| Summary: | Nonnegative matrix factorization (NMF) and its numerous variants have been extensively studied and used in hyperspectral unmixing (HU). With the aid of the designed deep structure, deep NMF-based methods demonstrate advantages in exploring the hierarchical features of complex data. However, a noise corruption problem commonly exists in hyperspectral data and severely degrades the unmixing performance of deep NMF-based methods when applied to HU. In this study, we propose an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">ℓ</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula> norm-based robust deep nonnegative matrix factorization (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">ℓ</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula>-RDNMF) for HU, which incorporates an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">ℓ</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula> norm into the two stages of the deep structure to achieve robustness. The multiplicative updating rules of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">ℓ</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula>-RDNMF are efficiently learned and provided. The efficiency of the presented method is verified in experiments using both synthetic and genuine data.
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