Comparison between Mallat's and the 'a trous' discrete wavelet transform based algorithms for the fusion of multispectral and panchromatic images

In the last few years, several researchers have proposed different procedures for the fusion of multispectral and panchromatic images based on the wavelet transform, which provide satisfactory high spatial resolution images keeping the spectral properties of the original multispectral data. The discrete approach of the wavelet transform can be performed with different algorithms, Mallat's and the 'a trous' being the most popular ones for image fusion purposes. Each algorithm has its particular mathematical properties and leads to different image decompositions. In this article, both algorithms are compared by the analysis of the spectral and spatial quality of the merged images which were obtained by applying several wavelet based, image fusion methods. All these have been used to merge Ikonos multispectral and panchromatic spatially degraded images. Comparison of the fused images is based on spectral and spatial characteristics and it is performed visually and quantitatively using statistical parameters and quantitative indexes. In spite of its a priori lower theoretical mathematical suitability to extract detail in a multiresolution scheme, the 'a trous' algorithm has worked out better than Mallat's algorithm for image merging purposes.