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Dictionary Learning for Sparse Representation Based Image Fusion

Sparse representation based fusion of optical satellite images that have different spectral and spatial resolution is a rapidly growing research field. The central idea behind these methods is that patches of the fusion result, an image with high spectral and spatial resolution, have 
a sparse representation in a dictionary that is constructed from an input image with low spectral and high spatial resolution. Given the importance of this dictionary to the quality of the final high resolutions multispectral image, it is essential to use an intelligent dictionary selection or modification method. The pan-sharpening reconstruction performance for the state of the art J-SparseFI algorithm is investigated for the selection and training of coupled, local low and high resolution dictionaries, composed of corresponding low and high resolution panchromatic image patches. The performance is assessed for ten separate 
local dictionary selection methods, selecting coupled local dictionary atoms on the basis of distance, similarity or probabilistic dissimilarity to the current patch under reconstruction. Findings suggest an intriguing and counterintuitive tradeoff between spectral fidelity and spatial performance. Dictionary selection recommendations based spatial performance, robustness and spectral performance are made. A K-SVD based dictionary post training algorithm is also proposed. Modest performance improvements are observed when sharping a mutually uncorrelated WorldView-2 red-edge multispectral channel. Recommendations are made for future investigations into dictionary selection and training for J-SparseFI, with 
provision for extension into the Hyperspectral-Multispectral data fusion regime.