Research On Nonlinear Nixing Model-based Unmixing Technology In Hyperspectral Imagery

Hyperspectral remote sensing image has the characteristics of high spectral resolution and image-spectrum integration.It has a strong ability to recognize and distinguish the fine features,making it suitable for vegetation detection,precision agriculture,atmospheric detection,geological exploration,water quality monitoring,and military reconnaissance.However,due to the low spatial resolution of hyperspectral imaging systems and complex distribution of substances,mixed pixels commonly exist in hyperspectral images.The presence of mixed pixels limits the pixel-level application of hyperspectral images,such as target detection and object classification.Spectral unmixing is the basic technique to decompose the pixels into characteristic spectra(endmembers)and their constituent proportions(abundances)under the assumption that the pixels are mixed based on linear mixing model or nonlinear mixing model.Linear mixing model is the most common and simplest mixing model,but due to the complexity of the substances distribution,there are obvious nonlinear mixtures in many practical applications,especially in complex scenes such as vegetation and urban scenes.Therefore,the nonlinear mixing model can reflect the true distribution of substances more effectively.The common nonlinear unmixing algorithm is to solve a specifical nonlinear mixing model by numerical optimization to obtain the estimates of endmembers,abundances,and other nonlinear coefficients.However,due to the complexity of nonlinear mixing models and its highly non-convex objective functions,the supervised/unsupervised nonlinear unmixing algorithms based on gradient methods have problems such as slow convergence and unstable convergence,which require further optimization to improve performance.In addition,most of the nonlinear mixing models only consider the basic physical constraints,but the sparse feature widely existing in real mixture is not negligible factors,which is also necessary for improving solving the nonlinear mixing models.This article will focus on the nonlinear mixing model-based unmixing technology,and carry out research work from the following aspects:(1)The Hopfield neural network(HNN)-based optimization method is used to solve the generalized bilinear model to achieve supervised nonlinear unmixing.The objective function is transformed into two alternately solved optimization problems.Based on the corresponding relationship between the two optimization problems and the HNN energy function,two HNNs are constructed in turn to optimize the estimation of the abundance and the estimation of the nonlinear coefficient.Then,the state equations of the two networks are analyzed and deduced.The abundance nonnegative constraint and the nonlinear coefficient boundary constraint in the nonlinear unmixing problem are naturally embedded into the equation of state by fine-tuning the activation function.Then based on the state equations,the expressions of the states and outputs of the two networks over time are derived.Finally,the iterative update rules of abundances and nonlinear coefficients are obtained according to their correspondence with the neurons in the HNN.Synthetic experiments and real experiments show that the proposed supervised nonlinear unmixing algorithm based on HNN(GBM-HNN)has higher accuracy and higher execution efficiency than other supervised nonlinear unmixing algorithms.(2)Study the sparsity constrained Fan model to discover the sparsity property of endmember distribution that are still essentially present in nonlinear mixture,and reduce the solution space of non-negative matrix factorization algorithms,making them more easily converge to a satisfactory minimum or local minimum.In order to achieve a better measure of sparseness,a smooth approximate L0 norm sparseness measure is designed and introduced as a sparsity regularization item in an unsupervised nonlinear unmixing framework based on NMF.Then an iterative updating rule for solving the sparsity constrained Fan model is deduced,and the simultaneous solution of endmembers and abundances is achieved.It can be found in the experiment that this sparsity constrained nonlinear unmixing algorithm can exploit the sparsity characteristics of the data,and the algorithm's unmixing performance is better than other nonlinear unmixing algorithms.(3)For the problem of relatively large number of parameters and complex models in unsupervised nonlinear unmixing,the original objective function is transformed into two or three constrained least squares problems by matrix splitting,so that the endmembers,abundances,and nonlinear coefficients can be solved in an alternating manner.Then the variables to be solved are parameterized by Sigmoid function,and the constrained least squares problems are transformed into unconstrained parameterized nonlinear least squares(PNLS)problems.Through parameterization,the nonnegative constraints of endmembers and abundances and the boundary constraints of nonlinear coefficients are completely relaxed,making the optimization problem easier to solve.Finally,a Gauss-Newton-based PNLS optimization algorithm is proposed,and iterative update rules for solving the generalized bilinear model and the Fan model are deduced,respectively.Experiments show that the PNLS algorithm converges faster than the unsupervised nonlinear unmixing algorithm based on NMF,and can obtain better estimates of endmembers,abundances,and nonlinear coefficients.