Fully constrained oblique projection approach to mixed pixel linear unmixing

Mixed pixels, which are inevitable in remote sensing images, often result in a lot of limitations in their applications. A novel approach for mixed pixel's fully constrained unmixing, Fully Constrained Oblique Subspace Projection (FCOBSP) Linear Unmixing algorithm, is proposed to handle this problem. The Oblique Subspace Projection, in which the signal space is oblique to the background space, is introduced to the settlement of the Linear Mixture Model (LMM). The abundance of constitutional spectral signature can be obtained through projecting the mixed pixel to the spectral signature subspace. One of the two well-known constraints of LMM, namely the non-negative constraint, is met by projecting mixed pixels to continually modified background space. The other constraint, namely the sum-to-one constraint, is embedded into the LMM to realize fully constrained linear unmixing. The performance of the proposed algorithm is evaluated by synthetic multispectral pixels decomposition. Compared with the popular Fully Constrained Least Square unmixing (FCLS) algorithm and Oblique Subspace Projection (OBSP), in terms of both RMSE and correlation coefficient with the real abundance, the proposed algorithm achieves significant improvement over these algorithms in spite of a little more time cost. The proposed algorithm has been used to handle the practical classification problems which dealing with the real multispectral and hyperspectral data, and the decomposition results show that the objects are well separated.