def wavelet_estimator(appro,
mask=None,
nb_vanishmoment=2,
norm=1,
q=np.array(2),
nbvoies=None,
distn=1,
wtype=1,
j1=2,
j2=8):
"""
This function estimate the Hurst exponent of a signal based
on Daubechies' Wavelet coeffecients.
It also allow l2 and tv regularisation.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
q: the order of the statistic used
nb_vanishmoment: the number of vanishing moments of the wavelet
((here only used in the plot title)
nbvoies: number of octaves
distn: Hypothesis on the data distribution or `singal type':
0: Gauss, 1: Non-G finite va
wtype: The kind of weighting used
0 - no weigthing (ie uniform weights)
1 - 1/nj weights (suitable for fully Gaussian data)
2 - use variance estimates varj
j1: the lower limit of the scales chosen, 1<= j1 <= scalemax-1
j2: the upper limit of the octaves chosen, 2<= j2 <= scalemax
0- no spatial regularisation
1- tv regularisation
2- l2 regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])
if appro.ndim > 2:
shape = (reduce(lambda a, b: a * b, (1, ) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
if nbvoies is None:
nbvoies = min(int(np.log2(l / (2 * nb_vanishmoment + 1))),
int(np.log2(l)))
dico = hdw_p(appro, nb_vanishmoment, norm, q, nbvoies, distn, wtype, j1,
j2, 0)
Hurst_exponent = dico['Zeta'] / 2.
return Hurst_exponent
def wavelet_estimator(appro, mask=None, nb_vanishmoment=2, norm=1, q=np.array(2), nbvoies=None,
distn=1, wtype=1, j1=2, j2=8):
"""
This function estimate the Hurst exponent of a signal based
on Daubechies' Wavelet coeffecients.
It also allow l2 and tv regularisation.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
q: the order of the statistic used
nb_vanishmoment: the number of vanishing moments of the wavelet
((here only used in the plot title)
nbvoies: number of octaves
distn: Hypothesis on the data distribution or `singal type':
0: Gauss, 1: Non-G finite va
wtype: The kind of weighting used
0 - no weigthing (ie uniform weights)
1 - 1/nj weights (suitable for fully Gaussian data)
2 - use variance estimates varj
j1: the lower limit of the scales chosen, 1<= j1 <= scalemax-1
j2: the upper limit of the octaves chosen, 2<= j2 <= scalemax
0- no spatial regularisation
1- tv regularisation
2- l2 regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])
if appro.ndim > 2:
shape = (reduce(lambda a,b : a*b , (1,) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
if nbvoies is None:
nbvoies = min(int(np.log2(l / (2 * nb_vanishmoment + 1))), int(np.log2(l)))
dico = hdw_p(appro, nb_vanishmoment, norm, q, nbvoies, distn, wtype, j1, j2, 0)
Hurst_exponent = dico['Zeta'] / 2.
return Hurst_exponent
def wavelet_l2_estimator(appro,
mask=None,
nb_vanishmoment=2,
norm=1,
q=np.array(2),
nbvoies=None,
distn=1,
wtype=1,
j1=2,
j2=8,
lbda=1):
"""
This function estimate the Hurst exponent of a signal based
on Daubechies' Wavelet coeffecients.
It also allow l2 and tv regularisation.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
q: the order of the statistic used
nb_vanishmoment: the number of vanishing moments of the wavelet
((here only used in the plot title)
nbvoies: number of octaves
distn: Hypothesis on the data distribution or `singal type':
0: Gauss, 1: Non-G finite va
wtype: The kind of weighting used
0 - no weigthing (ie uniform weights)
1 - 1/nj weights (suitable for fully Gaussian data)
2 - use variance estimates varj
j1: the lower limit of the scales chosen, 1<= j1 <= scalemax-1
j2: the upper limit of the octaves chosen, 2<= j2 <= scalemax
0- no spatial regularisation
1- tv regularisation
2- l2 regularisation
lbda: weight used in regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])
if appro.ndim > 2:
shape = (reduce(lambda a, b: a * b, (1, ) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
if nbvoies is None:
nbvoies = min(int(np.log2(l / (2 * nb_vanishmoment + 1))),
int(np.log2(l)))
dico = hdw_p(appro, nb_vanishmoment, norm, q, nbvoies, distn, wtype, j1,
j2, 0)
nonNanvalue = np.invert(dico['Nanvalue'])
Elog = dico['Elogmuqj'][:, 0][nonNanvalue]
Varlog = dico['Varlogmuqj'][:, 0][nonNanvalue]
nj = dico['nj']
estimate = dico['Zeta'][nonNanvalue] / 2.
