A Sparse Image Fusion Algorithm With Application to Pan-Sharpening

Data provided by most optical Earth observation satellites such as IKONOS, QuickBird, 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 an HR panchromatic and the corresponding LR spectral channels is called "pan-sharpening." It aims at obtaining an HR multispectral image. In this paper, we propose a new pan-sharpening method named Sparse Fusion of Images (SparseFI, pronounced as "sparsify"). SparseFI is based on the compressive sensing theory and explores the sparse representation of HR/LR multispectral image patches in the dictionary pairs cotrained from the panchromatic image and its downsampled LR version. Compared with 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 due 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 with the conventional methods.