Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery

Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods