The hyperspectral sensors gather huge information with as many as hundreds of contiguous spectral bands across from ultraviolet to short wave infrared regions, However, due to insufficient spatial resolution and mixing effects in surfaces, a hyperspectral image pixel may cover more than one pure macroscopic component, referred to as endmembers, within the instantaneous field of view (IFOV) of the sensor. Such pixels are called mixed pixels, which cause great difficulties for the measurement and analysis of ground targets. Hence, hyperspectral unmixing has become an important issue that has received intensive interest over the few last decades for hyperspectral data exploitation. It consist of two procedures, extracting endmember spectra present in the image, referred to as endmembers extraction, and identifying their proportions at each pixel, known as abudance estimation. Due to the simple physical interpretation and analytically tractable solution with low complexity, linear spectral mixture model (LSMM) is the most studied case most works of the literature. However, the LSMM is reasonable only when the mixing process occurs at a macroscopic scale and single reflections of the materials are present within a pixel, which is not always the case for real hyperspectral data set. Therefore, some nonlinear spectral mixture models (NSMMs) are considered to characterize nonlinear effects in hyperspectral images and overcome the inherent limitations of the NSMMs. The aim of this work is to propose effcient linear and nonlinear model-based hyperspectral unmixing (HU) methods to exploit plentiful information in hyperspectral imagery. The main innovations of our research can be described into four aspects as follows:1. A new fast Cayley-Menger determinant-based endmember extraction algorithm for hyperspectral unmixing is proposed. As a LSMM-based geometrical method, the algorithm is to find the maximum volume simplex enclosing the hyperspectral data cloud. Firstly, by use of Cayley-Menger determinant, we calculate and analyze the volume of simplex with low dimensionality in original high dimensional observation space. Then, with the features of Hermite matrix, a fast recurrence relation is proposed to extract endmember signatures one by one sequentially with low computational complexity.2. A novel fully constrained linear spectral unmixing algorithm based on distance geometry is presented. Under LSMM, HU can be considered as a convex geometry problem. According to the position relationship between the observation points and endmember simplex, the observation pixels in the hyperspectral images can be divided into three types:interior points, exterior points Ⅰ, and exterior points Ⅱ, respectively. Only the barycentric coordinates of interior points can be considered as the output abundances. Therefore, firstly, we proposed a new calculation formula for barycentric coordinates for interior points in the form of Cayley-Menger matrix. Then, two fast and accurate strategies are developed to reduce exterior points to interior points using convex geometry concepts and distance geometry constraints. Finally, an optimal result with the least distortion in geometric structure of original data is obtained. The entire method has a recursive implementation with low computational complexity.3. Two nonlinear unmixing algorithms based on constrained nonlinear least squares (CNLS) are developed. Firstly, we divide the unknown parameters into two sets: abundance fractions and nonlinearity parameters. Due to physical reason, they should obey three constraints:the abundance sum-to-one constraint (ASC), abundance nonnegative constraint (ANC) and bound constraints of nonlinearity parameters. With the specific penalty functions, the model-based nonlinear unmixing problem has been transformed into a CNLS problem. Secondly, two mixing mechanisms are used to describe the mixing process:superposition mixture and joint mixture. For the former, an alternating optimization algorithm is presented to solve two minimization sub-problem. For the latter, a joint optimization approach based structured total least squares (STLS) is considered to obtain the unknown parameters simultaneously. Current mixing models can be interpreted by either or both of these two mechanisms.4. A new new spatial-spectral similarity measure is proposed and applied to hypersepctral classification, dimensionality reduction and endmember extraction algorithms. In hyperspctral images, the observation pixels are spatially related and meaningful features can be extracted from both the spectral and spatial domains. Based on this, the proposed similarity measure integrates spatial information by using the spatial neighbors, mapping the distances between two image patches in the hyperspectral images. The new similarity measure can effectively exploit the rich spectral and spatial structures of data, thus improving hypersctral processing in pixel level, such as classification, dimensionality reduction and so on. Also, it can draw an effective distinction in sub-pixel level. As a result, we can adopt it in endmember extraction algorithm by combining the spectral, spatial and nonlinear features. |