基于pyWavelets的多层局部小波重构

Question

我正在寻找一种方法来部分重建小波分解的分支，这样和就可以重建原始信号。这可以通过使用Matlab来实现，使用：

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来实现同样的效果，但是我不确定该怎么做。pywt.waverec函数创建完全重建，但没有用于部分重建的level参数。pywt.upcoef函数完成了我在单个级别所需的功能，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.])

Answer 1

我设法编写了我自己版本的wrcoef函数，它看起来像预期的那样工作：

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]

Answer 2

目前pywt还没有实现wrcoef等价函数。但是你仍然可以分解一维多电平信号，然后分别重构它的各个分量。

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

我们需要对返回值进行切片，使其具有与输入信号相同的长度。然后，我们可以得到分解后的每个组件。

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 )