Hyperspectral Unmixing Based On Approximate Sparsity Constrainted Nonnegative Matrix Factorization

Hyperspectral remote sensing is a combined imaging technology and spectroscopy of multi-dimensional information retrieval technology, it can also obtain the two-dimensional geometric space and one dimension spectral information of image, which makes us to classification, detection and target recognition possible. However, due to the limit of spatial resolution of the sensor and the variant ground surface, the observation of one pixel maybe contain several substances, which makes mixed pixels are widely exist. The widely exist mixed pixels will seriously affect the accuracy of the identification and classification of objects. So hyperspectral unmixing more efficient has become an important problem for exploiting the hyperspectral dataNonnegative matrix factorization (NMF) is a matrix decomposition method, which can approximation decomposes a nonnegative matrix into a product of two nonnegative matrix. It is very similar to the mixed pixel unmixing model, so we can use it to solve the problem. However, it is difficult to obtain a globally optimal solution because of the nonconvexity of the NMF objective function. NMF is always utilized with other constraints to solve the problem. Sparse model is a research focus in the field of image. It can capture the data of main information and the intrinsic geometric structure by using the coefficient of very little, and is more robust to noise and error. Because of the sparsity of the abundance matrix, we can add the sparse constrained to the nonnegative matrix model. Therefore, we make owe main research on sparsity constrained nonnegative matrix factorization for hyperspectral unmixing. The major works are as follows:For NMF algorithm is easy to fall into the local minimum, we proposed a new approximate sparsity model to the objective function of NMF. Our sparsity model give sparser solutions than other and easy to solve. We application the approximate sparsity constrained of NMF model (ALo-NMF) to hyperspectral unmixing. The experiment of synthetic data and real data both illustrate the effect of our algorithm.On account of the performance of basic nonnegative matrix factorization algorithm maybe quite poor, we use the multilayer nonnegative matrix factorization to replace it. After research the multilayer nonnegative matrix factorization algorithm, we found we can add L1/2 sparsity constrained on it. Considering the approximate sparsity constrained, we proposed multilayer nonnegative matrix factorization based on approximate sparse constraint (MLNMFASC) algorithm and we application it to the hyperspectral unmixing. We illustrate the utility of our algorithm on synthetic data and real data and compared with other algorithms.