Pansharpening of Multispectral Data Based on Lagrange Optimization

Satellite data provides images of heterogenous resolutions of the scenes on the earth’s surface. It is of great practical value to fuse images of the same scene with different resolutions. Pansharpening is a pixel-level image fusion technique resulting in a high resolution multispectral image in terms of both spatial (pan) and spectral (XS) resolutions. The challenge lies in maintaining the spectral characteristics of each channel of the XS image when pan image is used to estimate the high spatial resolution XS image. The primary objective of the study is to preserve or maintain the spectral consistency of the multispectral data during the fusion process. A data-centric approach consisting of a linear regression model between the panchromatic and multispectral channels is proposed. In order to maximise the spectral consistency, Lagrange optimization is carried out. The proof of the proposed concept is initially established with the smaller 8×8 pixel images. Considering practical applications, the study is scaled up to 512×512 pixel images. Evaluation of the proposed method is carried out by comparing it with the existing methods of IHS, Brovey, PCA, SFIM, HPF and Multi under different performance criteria such as chi-square (
2) test,
2 test, root mean square error (RMSE), signal to noise ratio (SNR), spectral discrepancy (SD) and ERGAS. It is shown that that the proposed method generally outperforms the existing methods based on the performance criteria considered.