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摘要: 为了得到有效的图像多尺度几何表达，提出一种有效的基于Haar小波变换的平稳Tetrolet变换算法.平稳Tetrolet变换是一种由四个单位正方形通过边连接起来的新的自适应Haar类小波变换，对应的滤波器组简单而有效.与标准二维小波变换相比，平稳Tetrolet变换是一种新型基于四格拼板的多尺度几何变换工具，能够通过多方向选择有效地捕获图像中各向异性特性.本文对平稳Tetrolet变换的分解和重构算法进行了详细描述，对利用平稳Tetrolet变换对图像的分解进行了仿真与分析.实验结果表明，与传统算法相比，提出的算法在保留原始图像边缘和纹理信息的同时，可以有效地取得较好的稀疏表达，能消除Tetrolet变换算法对图像融合存在方块效应的缺陷.
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关键词:
- 图像处理 /
- 平稳Tetrolet变换 /
- 四格拼板 /
- Haar类小波变换 /
- 方块效应
Abstract: In order to get an efficient image multi-scale geometrical representation, an efficient stationary tetrolet transform algorithm based on haar wavelet transform is proposed. Stationary tetrolet transform is a new adaptive haar-type wavelet transform which is made by connecting four equal-sized squares. The corresponding filter bank algorithm is simple but very effective. Compared with the standard two dimensional wavelet transform, stationary tetrolet transform is a novel tetrominoes based multi-scale geometrical transform tool, which can capture image anisotropic geometrical structures information efficiently by multi-direction selection. In this paper, decomposition and reconstruction algorithms of the stationary tetrolet transform are described in detail, and the simulation and analysis of decomposition of the image using the stationary tetrolet transform are carried out. Experimental results show that compared with traditional algorithms, the proposed algorithm can get better sparse representation and eliminate the blocking artifacts in image fusion resulted from tetrolet transform algorithm. Meanwhile, the significant information of original image like textures and contour detail is well maintained.1) 本文责任编委 胡清华 -
图 2 Tetrolet基变换的22种四格拼板结构
Fig. 2 kinds of tetrominoes structures for tetrolet basis transformation
图 3 图像的Tetrolet变换的多尺度分解结构图
Fig. 3 Image multiscale decomposition structure using tetrolet transforms
图 4 采用Tetrolet变换不同层次分解的图像融合结果
Fig. 4 Image fusion results with different levels decomposition using tetrolet transform
图 5 图像的平稳Tetrolet变换的多尺度分解结构图
Fig. 5 Image multiscale decomposition structure using stationary tetrolet transform
图 6 小波变换和Tetrolet变换3层分解系数图像
Fig. 6 The three layer decomposition coefficient image using wavelet transform and tetrolet transform
图 7 平稳小波变换和平稳Tetrolet变换3层分解系数图像
Fig. 7 The three layer decomposition coefficient image using stationary wavelet transform and stationary tetrolet transform
图 8 采用Tetrolet变换不同层次分解的图像融合结果
Fig. 8 Image fusion results with different levels of decomposition using tetrolet transform
图 10 平稳小波和平稳Tetrolet变换分解归一化系数分布图
Fig. 10 Normalized coefficient distribution map using stationary wavelet transform and stationary tetrolet transform
图 11 遥感极化图像的水平极化方向图像
Fig. 11 Horizontally polarized images of remote sensing polarimetric image
图 12 平稳小波和平稳Tetrolet变换分解归一化系数分布图
Fig. 12 Normalized coefficient distribution map using stationary wavelet transform and stationary tetrolet transform
表 1 图 8中不同分解层次的融合图像定量指标
Table 1 Quantitative index of fusion image using different decomposition levels in Fig. 8
不同层次分解 均值 标准差 熵值 平均交叉熵 均方根交叉熵 2层分解 77.419 39.713 6.959 0.3635 0.4455 4层分解 77.408 39.941 6.974 0.2678 0.3283 5层分解 77.356 40.114 6.983 0.2318 0.2843 7层分解 77.287 40.334 6.999 0.2045 0.2509 
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表 2 不同分解方法的融合图像定量指标
Table 2 Quantitative index of fusion image using different decomposition methods
不同分解方法 均值 标准差 熵值 平均交叉熵 均方根交叉熵 WT 140.273 63.452 7.5993 0.4487 0.4502 SWT 140.318 63.866 7.5959 0.4440 0.4480 CT 140.561 63.226 7.6052 0.4302 0.4325 NSCT 140.356 63.703 7.5910 0.4412 0.4458 DT 140.411 61.289 7.5268 0.4897 0.4974 STT 140.309 63.216 7.6236 0.4462 0.4476
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