结构一致性ssim损失函数

### 结构一致性 SSIM 损失函数的应用

结构相似性指数 (SSIM) 被广泛应用于图像处理领域，特别是在深度学习框架下用于优化生成对抗网络(GANs)[^1]。相比于传统的均方误差(MSE)，SSIM 更加关注人类视觉系统的特性，能够更好地反映两幅图片间的感知差异。

#### 应用场景

- **超分辨率重建**：提高低分辨率图像的质量。
- **去噪**：去除噪声的同时保持边缘细节清晰可见。
- **风格迁移**：保留原始内容的基础上改变艺术风格。
- **医学影像分析**：辅助医生更精确地诊断疾病。

这些应用场景都依赖于高质量的图像恢复能力，而基于 SSIM 的损失函数正好满足这一需求。

### 实现方式

为了在 PyTorch 中实现 SSIM 损失函数，可以采用如下代码：

import torch
import torch.nn.functional as F
from math import exp

def gaussian(window_size, sigma):
    gauss = torch.Tensor([exp(-(x - window_size//2)**2/float(2*sigma**2)) for x in range(window_size)])
    return gauss/gauss.sum()

def create_window(window_size, channel=1):
    _1D_window = gaussian(window_size, 1.5).unsqueeze(1)
    _2D_window = _1D_window.mm(_1D_window.t()).float().unsqueeze(0).unsqueeze(0)
    window = _2D_window.expand(channel, 1, window_size, window_size).contiguous()
    return window

def ssim(img1, img2, val_range, window_size=11, window=None, size_average=True, full=False):
    L = val_range 

    padd = 0
    (_, channel, height, width) = img1.size()
    if window is None:
        real_size = min(window_size, height, width)
        window = create_window(real_size, channel=channel).to(img1.device)

    mu1 = F.conv2d(img1, window, padding=padd, groups=channel)
    mu2 = F.conv2d(img2, window, padding=padd, groups=channel)

    mu1_sq = mu1.pow(2)
    mu2_sq = mu2.pow(2)
    mu1_mu2 = mu1 * mu2

    sigma1_sq = F.conv2d(img1 * img1, window, padding=padd, groups=channel) - mu1_sq
    sigma2_sq = F.conv2d(img2 * img2, window, padding=padd, groups=channel) - mu2_sq
    sigma12 = F.conv2d(img1 * img2, window, padding=padd, groups=channel) - mu1_mu2

    C1 = (0.01 * L) ** 2
    C2 = (0.03 * L) ** 2

    v1 = 2.0 * sigma12 + C2
    v2 = sigma1_sq + sigma2_sq + C2
    cs = torch.mean(v1 / v2)  

    ssim_map = ((2 * mu1_mu2 + C1) * v1) / ((mu1_sq + mu2_sq + C1) * v2)

    if size_average:
        ret = ssim_map.mean()
    else:
        ret = ssim_map.mean(1).mean(1).mean(1)

    if full:
        return ret, cs
    return ret


class SSIM(torch.nn.Module):
    def __init__(self, window_size=11, size_average=True, val_range=None):
        super(SSIM, self).__init__()
        self.window_size = window_size
        self.size_average = size_average
        self.val_range = val_range

        # Assume 1 channel for SSIM
        self.channel = 1
        self.window = create_window(window_size)

    def forward(self, img1, img2):
        (_, channel, _, _) = img1.size()

        if channel == self.channel and self.window.dtype == img1.dtype:
            window = self.window
        else:
            window = create_window(self.window_size, channel).to(img1.device).type(img1.dtype)
            self.window = window
            self.channel = channel

        return ssim(img1, img2, val_range=self.val_range, window=window,
                    window_size=self.window_size, size_average=self.size_average)


def msssim(img1, img2, val_range, normalize=False):

    device = img1.device
    weights = torch.FloatTensor([0.0448, 0.2856, 0.3001, 0.2363, 0.1333]).to(device)
    levels = weights.size()[0]
    mssim = []
    mcs = []
    for _ in range(levels):
        sim, cs = ssim(img1, img2, val_range=val_range, full=True)
        mssim.append(sim)
        mcs.append(cs)

        filtered_im1 = F.avg_pool2d(img1, kernel_size=2, stride=2)
        filtered_im2 = F.avg_pool2d(img2, kernel_size=2, stride=2)
        img1 = filtered_im1
        img2 = filtered_im2

    mssim = torch.stack(mssim)
    mcs = torch.stack(mcs)

    # Normalize (to avoid NaNs during training unstable models, not compliant with original definition)
    if normalize:
        while mssim.dim() > 0:
            mssim = mssim.mean()
            mcs = mcs.mean()

        power_factors = weights
        mssim = torch.prod(mcs[:-1] ** power_factors[:-1] * mssim[-1] ** power_factors[-1])
        return mssim

    mssim = (mssim + 1) / 2
    msc = (mcs + 1) / 2
    pow1 = msc ** weights
    pow2 = mssim ** weights
    output = torch.prod(pow1[:-1] * pow2[-1])
    return output


class MSSSIM(torch.nn.Module):
    def __init__(self, window_size=11, size_average=True, channel=3):
        super(MSSSIM, self).__init__()
        self.window_size = window_size
        self.size_average = size_average
        self.channel = channel

    def forward(self, img1, img2):
        # TODO: store windows between calls if possible.
        return msssim(img1, img2, normalize=True)

此段代码定义了一个简单的 `SSIM` 类以及一个多尺度版本 `MSSSIM` ，可用于计算两张输入图像之间的 SSIM 值。这有助于训练过程中最小化预测图与目标图之间差距，从而提升最终输出效果。