M.Sc Student | Kizel Fadi |
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Subject | Dynamic Adaptive Hyper-Spectral Unmixing |

Department | Department of Civil and Environmental Engineering |

Supervisor | Professor Maxim Shoshany |

Full Thesis text - in Hebrew |

Hyper-spectral Remote sensing adds new dimensions of surface mapping due to its sensitivity to the chemical, physical and biological properties of the exposed materials. In real applications the information extraction capabilities are influenced by acquisition effects, the sensor's instantaneous field of view and the spatial heterogeneity of surface properties and materials. Where the pixel is larger than the spatial rate of surface properties' change, the signal obtained by the sensor represents a mixture of materials. The mixing of different materials causes a major obstacle in their mapping from the integrated spectral signal. Considering the size of satellite sensors' foot print and considering the limited number of spectral bands in such sensor systems, the mixing problem results major limitations on the capability of extracting surface information in particular and classifying correctly the images in general.

Unmixing techniques have been thus developed for determining the fractions of these surface components. The set of 'pure' potential components is called "endmembers set" represented by their spectral signatures. The vector of integrated spectral reflectance at each mixed pixel is assumed to be represented by the vector multiplication of the fractions' vector with the spectral reflectance matrix. In addition, a constraint of the sum of all fractions equal to 1 may apply. Thus, the fraction vector can be determined inversely by least square approximation. This is actually the most common technique called linear unmixing, which has several drawbacks: it requires orthogonalization of the different spectral signatures and it is most limited in resolving fractions where spectral signatures are co-linear.

In this study we present a new Discrete Search approach which allows for the assessment of large number of different spectral endmembers' combinations. For restricting the number of such possible combinations to those which are more likely to compose a specific mixture, an approximate solution was derived based on estimating fractions from the inverse of the Spectral Angle Mapper (SAM). Then progressing toward convergence to the real spectral solution, is conducted with reference to the objective function of minimizing the SAM between the spectra assembled from the combined endmembers' fractions and that of the original integrated spectra. This algorithm allows for incorporation of different combinations of signatures and it functions well in cases representing collinearity.

In addition the mathematical Steepest Descent technique was also applied, where the progress in each step of the convergence process progress along the gradient of maximal change in the objective function.