Semi-blind hyperspectral and multispectral image fusion via generalized inverse matrix optimization

Combining a low spatial resolution hyperspectral image (HSI) with a high spatial resolution multispectral image (MSI) is an economical way to obtain a high spatial resolution hyperspectral image (HR-HSI). However, existing fusion methods often rely on a critical variable, the point spread function (PSF), which is difficult to obtain in practice. Additionally, these methods often require a long fusion time and have many parameters that need re-debugging on different datasets to achieve satisfactory results. Many existing methods lack robustness in handling complex scenarios, such as complex PSF, changing spatial downsampling factors, and large-scale datasets. These issues can result in degraded performance or render the methods inapplicable to practical scenarios. Therefore, we propose an efficient and parameterless semi-blind fusion method based on generalized inverse matrix optimization (GIMO), which is robust for multiple complex situations. Our method uses the definition of generalized inverse matrix and the relationship among HSI, MSI, and HR-HSI to approximate the function module of PSF. Then, we calculate the generalized inverse matrix of the spectral response function (SRF). Finally, we optimize the generalized inverse matrix of SRF using the Sylvester equation and multiply it with MSI to obtain HR-HSI. This is the first proposed method to achieve hyperspectral image super-resolution by optimizing the inverse matrix of the spectral response function. Experiments on multiple simulated datasets and one real dataset have validated that our GIMO method outperforms existing state-of-the-art methods, especially regarding fusion time and robustness for various complex scenarios.