A No-Reference Multivariate Gaussian-Based Spectral Distortion Index for Pansharpened Images

Pansharpening is a fundamental image fusion technique used to enhance the spatial resolution of remote sensing imagery; however, it inevitably introduces spectral distortions that compromise the reliability of downstream analyses. Existing no-reference (NR) quality assessment methods often fail to exclusively isolate these spectral errors from spatial artifacts or lack sensitivity to specific radiometric inconsistencies. To address this gap, this paper proposes a novel No-Reference Multivariate Gaussian-based Spectral Distortion Index (MVG-SDI) specifically designed for pansharpened images. The methodology extracts a hybrid feature set, combining First Digit Distribution (FDD) features derived from Benford's Law in the hyperspherical color space (HCS) and Color Moment (CM) features. These features are then used to fit Multivariate Gaussian (MVG) models to both the original multispectral and fused images, with spectral distortion quantified via the Mahalanobis distance between their statistical parameters. Experiments on the NBU dataset showed that the MVG-SDI correlates more strongly with standard full-reference benchmarks (such as SAM and CC) than existing NR methods like QNR. Tests with simulated distortions confirmed that the proposed index remains stable and accurate even when facing specific spectral degradations like hue shifts or saturation changes.