A Sparse Image Fusion Algorithm with Application to Pan-sharpening

Data provided by most optical earth observation satellites such as IKONOS, Quick Bird and GeoEye are composed of a panchromatic channel of high spatial resolution (HR) and several multispectral channels at a lower spatial resolution (LR). The fusion of a HR panchromatic and the corresponding LR spectral channels is called “pan-sharpening”. It aims at obtaining a HR multispectral image. In this paper, we propose a new pan-sharpening method named Sparse Fusion of Images (SparseFI, pronounced "sparsify"). SparseFI is based on the compressive sensing theory and explores the sparse representation of HR/LR multispectral image patches in the dictionary pairs co-trained from the panchromatic image and its downsampled LR version. Compared to conventional methods it “learns” from, i.e. adapts itself to, the data and has generally better performance than existing methods. Due to the fact that the SparseFI method does not assume any spectral composition model of the panchromatic image and thanks to the super-resolution capability and robustness of sparse signal reconstruction algorithms, it gives higher spatial resolution and in most cases less spectral distortion compared to the conventional methods