我正在寻找一种方法来部分重建小波分解的分支,这样总和将重新创建原始信号。这可以使用 Matlab 实现:
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 实现相同的目标,但我不知道该怎么做。该pywt.waverec
函数创建完整的重建,但没有用于部分重建的级别参数。该pywt.upcoef
函数完成了我对单个级别的需求,但我不确定如何将其扩展到多个级别:
>>> 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.])
我设法编写了我自己的wrcoef
函数版本,它似乎按预期工作:
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]
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