Remotely sensed spectral images, such as hyperspectral images (HSIs) and multispectral images (MSIs), are widely used across science and engineering fields, including agriculture, oceanography, forest monitoring, mineral discovery, and space exploration. These image modalities involve an inherent trade-off between spatial and spectral resolution: HSIs provide fine spectral detail but coarse spatial resolution, whereas MSIs offer the reverse. Spectral image fusion techniques seek to combine the strengths of both by integrating an HSI and MSI of the same region to produce fused images with high-resolution information in both domains, supporting various tasks such as pixel classification, target identification, and change detection. However, many existing fusion methods operate under the assumption that the spectral images are co-registered (i.e., covering the same region and sharing the same coordinates), whereas in practice the data are often spatially misaligned by pixel shifts, rotations, and other distortions (collectively referred to as “unregistered”), typically arising from differences in sensors or imaging platforms. Despite its fundamental practical importance and considerable interest, the fusion of unregistered spectral images still lacks rigorous theoretical underpinnings and reliable algorithms. This project addresses these gaps by developing new analytical and computational methods to establish a solid theoretical and algorithmic foundation for this long-standing