Hyperspectral Unmixing Using Nonlocal Similarity-Regularized Low-Rank Tensor Factorization

Recently, methods based on nonnegative tensor factorization (NTF), which benefits from the tensor representation of hyperspectral imagery (HSI) without any information loss, have attracted increasing attention. However, most existing methods fail to explore the internal spatial structure of data, resulting in low unmixing performance. Moreover, when the algorithm is optimized, the solution is unstable. In this article, a regularizer based on nonlocal tensor similarity is proposed, which can not only fully preserve the global information of HSI but also mine the internal information of data in the spatial domain. HSI is regarded as a 3-D tensor and is directly subjected to endmember extraction and abundance estimation. To fully explore the structural characteristics of data, we simultaneously use the local smoothing and low tensor rank prior of the data to constrain the unmixing model. First, several 4-D tensor groups can be obtained after the nonlocal similarity structure of HSI is learned. Subsequently, a low tensor rank prior is applied to each 4-D tensor, which can fully simulate the nonlocal similarity in the image. In addition, total variation (TV) is also used to explore the local spatial relationship of data, which can generate a smooth abundance map through edge preservation. The optimization is solved by the ADMM algorithm. Experiments on synthetic and real data illustrate the superiority of the proposed method.