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基于导热方程的图像去噪与锐化

XJTU “数学物理方程”课程 2023fall 的大作业代码。

本仓库储存了使用导热方程的解析解解法、数值解解法的代码实现。

快速开始指南

git clone https://github.com/yy4382/heat-denoise.git
cd heat-denoise

python -m venv venv

# Windows
venv\Scripts\activate
# Linux / macOS
source venv/bin/activate

pip install -r requirements.txt

python main.py

结果图存于 data/results 下

结论

使用代入解析解的方法时,对高斯噪音的效果相对较好(图一)由于计算机无法计算无穷级数,测试时级数累加至 10000。不够高的级数可能是丢失部分高频信息的原因。

使用迭代法时,对泊松噪音的效果较好(图二)

由于导热方程难以区分物体边缘和噪点,导致降噪后图片有不同程度模糊。当 t 增大时,模糊加剧。(图三)

图一

$$ Gaussian\ noise\ params:\ mean=0,\ \sigma=0.08\\ PDE\ params:\ a=1,\ t=0.4 $$

图二

$$ Poisson\ noise\ params:\ lam=35\\ PDE\ params:\ a=0.025,t=10^5 $$

图三

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