用pyWavelets進行多級部分小波重構

Question

我正在尋找一種方法來部分重構小波分解的分支，這樣總和會重新創建原始信號。這可以使用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 

我想用pywt實現同樣的功能，但我不確定如何去做這件事。 pywt.waverec函數創建完整重建，但沒有用於部分重建的級別參數。 的pywt.upcoef功能做什麼，我需要一個單一的水平，但我不知道如何擴大這個多層次上：如預期

>>> 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.]) 

Answer 1

我設法寫我自己這似乎工作wrcoef功能的版本：

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] 

Answer 2

目前，pywt還沒有實現wrcoef等價函數。但是，您仍然可以分解一維多電平信號，然後分別重建其組件。

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 

我們需要將返回值限制爲與輸入信號具有相同的長度。然後我們可以在分解後得到每個組件。

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)