Fast Spectral Unmixing based on Dykstra's Alternating Projection
This is an incremental improvement for hyperspectral image analysis, offering faster processing in real-world applications.
The paper tackles the spectral unmixing problem by proposing a fast algorithm based on Dykstra's alternating projection, which reduces computational complexity from quadratic to linear time and competes with state-of-the-art methods, especially when the number of endmembers is small.
This paper presents a fast spectral unmixing algorithm based on Dykstra's alternating projection. The proposed algorithm formulates the fully constrained least squares optimization problem associated with the spectral unmixing task as an unconstrained regression problem followed by a projection onto the intersection of several closed convex sets. This projection is achieved by iteratively projecting onto each of the convex sets individually, following Dyktra's scheme. The sequence thus obtained is guaranteed to converge to the sought projection. Thanks to the preliminary matrix decomposition and variable substitution, the projection is implemented intrinsically in a subspace, whose dimension is very often much lower than the number of bands. A benefit of this strategy is that the order of the computational complexity for each projection is decreased from quadratic to linear time. Numerical experiments considering diverse spectral unmixing scenarios provide evidence that the proposed algorithm competes with the state-of-the-art, namely when the number of endmembers is relatively small, a circumstance often observed in real hyperspectral applications.