Fusion of Hyperspectral and Multispectral Images Based on a Centralized Non-local Sparsity Model of Abundance Maps

Objective: Hyperspectral (HS) imaging systems are commonly used in a diverse range of applications that involve detection and classification tasks. However, the low spatial resolution of hyperspectral images may limit the performance of the involved tasks in such applications. In the last years, fusing the information of an HS image with high spatial resolution multispectral (MS) or panchromatic (PAN) images has been widely studied to enhance the spatial resolution. Image fusion has been formulated as an inverse problem whose solution is an HS image which assumed to be sparse in an analytic or learned dictionary. This work proposes a non-local centralized sparse representation model on a set of learned dictionaries in order to regularize the conventional fusion problem. Methodology: The dictionaries are learned from the estimated abundance data taking advantage of the depth correlation between abundance maps and the non-local self- similarity over the spatial domain. Then, conditionally on these dictionaries, the fusion problem is solved by an alternating iterative numerical algorithm. Results: Experimental results with real data show that the proposed method outperforms the state-of-the-art methods under different quantitative assessments. Conclusions: In this work, we propose a hyperspectral and multispectral image fusion method based on a non-local centralized sparse representation on abundance maps. This model allows us to include the non-local redundancy of abundance maps in the fusion problem using spectral unmixing and improve the performance of the sparsity-based fusion approaches