详解ADMM-CSNet（Python代码解析）

文章目录

前言
一、ADMM算法
- （1）算法内容
- （2）网络结构
二、代码解析
- - - 1.重建层初始化：
    - 2.第一个卷积层：
    - 3.非线性层 :
    - 4.第二个卷积层：
    - 5.减法层：
    - 6.乘数更新层初始化：
    - 7.重建层更新层：
    - 8.添加层：
    - 9.乘数更新层：
    - 8.重建层最终层：
总结

前言

论文名称：ADMM-CSNet: A Deep Learning Approach
for Image Compressive Sensing（ADMM-CSNet：一种用于图像压缩感知的深度学习方法）

⭐️ 论文地址：https://arxiv.org/abs/1705.06869

本文主要介绍ADMM-CSNet的网络结构及其代码实现部分，关于ADMM算法的具体推导过程大家可以读一下这篇论文：
🔥https://arxiv.org/abs/0912.3481
或者去网上查看其他博客，相关内容非常多，这里只做大概的介绍。

论文中给的代码其实是MATLAB实现的，但是对于神经网络个人认为Python看起来更容易理解一些，以下也是针对Pytorch框架写的代码进行分析的。

🚀 Python源码地址：lixing0810/Pytorch_ADMM-CSNet
👀 Matlab源码地址：https://github.com/yangyan92/Deep-ADMM-Net

一、ADMM算法

（1）算法内容

对于压缩感知模型的最优化问题为：

在图像域中引入辅助变量z并进行变量分离：

对应的增广拉格朗日函数为：

下面考虑3个子问题：

用迭代方法解上面3个问题：

1.重建层

2.辅助变量更新模块

最后的减去的部分可以进行分解为几个卷积层详解ADMM-CSNet（Python代码解析）和一个非线性激活层

详解ADMM-CSNet（Python代码解析）的迭代步骤对应到网络中为：

3.乘法器更新层

建议查看一下其他资料对上面整个迭代步骤了解更透彻一些，基本上每一层的输出又是其他层的输入，层与层之间联系密切，主要就是弄清楚每一层的输入和输出是什么。

（2）网络结构

二、代码解析

先看整个网络框架的代码：

import numpy as np
import torch.nn as nn
import torchpwl   
from scipy.io import loadmat
from os.path import join
import os
from utils.fftc import *
import torch


class CSNetADMMLayer(nn.Module):
    def __init__(
        self,
        mask,
        in_channels: int = 1,
        out_channels: int = 128,
        kernel_size: int = 5

    ):
        """
        Args:

        """
        super(CSNetADMMLayer, self).__init__()

        self.rho = nn.Parameter(torch.tensor([0.1]), requires_grad=True)
        self.gamma = nn.Parameter(torch.tensor([1.0]), requires_grad=True)
        self.mask = mask
        self.re_org_layer = ReconstructionOriginalLayer(self.rho, self.mask)
        self.conv1_layer = ConvolutionLayer1(in_channels, out_channels, kernel_size)
        self.nonlinear_layer = NonlinearLayer()
        self.conv2_layer = ConvolutionLayer2(out_channels, in_channels, kernel_size)
        self.min_layer = MinusLayer()
        self.multiple_org_layer = MultipleOriginalLayer(self.gamma)
        self.re_update_layer = ReconstructionUpdateLayer(self.rho, self.mask)
        self.add_layer = AdditionalLayer()
        self.multiple_update_layer = MultipleUpdateLayer(self.gamma)
        self.re_final_layer = ReconstructionFinalLayer(self.rho, self.mask)
        layers = []

        layers.append(self.re_org_layer)
        layers.append(self.conv1_layer)
        layers.append(self.nonlinear_layer)
        layers.append(self.conv2_layer)
        layers.append(self.min_layer)
        layers.append(self.multiple_org_layer)

        for i in range(8):
            layers.append(self.re_update_layer)
            layers.append(self.add_layer)
            layers.append(self.conv1_layer)
            layers.append(self.nonlinear_layer)
            layers.append(self.conv2_layer)
            layers.append(self.min_layer)
            layers.append(self.multiple_update_layer)

        layers.append(self.re_update_layer)
        layers.append(self.add_layer)
        layers.append(self.conv1_layer)
        layers.append(self.nonlinear_layer)
        layers.append(self.conv2_layer)
        layers.append(self.min_layer)
        layers.append(self.multiple_update_layer)

