Pan-sharpening: a fast variational fusion approach

A fast variational fusion model based on partial differential equations (PDEs) is presented for pansharpening. The functional framework consists of several energy terms. The gradient energy term is created by calculating the gradient vector field of the panchromatic image and the geometry of the pan is injected into the multi-spectral bands. The radiometric reduction energy term and the channel correlation energy term are defined to decrease the radiometric distortion and preserve the correlation of multi-spectral channels while enforcing the inter-bands coherence. Inspired by the shock-filtering model, an inverse diffusion term for image enhancement is put to PDEs which are deduced by minimizing the energy functional. In comparison with the state-of-the-art fusion approaches based on `a trous wavelet and non-sampled contourlet, our model can obtain the fused image with a high spatial or spectral quality by adjusting the weight coefficients of the energy terms. It can also achieve a rather good trade-off between the spatial resolution improvement and the spectral quality preserving. Our model's computational complexity for one time step is only O(N).