Research Of Fully Constraint Abundance Estimation Algorithm Combing Relax Variable

Hyperspectral remote sensing technology provides a way to analyze component and the fraction by spectral unmixing.The classical method is Least Squares algorithm.But it is defined without any constraint on the abundance.The Fully constrained Least Squares(FCLS)algorithm satisfies non-negative and sum-to-one constraints,which has practical physical significance.It has been widely used till now because of its physical significance.But when the number of endmembers is large,it gets much slow.And unmxing error is high if the endmembers are not found out completely and not ideal.Some improvements have been made in improving the efficiency of the algorithm,but the research on increasing accurateness is relatively few.Based on the traditional primal-dual interior point algorithm,this paper proposes two new constrained objective functions for the primal-dual interior-point method,considering the tatistical characteristic of abundance and the complex and ubiquitous noise in hyperspectral images.Firstly,the traditional primal-dual interior point algorithm is improved,and the interative points are located on the primal-dual center path by improving the selection step parameter,rather than the path tracing method.In addition,the estimation of parameters in dual clearance is required before moving direction,so that the original problem and dual problem tend to optimal.Secondly,because hyperspectral image has low spatial resolution,widespread noise,complex objects,unknown endmembers,and may not exist the pure end element,so the abundance sum-to-one constraint is no longer satisfied.As a result,a method specifically designed for the sum-to-one constraint can easily become vulnerable when the sum-to-one condition does not remain valid.In this paper,we relax the abundance sum-to-one constraint as this condition is rarely satisfied in reality and use the relaxed sum-to-one constraint instead to develop a constrained method.The relaxed primal-dual interior point algorithm control constraint by the relaxed variable,which is tested on both simulation and real hyperspectral images.Based on the above theory,this paper completes the theoretical and optimization process derivation of the above algorithm,and experiments on the proposed algorithm in the simulated hyperspectral image and the real high spectrum.Verified that the proposed algorithm is better than the original algorithm in abundance estimation accuracy and reconstruction error,and can still get stable unmixing solution when the endmember is unknown and unsatisfactory.