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The aim of fusing hyperspectral and multispectral images is to overcome the limitation of remote sensing hyperspectral sensors by improving their spatial resolutions. This process, also known as hypersharpening, generates an unobserved high-spatial-resolution hyperspectral image. To this end, several hypersharpening methods have been developed, however most of them do not consider the spectral variability phenomenon; therefore, neglecting this phenomenon may cause errors, which leads to reducing the spatial and spectral quality of the sharpened products. Recently, new approaches have been proposed to tackle this problem, particularly those based on spectral unmixing and using parametric models. Nevertheless, the reported methods need a large number of parameters to address spectral variability, which inevitably yields a higher computation time compared to the standard hypersharpening methods. In this paper, a new hypersharpening method addressing spectral variability by considering the spectra bundles-based method, namely the Automated Extraction of Endmember Bundles (AEEB), and the sparsity-based method called Sparse Unmixing by Variable Splitting and Augmented Lagrangian (SUnSAL), is introduced. This new method called Hyperspectral Super-resolution with Spectra Bundles dealing with Spectral Variability (HSB-SV) was tested on both synthetic and real data. Experimental results showed that HSB-SV provides sharpened products with higher spectral and spatial reconstruction fidelities with a very low computational complexity compared to other methods dealing with spectral variability, which are the main contributions of the designed method. [ABSTRACT FROM AUTHOR]