论文标题
对称分析的四阶降噪偏微分方程
Symmetry Analysis for a Fourth-order Noise-reduction Partial Differential Equation
论文作者
论文摘要
我们应用了谎言对称性的理论，以研究四阶$ 1+2 $进化部分偏微分方程，该方程已提议用于降低图像处理噪声。特别是，我们确定特定1+2部分微分方程的躺点对称性，并应用不变函数来确定相似性解决方案。对于静态溶液，我们观察到，减少的四阶普通微分方程将还原为最大对称的二阶普通微分方程。最后，还确定了非静态封闭式溶液。
We apply the theory of Lie symmetries in order to study a fourth-order $1+2$ evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries for the specific 1+2 partial differential equations and we apply the invariant functions to determine similarity solutions. For the static solutions we observe that the reduced fourth-order ordinary differential equations are reduced to second-order ordinary differential equations which are maximally symmetric. Finally, nonstatic closed-form solutions are also determined.
