Adaptive Feedback‐Driven Gram‐Schmidt Pansharpening: An Iterative Quality Enhancement Framework

ABSTRACT Gram‐Schmidt (GS) sharpening is a component‐substitution method that uses GS orthogonalization to inject spatial detail from the panchromatic (PAN) image into the multispectral (MS) bands. A simulated PAN is formed from the MS bands, a forward GS transform decorrelates the data, the high‐resolution PAN replaces the first component, and the inverse GS transform produces the sharpened MS image. In this work, an adaptive feedback‐driven pansharpening (AFDP) framework is proposed to enhance the GS method. The GS result is low‐pass filtered to create an updated low‐resolution MS image, which is fed back into the GS process and iterated until an established quality criterion, the QNR index in our case, is met. The mathematical analysis of the AFDP framework shows that PAN details are transferred gradually across iterations, not in a single step like with the classical GS method, allowing controlled and data‐driven detail injection. Experiments conducted on three satellite datasets, including WorldView‐2, QuickBird and Ikonos demonstrate that the AFDP‐GS method consistently enhances the fusion results, numerically and visually, compared to the classical GS method, along with a set of baseline methods including intensity‐hue‐saturation, principal component analysis, high‐pass filtering and high frequency modulation methods.