A regularization modification to linear spectral unmixing algorithm

Unmixing is an important technique to extract sub-pixel information contained in hyperspectral image. Many spectrum mixture models and unmixing algorithms have been proposed, but little of them consider unmixing as an inverse problem, which is usually ill-posedness, i.e. the uniqueness, existence and stability of solution may not be satisfied simultaneously. Traditional algorithms pay more attention to the former two conditions and neglect the last one. However, actual hyperspectral data is usually noise contaminated, that means the stability of unmixing algorithm is also crucial. Motivated by this, we propose a novel linear spectrum unmixing method based on regularizing operator. By modifying the original form of cost function with respect to linear mixture model, proposed unmixing algorithm reduces the condition number as well as sensitivity to noise of image. Taking semi-simulation hyperspectral image containing noise as test data, we proved thee performance on preserving unmixing effect of our method when unmixing image is noise contaminated.