Abstract: Symmetric fractional B-spline wavelet is more superior than traditional wavelets in obtaining the texture information of images due to its approximation properties, which is beneficial for image fusion. A technique based on symmetric fractional B-spline wavelet and PCA（Principal Component Analysis） transform is proposed for the fusion of high resolution panchromatic image and low resolution multispectral image. It performs PCA transform on the two source images to get the principal components. Two groups of approximate and detail coefficients are obtained by applying wavelet decomposition to the two first principal components. An inverse wavelet transform is performed on the new wavelet coefficients that are merged by different rules to generate a new first principal component. It uses the new first principal component and other principal components of the multispectral image to apply an inverse PCA transform to get the fused image. Experimental results testify that the fused image obtained by the proposed method has both high resolution and rich spectrums.

Key words: image fusion, Intensity Hue Saturation（IHS） transform, Principal Component Analysis（PCA） transform, fractional B-spline wavelet

摘要： 有良好逼近能力的对称分数B样条小波，在刻画图像纹理方面优于传统小波，为图像融合提供了有利条件。将其与PCA（Principal Component Analysis）变换相结合之后对高分辨率全色图像和低分辨率多光谱图像进行融合，提出了一种新的图像融合算法。对两幅源图像应用PCA变换，得到的两个第一主分量分别进行对称分数B样条小波变换，再对产生的两组高、低频小波系数采取不同的规则进行融合，生成两组新的高、低频系数，对其进行小波反变换得到新的第一主分量，与多光谱图像的其他主分量进行PCA反变换，得到最终的融合图像。实验结果表明，该方法使融合图像既提高了分辨率又保留了丰富的光谱信息。

关键词: 图像融合, 亮度-色度-饱和度（IHS）变换, 主成分分析（PCA）变换, 分数B样条小波