Linear spectral mixture analysis with the Open Leontief Input-Output Model

Abstract

Commonly, it requires two constraints imposed on the linear spectral mixture analysis (LSMA). One constraint is the abundance of sum-to-one, which requires the abundance fractions of materials presented in an image pixel to be one and is easy to deal with. The other constraint is that any abundance fractions are always nonnegative and difficult to solve with analytical solution. Most of approaches that provide the solution for the latter problem of LSMA use an optimization or maximization procedure. The results of solution resort to optimization strategies. The Leontief input-output model, of which parameters are very similar to LSMA, is represented by a linear system of equations and the system has a unique nonnegative solution. In this paper, we considered how to determine the parameters of LSMA model, and based on the open Leontief input-output model, we presented a fully constrained linear spectral (FCLS) mixture analysis method for estimating material abundance in spectral mixture pixel. The new FCLS method can not only make the abundance fractions of materials be nonnegative, but also keep them less than one, that always obtained by normalizing procedure in other methods. We also examine a number of approaches, previous FCLS and non-negative matrix factorization (NMF) spectral un-mixing, closely related. A series of computer simulations are conducted to demonstrate the performance of the proposed method in material quantification.