Wavelet image fusion based on the high order polynomial regression

In many applications of remote sensing there were demands to combine the high spatial and the high spectral resolutions for obtaining the most complete and accurate description of the observed scene. Some wavelet methods were utilized to fuse multispectral (MS) and panchromatic (PAN) images. Any image can be broken into various high- and low- frequency components through discrete wavelet transformation (DWT). By definition, the low-frequency image is of approximation and the high-frequency image contains the detail of the image. Many merging models of DWT coefficients were developed. As the representation of the true detail information the high-frequency part of high resolution image (HRI) used in the fusion was often overemphasized, and the spectral difference between HRI and the channels of low resolution image (LRI) was often ignored. In some researches though the correlation analysis between the HRI and LRI were take account as the weight in the detail and approximation coefficients combination, the spectral relationship might not be expressed by the first order polynomial. The high order polynomial (2 order and 3 order) methods were introduced and the quantitative comparison was analyzed in this study. For 2 order regression, the method in different DWT functions all showed better appearances in the quantity assessment. But the 3 order results appeared serious instability.