A fast variational fusion approach for pan-sharpening

A fast variational fusion model based on partial differential equation (PDE) is presented for pan-sharpening. The functional is constructed with several energy terms. The gradient energy term is created by calculating the gradient vector field of the panchromatic image. The visualization energy term is used for improving the perceptual effect and the spectral preserving energy term is designed for enforcing the spectral coherence. The channel correlation energy term and the radiometric reduction energy term are defined to preserve the correlation of multi-spectral channels and decrease the radiometric distortion. Inspired by the shock-filtering model, an inverse diffusion term for image enhancement is put to PDEs which is deduced by minimizing the energy functional. In comparison with the fusion models based on discrete wavelet transform, à trous wavelet transform and the contrast-based PDE, it is shown that our model can improve the spatial resolution of the multi-spectral bands while preserving the spectral quality more effectively. Our model's computational complexity for one time step is only O(N).