Enhanced gram-schmidt spectral sharpening based on multivariate regression of MS and pan data

In this work, a simple preprocessing patch is introduced before the Gram-Schmidt (GS) spectral sharpening method (as implemented in ENVI) such that the resulting fused multispectral (MS) data exhibit higher sharpness and spectral quality. This is achieved by defining a generalized intensity (GI) component as a weighted average of the MS bands, with weights taken either as percentages of overlap between the spectral responses of individual bands and the spectral response of panchromatic (Pan), or better as regression coefficients between the MS bands and the decimated Pan image. In the former case the weights are pre-calculated for each sensor. In the latter case, the weights are calculated by applying a multivariate regression to the data that are being fused. The above GI component is used as low-resolution approximation of the Pan image. Experimental results carried out on very-high resolution IKONOS data demonstrate that the proposed enhanced GS method visually outperforms both modes of the ENVI implementation of GS, especially in true color displays. Quantitative scores performed on spatially degraded data by means of such parameters as Wald's ERGAS and the novel Q4 score index based on quaternions theory, confirm the superiority of the enhanced GS method over its baseline.