An optimization perspective onwinter's endmember extraction belief

In this paper, we describe a continuous optimization perspective on Winter's simplex volume maximization belief for endmember extraction in hyperspectral remote sensing. Winter's belief, proposed in the late 90's, is very insightful and has led to one of the most widely used class of endmember extraction algorithms nowadays—N-FINDR. Our endeavor to revisit this problem is to provide an alternative, systematic, framework of formulating and understanding Winter's belief. Under the continuous optimization formulation of Winter's belief, we show a fundamental result that the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers, but also necessary. Then, we derive two Winter-based algorithms based on two different optimization strategies. Interestingly, the resulting algorithms are found to be similar to an N-FINDR variant and the vertex component analysis (VCA) algorithm. Hence, the developed framework provides linkage and alternative interpretations to these existing algorithms. Simulation results are also presented to compare the derived Winter algorithms and several existing algorithms.