Hyperspectral unmixing (HU) is one of the most active hyperspectral image (HSI) processing research fields, which aims to identify the materials and their corresponding proportions in each HSI pixel. The extensions of the nonnegative matrix factorization (NMF) have been proved effective for HU, which usually uses the sparsity of abundances and the correlation between the pixels to alleviate the non-convex problem. However, the commonly used $L_{1/2}$ sparse constraint will introduce an additional local minima because of the non-convexity, and the correlation between the pixels is not fully utilized because of the separation of the spatial and structural information. To overcome these limitations, a novel bilateral filter regularized $L_2$ sparse NMF is proposed for HU. Firstly, the $L_2$ -norm is utilized in order to improve the sparsity of the abundance matrix. Secondly, a bilateral filter regularizer is adopted so as to explore both the spatial information and the manifold structure of the abundance maps. In addition, NeNMF is used to solve the object function in order to improve the convergence rate. The results of the simulated and real data experiments have demonstrated the advantage of the proposed method.

The hyperspectral unmixing technique is of great significance for hyperspectral data analysis. The non-negative matrix factorization (NMF)-based method is one of the most popular unmixing methods. However, the sparse constraints commonly used in NMF methods are not differentiable at zero, which affects the stability and accuracy of the results. In addition, sparse constraints are supposed to have endmember departure limitations. An improved sparse NMF algorithm is proposed. First, a biased L_{1  /  2} sparse constraint is used to effectively explore the sparsity of abundances, which can also have a sparse effect under the condition of the abundance sum-to-one constraint. Second, to alleviate the endmember departure effect, a minimum energy difference constraint is introduced. Simulated and real-data experiments verify the advantages of the proposed method against state-of-the-art sparse NMF methods.

Sparse regression methods based on the spectral libraries have shown promise for hyperspectral unmixing, which assumes that the observed image can be represented linearly by a small subset of a known spectral library. However, the spectral mismatches are often assumed to occur between the actual endmembers and the corresponding signatures in the spectral library, which greatly limits the application of the sparse unmixing method. In this article, we address the abovementioned problem by adaptively adjusting the spectral library to match the current hyperspectral image during the unmixing procedure and propose a spectral library adaptive collaborative sparse unmixing model. In our model, we introduce both the spectral scaling factors and the spectral residual variables, which can adjust the spectral library in terms of spectral intensity and local spectral variations, respectively. Moreover, the first-order sparse property of the spectral difference is utilized to improve the accuracy of the spectral library adjustment. We solve our model by the alternating direction method of multipliers. Simulations and real-data experiments show that the proposed method is effective for reducing the impact of spectral library mismatches compared with state-of-the-art algorithms.

Sparse regression based on spectral libraries has become a promising alternative for addressing the hyperspectral unmixing problem. However, the actual endmembers of a scene are usually inconsistent with the corresponding spectral signatures in the spectral library, which largely limits the performance of sparse regression approaches. In this letter, a new sparse regression algorithm considering spectral library mismatch is proposed, which allows the spectral signatures in the spectral library to independently scale in each band and regularizes the differential of the scaling factors to be sparse. Moreover, a guided filter (GF)-based regularizer is introduced to explore the spatial-contextual information. The spectral library sparse scaling and GF constraints are combined to mitigate the impact of the spectral library mismatch. Experimental results on both synthetic and real data show that the proposed algorithm outperforms other methods that address the spectral library mismatch problem.