pytorch_wavelets包实现的小波变换和MWCNN中的小波变换的异同点

下载pytorch_wavelets：

git clone https://github.com/fbcotter/pytorch_wavelets

然后安装：

cd pytorch_wavelets
pip install .

Successfully built pytorch-wavelets
Installing collected packages: pytorch-wavelets
Successfully installed pytorch-wavelets-1.2.2

查看你能够使用的变换方法：

>>> import pywt
>>> pywt.wavelist(\'haar\')        
[\'haar\']
>>> pywt.wavelist(\'db\') 
[\'db1\', \'db2\', \'db3\', \'db4\', \'db5\', \'db6\', \'db7\', \'db8\', \'db9\', \'db10\', \'db11\', \'db12\', \'db13\', \'db14\', \'db15\', \'db16\', \'db17\', \'db18\', \'db19\', \'db20\', \'db21\', \'db22\', \'db23\', \'db24\', \'db25\', \'db26\', \'db27\', \'db28\', \'db29\', \'db30\', \'db31\', \'db32\', \'db33\', \'db34\', \'db35\', \'db36\', \'db37\', \'db38\']

详情可见：

https://pywavelets.readthedocs.io/en/latest/ref/wavelets.html

从pytorch_wavelets的源码https://github.com/fbcotter/pytorch_wavelets/blob/master/pytorch_wavelets/dwt/transform2d.py中可见其wave参数使用的是pywt.Wavelet：

class DWTForward(nn.Module):
    """ Performs a 2d DWT Forward decomposition of an image
    Args:
        J (int): Number of levels of decomposition
        wave (str or pywt.Wavelet): Which wavelet to use. Can be a string to
            pass to pywt.Wavelet constructor, can also be a pywt.Wavelet class,
            or can be a two tuple of array-like objects for the analysis low and
            high pass filters.
        mode (str): \'zero\', \'symmetric\', \'reflect\' or \'periodization\'. The
            padding scheme
        separable (bool): whether to do the filtering separably or not (the
            naive implementation can be faster on a gpu).
        """
    def __init__(self, J=1, wave=\'db1\', mode=\'zero\'):
        super().__init__()
        if isinstance(wave, str):
            wave = pywt.Wavelet(wave)
        if isinstance(wave, pywt.Wavelet):
            h0_col, h1_col = wave.dec_lo, wave.dec_hi
            h0_row, h1_row = h0_col, h1_col
...

举例说明：

#coding:utf-8
import torch.nn as nn
import torch

import os, torchvision
from PIL import Image
from torchvision import transforms as trans

def test3():
    from pytorch_wavelets import DWTForward, DWTInverse # (or import DWT, IDWT)
    #J为分解的层次数,wave表示使用的变换方法
    xfm = DWTForward(J=1, mode=\'zero\', wave=\'haar\')  # Accepts all wave types available to PyWavelets
    ifm = DWTInverse(mode=\'zero\', wave=\'haar\')

    img = Image.open(\'./1.jpg\')
    transform = trans.Compose([
        trans.ToTensor()
    ])
    img = transform(img).unsqueeze(0)
    Yl, Yh = xfm(img)
    print(Yl.shape)
    print(len(Yh))
    # print(Yh[0].shape)

    for i in range(len(Yh)):
        print(Yh[i].shape)
        if i == len(Yh)-1:
            h = torch.zeros([4,3,Yh[i].size(3),Yh[i].size(3)]).float()
            h[0,:,:,:] = Yl
        else:
            h = torch.zeros([3,3,Yh[i].size(3),Yh[i].size(3)]).float()
        for j in range(3):
            if i == len(Yh)-1:
                h[j+1,:,:,:] = Yh[i][:,:,j,:,:]
            else:
                h[j,:,:,:] = Yh[i][:,:,j,:,:]
        if i == len(Yh)-1:
            img_grid = torchvision.utils.make_grid(h, 2) #一行2张图片
        else:
            img_grid = torchvision.utils.make_grid(h, 3)
        torchvision.utils.save_image(img_grid, \'img_grid_{}.jpg\'.format(i))

if __name__ == \'__main__\':
    test3()

(deeplearning) bogon:learning user$ python delete.py 
torch.Size([1, 3, 56, 56])
1
torch.Size([1, 3, 3, 56, 56])

效果如下：

从这个结果上看和MWCNN中使用的haar小波变换 pytorch 的差不多

输出Yl的大小为 $(N, C_{i n}, H_{i n}^{'}, W_{i n}^{'})$ ，即 $(N, C_{i n}, H_{i n}^{'}, W_{i n}^{'})$

Yh的大小为 $l i s t (N, C_{i n}, 3, H_{i n}^{″}, W_{i n}^{″})$ $l i s t (N, C_{i n}, 3, H_{i n}^{″}, W_{i n}^{″})$

$l i s t (N, C_{i n}, 3, H_{i n}^{″}, W_{i n}^{″})$

如果进行的是三层小波，J=3：

(deeplearning) bogon:learning user$ python delete.py 
torch.Size([1, 3, 14, 14])
3
torch.Size([1, 3, 3, 56, 56])
torch.Size([1, 3, 3, 28, 28])
torch.Size([1, 3, 3, 14, 14])

效果：

如果J=2，是两层，返回：

(deeplearning) bogon:learning user$ python delete.py 
torch.Size([1, 3, 28, 28])
2
torch.Size([1, 3, 3, 56, 56])
torch.Size([1, 3, 3, 28, 28])

效果：