﻿ 应用均值滤波的舰船红外图像规整化复原算法
 舰船科学技术  2023, Vol. 45 Issue (13): 182-185    DOI: 10.3404/j.issn.1672-7649.2023.13.038 PDF

The regularization and restoration algorithm of ship infrared image using mean filtering
QIN Juan-ying
Xi'an Traffic Engineering Institute, Xi 'an 710300, China
Abstract: In order to solve the problem that infrared sensors are prone to signal pollution when collecting infrared images of ships, which leads to low output image quality, the regularization and restoration algorithm of ship infrared images using mean filter is studied. Using the method of non-local mean filtering, the similarity of neighborhood blocks of ship infrared images is calculated, weighted coefficients are constructed according to the similarity calculation results, weighted average processing is performed on ship infrared images, and the mean filtering results are output. The image restoration algorithm based on variable coefficient filter is applied to the ship infrared image after mean filtering, and the normalization penalty term is constructed and added to the cost function of the restoration algorithm. The experimental results show that this algorithm can realize the regularization restoration of ship infrared images, and the information entropy of ship infrared images after restoration is higher than 7, and the restoration effect is ideal.
Key words: mean filtering     ship infrared image     regularization     restoration algorithm     filter     constraint penalty term
0 引　言

1 舰船红外图像规整化复原算法 1.1 非局部均值滤波的舰船红外图像去噪

 $v\left( i \right) = u\left( i \right) + \delta n\left( i \right) ，$ (1)

 $\tilde u\left( i \right) = \sum\limits_{j \in \Omega } {w\left( {i,j} \right)v\left( j \right)} 。$ (2)

 ${d_{i,j}} = \left\| {v\left( {{N_i}} \right) - v\left( {{N_j}} \right)} \right\|_{2,a}^2，$ (3)
 $w\left( {i,j} \right) = \exp - \left\| {v\left( {{N_i}} \right) - v\left( {{N_j}} \right)} \right\|_{2,a}^2/z\left( i \right) 。$ (4)

1.2 基于可变系数滤波器的舰船红外图像复原

 $g\left( i \right) = f\left( i \right) * h\left( i \right) + n\left( i \right) 。$ (5)

 图 1 舰船红外图像复原结构图 Fig. 1 Ship infrared image restoration structure

u(i)与g(i)分别为图1中的可变系数滤波器以及退化的舰船红外图像，e(i)与 ${\hat f_N}\left( i \right)$ 分别表示 $\hat f\left( i \right)$ ${\hat f_N}\left( i \right)$ 的差值以及g(i)与u(i)的卷积结果。 ${\hat f_N}\left( i \right)$ 为满足有限支持域约束条件的，舰船红外图像真实空间上的投影，其表达式如下：

 ${\hat f_N}\left( i \right) = \left\{ {\begin{array}{*{20}{c}} \hat f\left( i \right),\hat f\left( i \right) \geqslant 0 ，& \left( i \right) \in D，\\ 0, \hat f\left( i \right) < 0 ，&\left( i \right) \in D，\\ L,& \left( i \right) \in \overline D 。\end{array}} \right.{\kern 1pt}$ (6)

 $\begin{split} J\left( u \right) = &\sum\limits_{\forall i} {\left[ {{{\hat f}_N}\left( i \right) - \hat f\left( i \right)} \right]} = \\ & {\sum\limits_{i \in \overline D } {{{\left[ {\hat f\left( i \right) - {L_B}} \right]}^2} + \gamma \left[ {\sum\limits_{\forall i} {u\left( i \right) - 1} } \right]} ^2}。\end{split}$ (7)

1.3 细节规整化的舰船红外图像复原

 ${J_\alpha }\left( u \right) = \frac{\alpha }{2}\int {\varphi \left( {\left| {\nabla \hat f\left( i \right)} \right|{\rm{d}}x{\rm{d}}y} \right)} 。$ (8)

 $\left| {\nabla \hat f\left( i \right)} \right| = \sqrt {{{\left( {\frac{{\partial \hat f\left( {x,y} \right)}}{{\partial x}}} \right)}^2} + {{\left( {\frac{{\partial \hat f\left( {x,y} \right)}}{{\partial y}}} \right)}^2}} ，$ (9)

 $\varphi \left( i \right) = \sqrt {1 + {i^2}}，$ (10)

 ${J_\alpha }\left( u \right) = \frac{\alpha }{2}\int {\left( {\sqrt {1 + {{\left( {\hat f_x^{}\left( i \right) + \hat f_y^{}\left( i \right)} \right)}^2}} } \right)} {\rm{d}}x{\rm{d}}y ，$ (11)

 $J'\left( u \right) = J\left( u \right) + {J_\alpha }\left( u \right) 。$ (12)

2 性能测试与分析

 图 2 原始舰船红外图像 Fig. 2 Infrared image of the original ship

 图 3 舰船红外图像均值滤波结果 Fig. 3 Ship infrared image mean filtering results

 图 4 舰船红外图像复原结果 Fig. 4 Ship infrared image restoration results

3 结　语

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