Total Variation and Signature-Based Regularizations on Coupled Nonnegative Matrix Factorization for Data Fusion

As an effective approach to gain the high-spatial-resolution hyperspectral images, data fusion is usually adopted to enhance the spatial resolution of hyperspectral images by the spatial information of multispectral images. In this paper, in order to remove the ill-posedness of well-known coupled non-negative matrix factorization, we formulate a well-posed fusion problem by incorporating total variation and signature-based regularizations for image smoothing and high-fidelity signature reconstruction. Then, the problem can be decoupled into two convex subproblems, which yield closed-form solutions separately by the alternating direction method of multipliers algorithms. Due to the large sizes of the problems, a few of constructed matrices and tensor operations are employed to simplify the expressions for reducing the computational complexities. Simulation and experimental results not only demonstrate that the performance of the proposed fusion algorithm is much better than that of state-of-the-art methods but also show that the total variation and signature-based regularizers are of paramount importance in yielding the high-spatial-resolution hyperspectral images.