ADMM for maximum correntropy criterion

Abstract

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 correntropybased unmixing is robust to outlier bands.