Lagrange constraint neural network for fully constrained subpixel classification in hyperspectral imagery

Linear unmixing approaches are used to estimate the abundance fractions of the endmembers resident in each pixel. Generally, two constraints will be applied. First, the abundance fractions of each endmembers should be nonnegative, which is called nonnegativity constraint. The second constraint, called sum-to-one constraint, says the sum of all abundance fractions should be one. One great challenge is to include the nonnegativity constraint while solving linear mixture model. In this paper, we propose a Lagrange constraint neural network (LCNN) approach to linearly unmix the spectrum with both sum-to-one and nonnegativity constraints.