ADMM for Maximum Correntropy Criterion
Résumé
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.
Mots clés
- image reconstruction
- maximum correntropy estimation
- hyperspectral image
- unmixing problem
- maximum correntropy criterion
- ADMM method
- alternating direction method of multipliers
- maximum entropy methods
- learning (artificial intelligence)
- Correntropy
- image denoising
- feature extraction
- noise acquisition
- hyperspectral image unmixing
- image decomposition
- pixel linear combination
- spectra linear combination
- endmember extraction
- nonnegativity constraints
- sum-to-one constraints
- signal-to-noise ratio
- outlier-insensitive machine learning
- atmospheric effects
- Hyperspectral imaging
- Robustness
- Kernel
- Optimization
- Bandwidth
- Linear programming
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