Robust Sparse Unmixing via Continuous Mixed Norm to Address Mixed Noise

Sparse unmixing, a critical task in hyperspectral image interpretation, aims to identify an optimal subset of endmembers from a predefined library and estimate the fractional abundances for each pixel. However, in real-world scenarios, various types of noise significantly degrade the performance of conventional sparse unmixing methods that usually rely on $\ell _{2}$ -norm loss function. To address this issue, this letter proposes a robust sparse unmixing method based on the continuous mixed norm (CMN), which exhibits resilience to mixed noise, particularly non-Gaussian impulsive noise. By adopting CMN as the reconstruction loss function, we formulate both the standard sparse unmixing problem and its augmented version with total variation (TV) regularizer for spatially piecewise smoothness. The corresponding algorithms are derived using the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real hyperspectral datasets validate the effectiveness and robustness of the proposed method in handling diverse and mixed noise conditions over comparing methods. The code is available at: https://github.com/JinchengGao/CMNSU.