [7.07106781, 5.65685425, 2.82842712, 0.70710678, 2.82842712, 7.07106781, 7.07106781, 6.36396103]
)
assert_allclose(
cD1, [-2.82842712, 4.24264069, -1.41421356, 3.53553391, -5.65685425, 1.41421356, -1.41421356, 2.12132034]
)
expected_cA2 = [7, 4.5, 4, 5.5, 7, 9.5, 10, 8.5]
assert_allclose(cA2, expected_cA2, rtol=1e-12)
expected_cD2 = [3, 3.5, 0, -4.5, -3, 0.5, 0, 0.5]
assert_allclose(cD2, expected_cD2, rtol=1e-12, atol=1e-14)
# level=1, start_level=1 decomposition should match level=2
res = pywt.swt(cA1, db1, level=1, start_level=1)
cA2, cD2 = res[0]
assert_allclose(cA2, expected_cA2, rtol=1e-12)
assert_allclose(cD2, expected_cD2, rtol=1e-12, atol=1e-14)
coeffs = pywt.swt(x, db1)
assert_(len(coeffs) == 3)
assert_(pywt.swt_max_level(len(x)) == 3)
def maxdeclevel(self):
maxlev = pywt.swt_max_level(len(self.data))
return maxlev
samprate, start_wf1, num_samp1 = gy.ReadWfm(wf1, wfdisc, start_e, end_e, station1, verbose)
#
# Pad with zeroes until length reaches the next power of two
#
w = wlt.Wavelet('db1')
N=1
n=1
while (len(wf1) > N):
N = N*2
if(len(wf1) < N):
for i in range(N-len(wf1)):
wf1.append(0.)
len1 = wlt.swt_max_level(N)
n1 = len(wf1)
len3 = wlt.swt_max_level(n1)
len2 = wlt.dwt_max_level(N, w.dec_len)
print(N, 'swt:',len1,'dwt:',len2,len3,n1)
n += 1
for i in range(N):
add.append(0.)
start_e += time_interval
for i in range(N) :
tt.append((float(i)/samprate))
if (test_case):
d1,d2 = gy.ReadSite(sfile, triad, 0)
theta1 = (theta1+90.)*np.pi/180.
dt1,dt2 = gy.CompDt(d1,d2,theta1,1.48)
for i in xrange (len(wf1)):
>>> print cA2
[ 7. 4.5 4. 5.5 7. 9.5 10. 8.5]
>>> print cD2
[ 3. 3.5 0. -4.5 -3. 0.5 0. 0.5]
>>> coeffs = pywt.swt(x, db1)
>>> len(coeffs)
3
>>> pywt.swt_max_level(len(x))
3
4 2D DWT和IDWT
4.1 2D一阶变换dwt2
dwt2(data, wavelet, mode=’sym’)
返回 (cA, (cH, cV, cD)), 分别是逼近、水平细节、垂直细节和对角线细节
>>> import pywt, numpy
>>> data = numpy.ones((4,4), dtype=numpy.float64)
def run(self):
self.list = []
# separate background from foreground
if int(self.FG_MEDIAN) % 2 == 0:
raise FeatureException('FG_MEDIAN must be an odd integer.')
if int(self.BG_MEDIAN) % 2 == 0:
raise FeatureException('BG_MEDIAN must be an odd integer.')
image_fg = cv2.medianBlur(self.image, int(self.FG_MEDIAN)).astype(np.float32)
image_bg = cv2.medianBlur(self.image, int(self.BG_MEDIAN)).astype(np.float32)
image_nobg = image_fg - image_bg
image_nobg = self._feature_scale(image_nobg, 0, 255, np.uint8)
self._image_debug_save('image_nobg', image_nobg)
# decompose the image into detail levels
input_len = self.image.shape[0]
maxl = pywt.swt_max_level(input_len)
coeffs = pywt.swt2(image_nobg, 'haar', level=maxl, start_level=0)
# horizontal detail mix l0 + l1
lh0 = coeffs[0][1][0]
lh1 = coeffs[1][1][0]
lh01 = cv2.addWeighted(lh0, self.L0MUL, lh1, self.L1MUL, 0)
# vertical detail mix l0 + l1
hl0 = coeffs[0][1][1]
hl1 = coeffs[1][1][1]
hl01 = cv2.addWeighted(hl0, self.L0MUL, hl1, self.L1MUL, 0)
# mix both together
img_mixed = cv2.addWeighted(lh01, 0.5, hl01, 0.5, 0)
# feature scale and cast to 8 bit unsigned
img_mixed = self._feature_scale(img_mixed, 0, 255, np.uint8)
# apply histogram equalisation and blur
img_mixed = cv2.medianBlur(img_mixed, 5).astype(np.uint8)
clahe = cv2.createCLAHE(clipLimit=2.0, tileGridSize=(8,8))
img_mixed = clahe.apply(img_mixed)
img_mixed = cv2.GaussianBlur(img_mixed, (9, 9), 0)
self._image_debug_save('Vert. + Horiz. L0+1 coefficients', img_mixed)
# calculate brightness histogram and thresholding values
img_ravel = img_mixed.ravel()
hist, bin_edges = np.histogram(img_ravel, 256, [0, 256], density=True)
loc, scale = norm.fit(img_ravel)
thresh_end = int(norm.ppf(0.5, loc=loc, scale=scale))
thresh_st1 = int(norm.ppf(0.005, loc=loc, scale=scale))
thresh_st2 = int(norm.ppf(0.001, loc=loc, scale=scale))
#print(thresh_end, thresh_st1, thresh_st2)
"""# attempt at removing image defects
lh4 = coeffs[3][1][0]
hl4 = coeffs[3][1][1]
l4 = cv2.addWeighted(lh4, 0.5, hl4, 0.5, 0)
l4 = coeffs[2][1][2]
