Analysis of error propagation in spectral unmixing

The linear mixing model (LMM) is often used to compute the relative fractions of the materials in an image pixel. As in any linear method, errors in the data and transformations are propagated in the solution. This paper presents an analytical derivation showing how error in the data affects the solution of the LMM. We show that for simple types of input error, the solution error can be expressed as a function of the end members. We present examples of 2 and 3 end member problems for both the constrained and the unconstrained solution. We show that the error in the fractions is inversely related to the spectral angle between end members in the unconstrained solution, and inversely related to the Euclidean distance between end members in the constrained solution.