The inverse-imaging problem comprising the fusing of a hyperspectral image, possessing high spectral resolution, with a multispectral image, having high spatial resolution, to yield an image with high resolution both spatially and spectrally is considered. In particular, a prior state-of-the-art approach—low-rank tensor approximation (LRTA)—is revisited with the goal of simplifying its implementation and accelerating its execution speed. Whereas the original LRTA incorporated low-rank objectives both spatially and spectrally, the revised algorithm employs spectral low-rankness exclusively. Additionally, the reliance of LRTA on singular value thresholding (SVT)—an operator widely used to impose low-rankness in optimizations—is replaced with a fixed-basis approximation that eliminates the computationally costly singular value decomposition required by the SVT. The proposed modifications ultimately result in significant runtime speedup; furthermore, empirical results reveal improved fusion quality when compared to the original LRTA.