        layers.append(self.re_final_layer)

        self.cs_net = nn.Sequential(*layers)
        self.reset_parameters()

    def reset_parameters(self):
        self.conv1_layer.conv.weight = torch.nn.init.normal_(self.conv1_layer.conv.weight, mean=0, std=1)
        self.conv2_layer.conv.weight = torch.nn.init.normal_(self.conv2_layer.conv.weight, mean=0, std=1)
        self.conv1_layer.conv.weight.data = self.conv1_layer.conv.weight.data * 0.025
        self.conv2_layer.conv.weight.data = self.conv2_layer.conv.weight.data * 0.025

    def forward(self, x):
        y = torch.mul(x, self.mask)
        x = self.cs_net(y)
        x = torch.fft.ifft2(y+(1-self.mask)*torch.fft.fft2(x))
        return x


# reconstruction original layers
class ReconstructionOriginalLayer(nn.Module):
    def __init__(self, rho, mask):
        super(ReconstructionOriginalLayer,self).__init__()
        self.rho = rho
        self.mask = mask

    def forward(self, x):
        mask = self.mask
        denom = torch.add(mask.cuda(), self.rho)
        a = 1e-6
        value = torch.full(denom.size(), a).cuda()  
        denom = torch.where(denom == 0, value, denom)
        
        orig_output1 = torch.div(1, denom)
        orig_output2 = torch.mul(x, orig_output1)
        orig_output3 = torch.fft.ifft2(orig_output2)
        # define data dict
        cs_data = dict()
        cs_data['input'] = x
        cs_data['conv1_input'] = orig_output3
        return cs_data


# reconstruction middle layers
class ReconstructionUpdateLayer(nn.Module):
    def __init__(self, rho, mask):
        super(ReconstructionUpdateLayer,self).__init__()
        self.rho = rho
        self.mask = mask

    def forward(self, x):
        minus_output = x['minus_output']
        multiple_output = x['multi_output']
        input = x['input']
        mask = self.mask
        number = torch.add(input, self.rho * torch.fft.fft2(torch.sub(minus_output, multiple_output)))
        denom = torch.add(mask.cuda(), self.rho)
        a = 1e-6
        value = torch.full(denom.size(), a).cuda()
        denom = torch.where(denom == 0, value, denom)
        orig_output1 = torch.div(1, denom)
        orig_output2 = torch.mul(number, orig_output1)
        orig_output3 = torch.fft.ifft2(orig_output2)
        x['re_mid_output'] = orig_output3
        return x


# reconstruction middle layers
class ReconstructionFinalLayer(nn.Module):
    def __init__(self, rho, mask):
        super(ReconstructionFinalLayer, self).__init__()
        self.rho = rho
        self.mask = mask

    def forward(self, x):
        minus_output = x['minus_output']
        multiple_output = x['multi_output']
        input = x['input']
        mask = self.mask
        number = torch.add(input, self.rho * torch.fft.fft2(torch.sub(minus_output, multiple_output)))
        denom = torch.add(mask.cuda(), self.rho)
        a = 1e-6
        value = torch.full(denom.size(), a).cuda()
        denom = torch.where(denom == 0, value, denom)
        orig_output1 = torch.div(1, denom)
        orig_output2 = torch.mul(number, orig_output1)
        orig_output3 = torch.fft.ifft2(orig_output2)
        x['re_final_output'] = orig_output3
        return x['re_final_output']


# multiple original layer
class MultipleOriginalLayer(nn.Module):
    def __init__(self,gamma):
        super(MultipleOriginalLayer,self).__init__()
        self.gamma = gamma

    def forward(self,x):
        org_output = x['conv1_input']
        minus_output = x['minus_output']
        output= torch.mul(self.gamma,torch.sub(org_output, minus_output))
        x['multi_output'] = output
        return x


# multiple middle layer
class MultipleUpdateLayer(nn.Module):
    def __init__(self,gamma):
        super(MultipleUpdateLayer,self).__init__()
        self.gamma = gamma

    def forward(self, x):
        multiple_output = x['multi_output']
        re_mid_output = x['re_mid_output']
        minus_output = x['minus_output']
        output= torch.add(multiple_output,torch.mul(self.gamma,torch.sub(re_mid_output , minus_output)))
        x['multi_output'] = output
        return x