l4 = self._feature_scale(l4, 0, 255, np.uint8)
#l4 = cv2.GaussianBlur(l4, (3, 3), 0)
l4 = cv2.medianBlur(l4, 5).astype(np.uint8)
t, l4thresh = cv2.threshold(l4, int(norm.ppf(0.002, loc=loc, scale=scale)), thresh_end, cv2.THRESH_TOZERO_INV)
#t, l4thresh2 = cv2.threshold(l4thresh, int(norm.ppf(0.001, loc=loc, scale=scale)), thresh_end, cv2.THRESH_BINARY_INV)
self._image_debug_save('Vert. + Horiz. L3 coefficients', l4thresh)"""
"""# debug histogram plot
fig, ax = plt.subplots(1, 1)
#ax.plot(x, pdf)
plt.hist(img_ravel, 256, [0, 256])
plt.show()"""
# prominent features
t, img_thresh1 = cv2.threshold(img_mixed, thresh_st1, thresh_end, cv2.THRESH_TRUNC)
self._image_debug_save('After first threshold', img_thresh1)
t, img_thresh2 = cv2.threshold(img_mixed, thresh_st2, thresh_end, cv2.THRESH_BINARY_INV)
self._image_debug_save('After second threshold', img_thresh2)
labels = self._thresh_and_label(img_thresh2)
# discriminate based on expected properties
labels_work = labels
labels_large = []
self.MIN_FEATURE_AREA = int(self.MIN_FEATURE_AREA)
self.MAX_BBOX_OVERLAP = float(self.MAX_BBOX_OVERLAP)
self.MAX_OVERLAP = float(self.MAX_OVERLAP)
for region1 in labels:
# remove very small features
if region1.area < self.MIN_FEATURE_AREA:
labels_work.remove(region1)
continue
# remove obvious artifacts (features with too low width / height ratio)
dim = region1.dim
ratio = min(dim[0], dim[1]) / max(dim[0], dim[1])
if ratio < 0.1:
labels_work.remove(region1)
continue
# remove overlapping features
for region2 in labels:
if region1 == region2:
continue
if region1.bboxarea > region2.bboxarea:
continue
overlap = region1.overlap(region2)
if (overlap[3] >= self.MAX_OVERLAP or overlap[2] >= self.MAX_BBOX_OVERLAP) and region1 in labels_work:
labels_work.remove(region1)
break
# if the feature is large, save it for the next pass
if region1.area >= self.LARGE_FEATURE_AREA:
region1.is_unclear = True
labels_large.append(region1)
labels = labels_work
# pass to break up "large" features
for region in labels_large:
img_slice = img_mixed[region.br1:region.br2, region.bc1:region.bc2]
t, img_thresh = cv2.threshold(img_slice, thresh_st2, thresh_end, cv2.THRESH_BINARY_INV)
labels_new = self._thresh_and_label(img_thresh)
# translate the newly found features with respect to their slice coordinates
for f in labels_new:
f.move(region.bx1 + f.x, region.by1 + f.y)
labels = labels + labels_new
# final pass to remove overlapping features
labels_work = labels
for region1 in labels:
if region1.is_unclear == True:
continue
for region2 in labels:
if region1 == region2:
continue
if region1.bboxarea > region2.bboxarea:
continue
if region2.is_unclear == True:
continue
overlap = region1.overlap(region2)
if (overlap[2] >= self.MAX_BBOX_OVERLAP) and region1 in labels_work:
#labels_work.remove(region1)
break
labels = labels_work
#print('len(labels)', len(labels))
self.list = labels
def modelling_cycle():
#--------------- initialization -------------------#
# initial_data = test_data
initial_data = test_data_one
# fig_init = plt.figure()
# fig_init.canvas.manager.set_window_title('Initial data')
# plt.plot(initial_data, color='g')
wavelet_families = pywt.families()
print 'Wavelet families:', ', '.join(wavelet_families)
wavelet_family = wavelet_families[4]
selected_wavelet = pywt.wavelist(wavelet_family)[0]
wavelet = pywt.Wavelet(selected_wavelet)
print 'Selected wavelet:', selected_wavelet
max_level = pywt.swt_max_level(len(initial_data))
# decomposition_level = max_level / 2
decomposition_level = 3
print 'Max level:', max_level, '\t Decomposition level:', decomposition_level
#--------------- decomposition -------------------#
w_initial_coefficients = pywt.swt(initial_data, wavelet, level=decomposition_level)
w_selected_coefficiets = select_levels_from_swt(w_initial_coefficients)
w_node_coefficients = select_node_levels_from_swt(w_initial_coefficients) #something terribly wrong here, yet the rest works!