aest = dico['aest'][nonNanvalue]
mask[mask] = np.all((mask[mask], nonNanvalue), axis=0)
f = lambda x, lbda: l2_penalization_on_grad(
x, aest, Elog, Varlog, nj, j1, j2, mask, l=lbda)
#We set epsilon to 0
g = lambda x, lbda: grad_l2_penalization_on_grad(
x, aest, Elog, Varlog, nj, j1, j2, mask, l=lbda)
fg = lambda x, lbda, **kwargs: (f(x, lbda), g(x, lbda))
#For each lambda we use blgs algorithm to find the minimum
# We start from the
l2_algo = lambda lbda: fmin_l_bfgs_b(lambda x: fg(x, lbda), estimate)
Hmin = l2_algo(lbda)
retour = 0.4 * np.ones(dico['Zeta'].shape)
retour[nonNanvalue] = Hmin[0]
return dico['Zeta'] / 2, retour
def wavelet_tv_estimator(appro, mask=None, nb_vanishmoment=2, norm=1, q=np.array(2), nbvoies=None,
distn=1, wtype=1, j1=2, j2=8, lbda=1):
"""
This function estimate the Hurst exponent of a signal based
on Daubechies' Wavelet coeffecients.
It also allow l2 and tv regularisation.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
q: the order of the statistic used
nb_vanishmoment: the number of vanishing moments of the wavelet
((here only used in the plot title)
nbvoies: number of octaves
distn: Hypothesis on the data distribution or `singal type':
0: Gauss, 1: Non-G finite va
wtype: The kind of weighting used
0 - no weigthing (ie uniform weights)
1 - 1/nj weights (suitable for fully Gaussian data)
2 - use variance estimates varj
j1: the lower limit of the scales chosen, 1<= j1 <= scalemax-1
j2: the upper limit of the octaves chosen, 2<= j2 <= scalemax
0- no spatial regularisation
1- tv regularisation
2- l2 regularisation
lbda: weight used in regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])
if appro.ndim > 2:
shape = (reduce(lambda a,b : a*b , (1,) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
if nbvoies is None:
nbvoies = min(int(np.log2(l / (2 * nb_vanishmoment + 1))), int(np.log2(l)))
dico = hdw_p(appro, nb_vanishmoment, norm, q, nbvoies, distn, wtype, j1, j2, 0)
nonNanvalue = np.invert(dico['Nanvalue'])
Elog = dico['Elogmuqj'][:, 0][nonNanvalue]
Varlog = dico['Varlogmuqj'][:, 0][nonNanvalue]
nj = dico['nj']
estimate = dico['Zeta'][nonNanvalue] / 2.
aest = dico['aest'][nonNanvalue]
mask[mask] = np.all((mask[mask], nonNanvalue), axis=0)
lipschitz_constant = lipschitz_constant_gradf(j1,j2,Varlog, nj, wtype)
l1_ratio = 0
tv_algo = lambda lbda: mtvsolver(estimate, aest,
Elog, Varlog,
nj, j1, j2,mask,
lipschitz_constant=lipschitz_constant,
l1_ratio = l1_ratio, l=lbda, verbose=0)
Hmin = tv_algo(lbda)
retour = 0.4 * np.ones(dico['Zeta'].shape)
retour[nonNanvalue] = Hmin[0]
return dico['Zeta']/2, retour