Quantum annealing for linear spectral unmixing: a proof-of-concept

Spectral unmixing is a popular technique in remote sensing, in which the measured spectrum of light is decomposed to determine which materials have produced the reflected signal. The technique gives insight into which materials are present on the target surface, making it useful in a wide variety of geoscience applications. However, the spectral unmixing problem tends to be computationally taxing to solve, limiting the extent to which the technique can be applied. This work serves as a proof-of-concept for the potential application of a particular type of quantum computing, quantum annealing, on the spectral unmixing problem. To do this, we devised the first Quadratic Unconstrained Binary Optimisation (QUBO) formulation for linear spectral unmixing. This formulation of the problem can be solved using simulated or quantum annealing. Using artificial spectral mixtures, the QUBO formulation and both annealing methods were tested on accuracy and required computation time. The results were compared to the popular Multiple Endmember Spectral Mixture Analysis (MESMA) algorithm. The MESMA algorithm and simulated annealing achieve comparable accuracy at equal computation time, indicating some potential of annealing in spectral unmixing applications. Solving the QUBO formulation by means of quantum annealing was possible only on simplified versions of the unmixing problem due to current hardware restrictions. However, quantum annealing requires a fraction of the computation time of the MESMA algorithm or simulated annealing, indicating the potential of quantum annealing for these types of problems. If quantum computing devices continue to improve in the following years, practical applications of spectral unmixing may become more efficiently solvable using quantum annealing.