#------------------ threshold --------------------#
threshold = measure_threshold(w_initial_coefficients)
w_threshold_coeff = w_initial_coefficients[:]
apply_threshold(w_threshold_coeff)
plot_initial_updated(w_initial_coefficients, w_threshold_coeff)
# plt.figure()
# for coeff in w_selected_coefficiets:
# plt.plot(coeff)
# plt.figure()
# for coeff in w_node_coefficients:
# plt.plot(coeff)
# plt.show()
#--------------- modification -------------------#
r = R()
w_new_coefficients = [0] * len(w_selected_coefficiets)
for index in range(0, len(w_selected_coefficiets)):
r.i_data = w_selected_coefficiets[index]
r('hw <- HoltWinters( ts(i_data, frequency = 12), gamma = TRUE )')
r('pred <- predict(hw, 50, prediction.interval = TRUE)')
w_new_coefficients[index] = append(w_selected_coefficiets[index], r.pred[:,0])
index += 1
w_new_node_coefficients = [0] * len(w_node_coefficients)
for index in range(0, len(w_node_coefficients)):
r.i_data = w_node_coefficients[index]
r('hw <- HoltWinters( ts(i_data, frequency = 12), gamma = TRUE )')
r('pred <- predict(hw, 50, prediction.interval = TRUE)')
w_new_node_coefficients[index] = append(w_node_coefficients[index], r.pred[:,0])
index += 1
#----
# plt.figure()
# for coeff in w_new_coefficients:
# plt.plot(coeff)
# plt.figure()
# for coeff in w_new_node_coefficients:
# plt.plot(coeff)
# plt.show()
#--------------- reconstruction -------------------#
# wInitialwithUpdated_Nodes = update_node_levels_swt(w_initial_coefficients, w_new_node_coefficients)
# plot_initial_updated(w_initial_coefficients, w_new_node_coefficients, True)
# plot_initial_updated(w_initial_coefficients, wInitialwithUpdated_Nodes) (!)
# plt.figure()
# for dyad in wInitialwithUpdated_Nodes:
# plt.plot(dyad[0])
# plt.plot(dyad[1])
#
# plt.figure()
# for dyad in w_initial_coefficients:
# plt.plot(dyad[0])
# plt.plot(dyad[1])
#
# plt.show()
# w_updated_coefficients = update_selected_levels_swt(w_initial_coefficients, w_selected_coefficiets)
# w_updated_coefficients = update_selected_levels_swt(w_initial_coefficients, w_new_coefficients)
#----
# w_updated_coefficients = update_swt(w_initial_coefficients, w_selected_coefficiets, w_node_coefficients)
w_updated_coefficients_nodes = update_swt(w_initial_coefficients, w_new_coefficients, w_new_node_coefficients)
w_updated_coefficients = update_selected_levels_swt(w_initial_coefficients, w_new_coefficients)
plot_initial_updated(w_initial_coefficients, w_updated_coefficients_nodes)
plot_initial_updated(w_initial_coefficients, w_updated_coefficients)
reconstructed_Stationary_nodes = iswt(w_updated_coefficients_nodes, selected_wavelet)
reconstructed_Stationary = iswt(w_updated_coefficients, selected_wavelet)
fig_sta_r = plt.figure()
fig_sta_r.canvas.manager.set_window_title('SWT reconstruction')
plt.plot(reconstructed_Stationary)
fig_sta_r_n = plt.figure()
fig_sta_r_n.canvas.manager.set_window_title('SWT reconstruction (nodes)')
plt.plot(reconstructed_Stationary_nodes)
plt.show()
print ("Filtered 2, length:", len(wf2))
fltwf3 = scipy.signal.lfilter(b, a, wf3)
print ("Filtered 3, length:", len(wf3))
n1 = len(wf1)
elif(wavelet_transform):
w = wlt.Wavelet(wlt_type)
N=1
n=1
while (len(wf1) > N):
N = N*2
if(len(wf1) < N):
for i in range(N-len(wf1)):
wf1.append(0.)
wf2.append(0.)
wf3.append(0.)
len1 = wlt.swt_max_level(N)
n1 = len(wf1)
len3 = wlt.swt_max_level(n1)
len2 = wlt.dwt_max_level(N, w.dec_len)
print(N, 'swt:',len1,'dwt:',len2,len3,n1)
n += 1
for i in range(N):
add1.append(0.)
add2.append(0.)
add3.append(0.)
[(cA7, cD7),(cA6, cD6),(cA5, cD5),(cA4, cD4),(cA3, cD3),(cA2, cD2), (cA1, cD1)] = wlt.swt(wf1, wlt_type, 7, start_level=start_level)
if(len(add_levels) > 0):
# figadd = plt.figure(figsize=(10,6))
# ax1=plt.subplot(511)
# plt.title(label)
