Fast Orthogonal Projection for Hyperspectral Unmixing

Spectral unmixing plays a vital role in hyperspectral image analysis. It mainly consists of two procedures, i.e., endmember extraction and abundance estimation. Although most algorithms for each of the two procedures may exhibit good performance, few studies have been done considering both problems simultaneously. Therefore, hyperspectral unmixing accuracy is normally achieved by exploring all possible combinations of the two types of algorithms, which renders high computational overloads. We propose a novel orthogonal projection framework to conduct fast hyperspectral unmixing. It addresses both endmember extraction and abundance estimation with orthogonal projection endmember (OPE) and orthogonal projection abundance (OPA), respectively. Especially, the pixel with the largest orthogonal projection on any pixel is considered to be an endmember. We randomly choose one pixel from the hyperspectral data to compute the orthogonal projections of all pixels and extract the pixel with the largest projection as the first endmember. To avoid extracting the same endmembers, we compute orthogonal projections of all pixels to endmembers that have been previously extracted, and the pixel with the largest projection is considered as the next endmember. In terms of abundance estimation, we also utilize the concept of orthogonal projection and search for a diagonal matrix whose multiplication with the endmember matrix is not only a square matrix but also a diagonal matrix. Then, we exploit some specific matrix operations to estimate the abundance of each endmember at every pixel. We have evaluated the proposed OPE and OPA algorithms on synthetic and real data, and experimental results have validated their effectiveness and efficiency in hyperspectral unmixing.