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A Neural Network Based Hybrid Mixture Model to Extract Information from Non-linear Mixed Pixels

Signals acquired by sensors in the real world are non-linear combinations, requiring non-linear mixture models to describe the resultant mixture spectra for the endmember’s (pure pixel’s) distribution. This communication discusses inferring class fraction through a novel hybrid mixture model (HMM). HMM is a three-step process, where the endmembers are first derived from the images themselves using the N-FINDR algorithm. These endmembers are used by the linear mixture model (LMM) in the second step that provides an abundance estimation in a linear fashion. Finally, the abundance values along with the training samples representing the actual ground proportions are fed into neural network based multi-layer perceptron (MLP) architecture as input to train the neurons. The neural output further refines the abundance estimates to account for the non-linear nature of the mixing classes of interest. HMM is first implemented and validated on simulated hyper spectral data of 200 bands and subsequently on real time MODIS data with a spatial resolution of 250 m. The results on computer simulated data show that the method gives acceptable results for unmixing pixels with an overall RMSE of 0.0089 ± 0.0022 with LMM and 0.0030 ± 0.0001 with the HMM when compared to actual class proportions. The unmixed MODIS images showed overall RMSE with HMM as 0.0191 ± 0.022 as compared to the LMM output considered alone that had an overall RMSE of 0.2005 ± 0.41, indicating that individual class abundances obtained from HMM are very close to the real observations.