Bilateral Filter Regularized L2 Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing

Abstract

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.

Sparse Constrained Low Tensor Rank Representation Framework for Hyperspectral Unmixing

“…NMF aims at finding a set of bases that can express the data as accurately as possible and the expression coefficients of the data under the bases [10]. However, the NMF framework that regards unmixing as a blind source separation problem is non-convex problem with respect to two matrices obtained, which is greatly affected by the initial value and the solution is not stable enough [11]. Therefore, to improve the performance of unmixing, many regularizations are added to the NMF framework based on the prior knowledge about hyperspectral data, such as sparse regularization [12][13][14], smoothing regularization [15,16], non-local similarity regularization [17], manifold regularization [18], and low-rank regularization [19,20].…”

Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Endmember Independence and Spatial Weighted Abundance

“…The algorithms of VCA and FCLS are often adopted as the initial method for endmember extraction and abundance estimation in the experiment. In addition, numerous different algorithms have been proposed, including the geometric analysis method [15], filtering method [16], deep learning [17], etc. Based on the characteristics of hyperspectral images and some prior information, researchers present a series of abundance estimation algorithms.…”

A Multiscale Hierarchical Model for Sparse Hyperspectral Unmixing

“…The most popular algorithms for NMF belong to the class of multiplicative Lee-Seung algorithms, which have relatively low complexity but are characterized by slow convergence and risk becoming stuck in local minima [9]. To improve the performance of the NMF based hyperspectral unmixing method, further constraints were imposed on NMF [10][11][12][13][14]. Miao and Qi proposed a minimum volume constrained non-negative matrix factorization [15].…”