本文介绍了TV模型的基本原理，并给出了C++代码实现。

一、TV模型原理

二、C++实现

关于Matlab的程序实现，有一个经典的主页： http://visl.technion.ac.il/~gilboa/PDE-filt/tv_denoising.html

有博主改成了C++代码：见经典的变分法图像去噪的C++实现

另有博主改成了更简洁的版本：见【图像处理】全分发TV图像去噪

本文代码基本参照上面的版本

void CImageObj::Total_Variation(int iter, double dt, double epsilon, double lambda)
{
	int i, j;
	double ep2 = epsilon * epsilon;

	double** I_t = NewDoubleMatrix(m_width, m_height);
	for (i = 0; i < m_height; i++)
		for (j = 0; j < m_width; j++)
			I_t[i][j] = m_imgData[i][j];

	for (int t = 0; t < iter; t++)
	{
		for (i = 1; i < m_height - 1; i++)
		{
			for (j = 1; j < m_width - 1; j++)
			{
				double tmp_x = (I_t[i][j + 1] - I_t[i][j - 1]) / 2.0;
				double tmp_y = (I_t[i + 1][j] - I_t[i - 1][j]) / 2.0;
				double tmp_xx = I_t[i][j + 1] + I_t[i][j - 1] - 2 * I_t[i][j];
				double tmp_yy = I_t[i + 1][j] + I_t[i - 1][j] - 2 * I_t[i][j];
				double tmp_xy = (I_t[i + 1][j + 1] + I_t[i - 1][j - 1] - I_t[i - 1][j] - I_t[i][j - 1]) / 4.0;
				double tmp_num = tmp_yy * (tmp_x * tmp_x + ep2) + tmp_xx * (tmp_y * tmp_y + ep2) - 2 * tmp_x * tmp_y * tmp_xy;
				double tmp_den = pow(tmp_x * tmp_x + tmp_y * tmp_y + ep2, 1.5);

				I_t[i][j] += dt*(tmp_num / tmp_den + lambda*(m_imgData[i][j] - I_t[i][j]));
			}
		}

	} // 迭代结束

	// 给图像赋值
	for (i = 0; i < m_height; i++)
		for (j = 0; j < m_width; j++)
		{
			double tmp = I_t[i][j];
<span style="white-space:pre">			</span>tmp = max(0,min(tmp, 255));
			m_imgData[i][j] = (unsigned char)tmp;
		}

	DeleteDoubleMatrix(I_t, m_width, m_height);
}