# convolution layer
class ConvolutionLayer1(nn.Module):
    def __init__(self, in_channels: int, out_channels: int,kernel_size:int):
        super(ConvolutionLayer1,self).__init__()
        self.in_channels = in_channels
        self.out_channels = out_channels
        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size, padding=int((kernel_size-1)/2), stride=1, dilation= 1,bias=True)

    def forward(self, x):
        conv1_input = x['conv1_input']
        real = self.conv(conv1_input.real)
        imag = self.conv(conv1_input.imag)
        output = torch.complex(real, imag)
        x['conv1_output'] = output
        return x


# convolution layer
class ConvolutionLayer2(nn.Module):
    def __init__(self, in_channels: int, out_channels: int, kernel_size: int):
        super(ConvolutionLayer2, self).__init__()
        self.in_channels = in_channels
        self.out_channels = out_channels
        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size, padding=int((kernel_size - 1) / 2),
                              stride=1, dilation=1, bias=True)

    def forward(self, x):
        nonlinear_output = x['nonlinear_output']
        real = self.conv(nonlinear_output.real)
        imag = self.conv(nonlinear_output.imag)
        output = torch.complex(real, imag)

        x['conv2_output'] = output
        return x


# nonlinear layer
class NonlinearLayer(nn.Module):
    def __init__(self):
        super(NonlinearLayer,self).__init__()
        self.pwl = torchpwl.PWL(num_channels=128, num_breakpoints=101)

    def forward(self, x):
        conv1_output = x['conv1_output']
        y_real = self.pwl(conv1_output.real)
        y_imag = self.pwl(conv1_output.imag)
        output = torch.complex(y_real, y_imag)
        x['nonlinear_output'] = output
        return x


# minus layer
class MinusLayer(nn.Module):
    def __init__(self):
        super(MinusLayer, self).__init__()

    def forward(self, x):
        minus_input = x['conv1_input']
        conv2_output = x['conv2_output']
        output= torch.sub(minus_input, conv2_output)
        x['minus_output'] = output
        return x


# addtional layer
class AdditionalLayer(nn.Module):
    def __init__(self):
        super(AdditionalLayer,self).__init__()

    def forward(self, x):
        mid_output = x['re_mid_output']
        multi_output = x['multi_output']
        output= torch.add(mid_output,multi_output)
        x['conv1_input'] = output
        return x
  
# 将网络结构打印出来  
bb = CSNetADMMLayer(mask=1)
print(bb)

网络结构主要分为三个层次：(见下图)
1. 网络初始化部分。
2. 中间更新迭代的过程。（共迭代了9次，但是他这里分开写了，不知道为什么）
3. 最后的重建层，输出最终重建的结果。（也就是最后一个重建层）

下面按照这三个部分具体分析每一层迭代更新的实现过程：

解释代码之前先来了解一下其中的几个函数：(如果对这些函数很熟悉，可跳过这一part~)
	torch.where(condition, x, y)
	torch.full(size, fill_value)
	torch.sub(input, other, alpha=1, out=None) -> Tensor

(1).torch.where(condition, x, y)
condition是一个布尔张量，如果condition中的某个元素为True，则返回的张量中相应的元素为x中对应的元素，否则为y中对应的元素。

(2). torch.full(size, fill_value)

torch.full((2, 3), 5)将创建一个形状为(2, 3)的张量，每个元素都填充为5。

(3). torch.sub(input, other, alpha=1, out=None) -> Tensor

1.重建层初始化：

主代码：

# reconstruction original layers
class ReconstructionOriginalLayer(nn.Module):
    def __init__(self, rho, mask):
        super(ReconstructionOriginalLayer,self).__init__()
        self.rho = rho
        self.mask = mask

    def forward(self, x):
        mask = self.mask
        denom = torch.add(mask.cuda(), self.rho)
        a = 1e-6
        value = torch.full(denom.size(), a).cuda()  
        denom = torch.where(denom == 0, value, denom)
       
        orig_output1 = torch.div(1, denom)
        orig_output2 = torch.mul(x, orig_output1)
        orig_output3 = torch.fft.ifft2(orig_output2)
        # define data dict
        cs_data = dict()
        cs_data['input'] = x
        cs_data['conv1_input'] = orig_output3
        return cs_data