文章目录

00 写在前面

在医学图像重建过程中，经常在代价方程中加入TV 正则项，该正则项作为去噪项，对于重建可以起到很大帮助作用。但是对于一些纹理细节要求较高的任务，加入TV 正则项，在一定程度上可能会降低纹理细节。

对于连续函数，其表达式为：

对于图片而言，即为离散的数值，求每一个像素和横向下一个像素的差的平方，加上纵向下一个像素的差的平方，再开β/2次根：

01 基于Pytorch版本的TV Loss代码

import torch
from torch.autograd import Variable


class TVLoss(torch.nn.Module):
    """
    TV loss
    """

    def __init__(self, weight=1):
        super(TVLoss, self).__init__()
        self.weight = weight

    def forward(self, x):
        batch_size = x.size()[0]
        h_x = x.size()[2]
        w_x = x.size()[3]
        count_h = self._tensor_size(x[:, :, 1:, :])
        count_w = self._tensor_size(x[:, :, :, 1:])
        h_tv = torch.pow((x[:, :, 1:, :] - x[:, :, :h_x - 1, :]), 2).sum()
        w_tv = torch.pow((x[:, :, :, 1:] - x[:, :, :, :w_x - 1]), 2).sum()
        return self.weight * 2 * (h_tv / count_h + w_tv / count_w) / batch_size

    def _tensor_size(self, t):
        return t.size()[1] * t.size()[2] * t.size()[3]


if __name__ == "__main__":
    x = Variable(
        torch.FloatTensor([[[1, 2, 3], [4, 5, 6], [7, 8, 9]], [[1, 2, 3], [4, 5, 6], [7, 8, 9]]]).view(1, 2, 3, 3),
        requires_grad=True)
    tv = TVLoss()
    result = tv(x)
    print(result)

02 论文下载

Understanding Deep Image Representations by Inverting Them