Sparse Hyperspectral Unmixing via Heuristic lp-Norm Approach

In this paper, we propose a new approach to approximate the l(0) -norm for linear sparse hyperspectral unmixing of images. We approximate the l(0) -norm with the l(p)-norm and iteratively reduce p to enhance the results. The p-changing heuristic scheme that reduces the value of p smoothly and iteratively, results in an enhanced sparse solution. We introduce an iteratively reweighted l(2) -norm to approximate the l(p) -norm. In this approach, a parameter epsilon is involved to deal with the fact that l(p) -norm problem is not Lipschitz continuous for the region of p < 1. We propose two different methods to update the pair (p, epsilon). Finally, we evaluate our proposed heuristic l(p) -norm method over the synthetic data as well as real hyperspectral dataset. Experimental results show that our algorithm outperforms several state-of-the-art algorithms in terms of the reconstruction errors and their probability of success.