Double-population differential evolution algorithm for bilinear spectral unmixing based on FAN model

Abstract

Hyperspectral unmixing plays an important role in remote sensing applications by extracting the pure constituent spectra and correspondent fractions in mixing pixels. Bilinear mixing models have recently become a hot topic in nonlinear spectral unmixing research. Nevertheless, most of the existing bilinear unmixing algorithms require prior knowledge about the endmembers, which can be regarded as supervised algorithms. This paper reports on a new unsupervised unmixing algorithm based on the FAN bilinear mixing model by employing the differential evolution (DE) algorithm (i.e., DE-FAN), which can solve the bilinear unmixing problems more efficiently and accurately compare with existing unsupervised bilinear unmixing algorithms.Considering the bilinear unmixing problem with hyperspectral imagery, the proposed algorithm makes the following improvements on the standard DE algorithm. First, the mutation factor is tuned dynamically rather than fixed during the iterative process, which can significantly enhance the neighborhood search capability. Second, considering the acceleration of the convergence rate, DE-FAN constructs a double-population (i.e., endmember population and abundance population) framework such that an alternative evolution procedure is presented. Third, the population re-initialization tactic is introduced to enhance the capability of large-scale optimization. It can decrease the number of required population individuals, thus improving the computational efficiency. It can also significantly lower the trapping risk in local optimums. Finally, a cooperative co-evolution tactic is considered. The hyperspectral image is divided into several sub-images and then processed by the DE-FAN algorithm separately. The final solution of the endmember estimation can be obtained by averaging the best solutions from the sub-images. The remaining iterations can continue by fixing the endmember variables with the final endmember solution. The final solution of abundance estimation is achieved when the stopping criteria is met. We validate the DE-FAN algorithm by adopting synthetic datasets and real airborne visible/infrared imaging spectrometer images. Different endmember numbers, signal-to-noise ratios, and maximum abundances are also considered. Several state-of-the-art algorithms (i.e., MVC-NMF, SISAL+FCLS, MU-LQM, N-FINDR+CNLS, geodesic simplex volume maximization, and PG-FAN) are compared. Experimental results conducted utilizing both synthetic and real datasets indicate that the proposed DE-FAN algorithm outperforms other algorithms by obtaining more accurate endmembers and abundance.The DE-FAN algorithm overcomes the LMM shortcomings and solves the bilinear unmixing problem. The unmixing experiments demonstrate that DE-FAN can obtain more accurate results than other classical unmixing algorithms. We will consider the influence of the penalty coefficient and attempt an adaptive method in future work. We will also extend our proposed DE-FAN to more bilinear models such as the polynomial post-nonlinear model and generalized bilinear model.