使用pytorch实现小波散射网络

小波散射网络（Scattering Transform）是一种基于小波变换的卷积神经网络，适用于信号或图像分类等任务。下面是使用Pytorch实现小波散射网络的简单步骤：

1. 安装必要的库，如Pytorch，PyWavelets等。

2. 定义小波滤波器，可以使用PyWavelets库中的函数，如pywt.Wavelet('db1')。

3. 定义小波散射层，可以使用Pytorch的nn.Module类来实现。

import torch
import torch.nn as nn
import pywt

class ScatteringLayer(nn.Module):
    def __init__(self, J, L):
        super(ScatteringLayer, self).__init__()
        self.J = J
        self.L = L
        self.phi, self.psi = self.build_filters()
        
    def build_filters(self):
        filters = []
        filters.append(pywt.Wavelet('db1'))
        for j in range(1, self.J + 1):
            for l in range(0, self.L):
                filters.append(pywt.Wavelet('db1', offset=j, trim_approx=l))
        return filters
    
    def forward(self, x):
        S = []
        for j in range(len(self.psi)):
            U = nn.functional.conv1d(x, torch.tensor(self.psi[j], dtype=torch.float32).unsqueeze(0), stride=2**(j+1), padding=0)
            V = nn.functional.max_pool1d(U, kernel_size=2**(j+1), stride=2**(j+1), padding=0)
            S.append(V)
        U = nn.functional.conv1d(x, torch.tensor(self.phi, dtype=torch.float32).unsqueeze(0), stride=2**self.J, padding=0)
        V = nn.functional.max_pool1d(U, kernel_size=2**self.J, stride=2**self.J, padding=0)
        S.append(V)
        return torch.cat(S, dim=1)

4. 定义小波散射网络，可以使用Pytorch的nn.Sequential类来实现。

import torch.nn.functional as F

class ScatteringNet(nn.Sequential):
    def __init__(self, J, L):
        super(ScatteringNet, self).__init__()
        self.add_module('scattering', ScatteringLayer(J, L))
        
    def forward(self, x):
        x = self.scattering(x)
        x = x.view(x.size(0), -1)
        x = F.normalize(x, p=2, dim=1)
        return x

5. 使用定义好的小波散射网络进行训练和测试。

model = ScatteringNet(J=2, L=8)
criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters())

# 训练模型
for epoch in range(num_epochs):
    for i, (images, labels) in enumerate(train_loader):
        images = images.to(device)
        labels = labels.to(device)
        
        optimizer.zero_grad()
        outputs = model(images)
        loss = criterion(outputs, labels)
        loss.backward()
        optimizer.step()

# 测试模型
with torch.no_grad():
    correct = 0
    total = 0
    for images, labels in test_loader:
        images = images.to(device)
        labels = labels.to(device)
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)
        total += labels.size(0)
        correct += (predicted == labels).sum().item()
    accuracy = 100 * correct / total
    print('Accuracy: {:.2f}%'.format(accuracy))

这样就可以通过Pytorch实现小波散射网络了。