变形L1正则化的高光谱图像稀疏解混

如何准确地刻画易于求解的稀疏正则化函数是高光谱图像稀疏解混的难点。变形L₁正则化函数是一类由绝对值函数组成的双线性变换的单参数族,类似于L_pp∈0,1范数,通过调整参数a∈0,可以准确表征L₀和L₁之间的任意范数,并具有无偏、稀疏和Lipschitz连续性。论文首先研究变形L₁正则化函数,然后提出变形L₁正则化的高光谱稀疏解混变分模型,最后提出变形L₁正则化高光谱稀疏解混模型的凸函数差分求解算法。通过模拟和真实的高光谱数据实验,与经典的SUnSAL算法相比,表明提出的算法能够更准确地刻画丰度系数的稀疏性,并获得更高的解混精度。

Transformed L1 regularization for hyperspectral sparse unmixing

How to accurately characterize the sparse regularization function which is easy to be solved is difficult for sparse hyperspectral unmixing.Transformed L₁TL₁regularization function is a one parameter family of bilinear transformations composed with the absolute value function,similar to L_p norm with p∈0,1,it represents any norms from L₀ to L₁exactly through a nonnegative parameter a∈0,,and satisfies unbiasedness,sparsity and Lipschitz continuity properties.In this paper,we study TL₁regularization function and propose sparse hyperspectral unmixing model with TL₁regularization.Meanwhile,a difference of convex algorithm for TL₁in computing TL₁regularized sparse unmixing problems is presented.Experimental results on both simulated and real hyperspectral data demonstrate that the TL₁regularization function describes the sparsity of endmembers more accurately and the proposed algorithm is much more accurate than SUnSAL algorithm.