ADMM for maximum correntropy criterion

The correntropy provides a robust criterion for outlier-insensitive machine learning, and its maximisation has been increasingly investigated in signal and image processing. In this paper, we investigate the problem of unmixing hyperspectral images, namely decomposing each pixel/spectrum of a given image as a linear combination of other pixels/spectra called endmembers. The coefficients of the combination need to be estimated subject to the nonnegativity and the sum-to-one constraints. In practice, some spectral bands suffer from low signal-to-noise ratio due to acquisition noise and atmospheric effects, thus requiring robust techniques for the unmixing problem. In this work, we cast the unmixing problem as the maximization of a correntropy criterion, and provide a relevant solution using the alternating direction method of multipliers (ADMM) method. Finally, the relevance of the proposed approach is validated on synthetic and real hyperspectral images, demonstrating that the correntropy-based unmixing is robust to outlier bands.