A New Pan-Sharpening Algorithm Using A Variational Model

The remote sensing image fusion has been a focus in the study of image processing problems. With the rapid development of sensing and detection technology, to obtain the spatial quality and spectral fidelity of the multispectral image simultaneously has become more and more urgent. With the focus from scientific research scholars on the issue, in recent years, many excellent works and algorithms have sprung up and make the solutions diversify. Compare to spatial quality improvement, the spectral characteristics of fidelity has a great room for improvement.In this paper, we start from the variational models. We analyze the present works and introduce the new spatial information constraint and spectral information constraint. Two new image fusion algorithms are proposed to multi-band image fusion. The works of this paper are mainly on the following points:First, at present, the remote sensing image fusion algorithm cannot improve the spatial quality and spectral fidelity of the multispectral image simultaneously. A variational image fusion algorithm based on spatial and spectral constraints is proposed to solve this problem. Firstly, the difference of each band before and after fusion and the difference of the observed spatial quality are assumed to be consistent. Based on the assumption, the edge-based spatial information constraint is proposed. And then on the assumption that the correlation of bands remains unchanged before and after the fusion, the spectral-band-ratio-based spectral information constraint is proposed. Finally, these two constraints are integrated into the variational model, which is minimized by a gradient descent method.Second, a weighted dynamic gradient sparsity penalty is thus proposed for regularization. This penalty can effectively exploit reference invariant between multi-spectral image and the panchromatic image and keep the correlation and the difference between the multi spectral images before and after. This ensures spectral fidelity in injection spatial information simultaneously.Finally, the fusion algorithms based on the variational model use Gauss kernel to approximate the actual fuzzy kernel when the image is degraded. To improve the spectral fidelity and express image degradation processes, a salient edge kernel estimation algorithm is proposed.In addition, experiments using Pleiades, QuickBird and WordView-2 data sets and more comparison with state-of-the-art algorithms show that our fusion images are more prominent and better on spatial detail and spectral fidelity than other state-of-the-art algorithms.