wavedecn

 wavedecn(data, wavelet, mode='symmetric', level=None, axes=None)

    Multilevel nD Discrete Wavelet Transform.Parameters----------data : ndarraynD input data# 可通过设置axes参数，来确定小波变化的维度axes : sequence of ints, optionalAxes over which to compute the DWT. Axes may not be repeated. Thedefault is None, which means transform all axes(``axes = range(data.ndim)``).Returns-------[cAn, {details_level_n}, ... {details_level_1}] : listCoefficients list.  Coefficients are listed in descending order ofdecomposition level.  `cAn` are the approximation coefficients atlevel `n`.  Each `details_level_i` element is a dictionarycontaining detail coefficients at level `i` of the decomposition.  Asa concrete example, a 3D decomposition would have the following set ofkeys in each `details_level_i` dictionary::{'aad', 'ada', 'daa', 'add', 'dad', 'dda', 'ddd'}where the order of the characters in each key map to the specified`axes`.# 字符顺序与axes的顺序一致# 若输入三维data，aad分别对应channel，height，width

2D_DWT

import numpy as np
import pywtinput = np.ones((4, 4))
coeffs = pywt.wavedecn(input, wavelet='haar', level=2)

2D coefficient dictionary和 2D array之间的转换关系：
Handling DWT Coefficients

3D_DWT

三维图像经过一级小波变换可以得到八张子图。

import cv2
import numpy as np
import pywtfile = '1.jpg'
img = cv2.imread(file)
# img  (224,224,3)
img = cv2.resize(img, (224, 224))
# img  (3,224,224)
img = np.array([img[:, :, i] for i in range(3)])
coeffs = pywt.wavedecn(img, wavelet='haar', level=3)print(coeffs[3]['aad'].shape)  # (2, 112, 112)
print(coeffs[2]['aad'].shape)  # (1, 56, 56)
print(coeffs[1]['aad'].shape)  # (1, 28, 28)

（1，H，W）的图像进行小波变换，{'daa', 'dad', 'dda', 'ddd'}结果都为0

input = np.arange(4).reshape((2, 2))
print(pywt.wavedecn(input, wavelet='haar', level=1))
# [array([[3.]]), {'ad': array([[-1.]]), 'da': array([[-2.]]), 'dd': array([[0.]])}]input = np.arange(4).reshape((1, 2, 2))
print(pywt.wavedecn(input, wavelet='haar', level=1))
# [array([[[4.24264069]]]), 
# {'aad': array([[[-1.41421356]]]), 
# 'ada': array([[[-2.82842712]]]), 
# 'add': array([[[-2.22044605e-16]]]), 
# 'daa': array([[[0.]]]), 'dad': array([[[0.]]]), 
# 'dda': array([[[0.]]]), 'ddd': array([[[0.]]])}]

参考：Matlab Code for 3D DWT (3 Dimensonal Discrete Wavelet Transform