[英]Multilevel partial wavelet reconstruction with pyWavelets
我正在尋找一種部分重構小波分解分支的方法,以使總和可以重新創建原始信號。 這可以通過使用Matlab來實現:
DATA = [0,1,2,3,4,5,6,7,8,9]
N_LEVELS = 2;
WAVELET_NAME = 'db4';
[C,L] = wavedec(DATA, N_LEVELS, WAVELET_NAME);
A2 = wrcoef('a', C, L, WAVELET_NAME, 2);
D2 = wrcoef('d', C, L, WAVELET_NAME, 2);
D1 = wrcoef('d', C, L, WAVELET_NAME, 1);
A2+D2+D1
ans =
0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000
我想使用pywt來實現相同的目的,但是我不確定該怎么做。 pywt.waverec
函數創建完整的重構,但是沒有用於部分重構的level參數。 pywt.upcoef
函數可以完成單個級別的工作,但是我不確定如何將其擴展到多個級別:
>>> import pywt
>>> data = [1,2,3,4,5,6]
>>> (cA, cD) = pywt.dwt(data, 'db2', 'smooth')
>>> n = len(data)
>>> pywt.upcoef('a', cA, 'db2', take=n) + pywt.upcoef('d', cD, 'db2', take=n)
array([ 1., 2., 3., 4., 5., 6.])
我設法編寫了自己的wrcoef
函數版本,該版本似乎可以正常工作:
import pywt
import numpy as np
def wrcoef(X, coef_type, coeffs, wavename, level):
N = np.array(X).size
a, ds = coeffs[0], list(reversed(coeffs[1:]))
if coef_type =='a':
return pywt.upcoef('a', a, wavename, level=level)[:N]
elif coef_type == 'd':
return pywt.upcoef('d', ds[level-1], wavename, level=level)[:N]
else:
raise ValueError("Invalid coefficient type: {}".format(coef_type))
level = 4
X = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
coeffs = pywt.wavedec(X, 'db1', level=level)
A4 = wrcoef(X, 'a', coeffs, 'db1', level)
D4 = wrcoef(X, 'd', coeffs, 'db1', level)
D3 = wrcoef(X, 'd', coeffs, 'db1', 3)
D2 = wrcoef(X, 'd', coeffs, 'db1', 2)
D1 = wrcoef(X, 'd', coeffs, 'db1', 1)
print A4 + D4 + D3 + D2 + D1
# Results:
[ 9.99200722e-16 1.00000000e+00 2.00000000e+00 3.00000000e+00
4.00000000e+00 5.00000000e+00 6.00000000e+00 7.00000000e+00
8.00000000e+00 9.00000000e+00 1.00000000e+01 1.10000000e+01
1.20000000e+01 1.30000000e+01 1.40000000e+01 1.50000000e+01
1.60000000e+01 1.70000000e+01]
目前,pywt尚未實現wrcoef等效功能。 但是您仍然可以分解一維多電平信號,然后分別重構其分量。
import pywt
def decomposite(signal, coef_type='d', wname='db6', level=9):
w = pywt.Wavelet(wname)
a = data
ca = []
cd = []
for i in range(level):
(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))
if coef_type == 'd':
return rec_d
return rec_a
我們需要將返回值切成與輸入信號相同的長度。 然后我們可以分解后得到每個分量。
X = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
rec_d = decomposite(X, 'd', 'db6', level=9)
# slice rec_d
print sum(rec_d )
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