The paper provides an overview of hyperspectral unmixing methods, focusing on linear and nonlinear mixing models. Hyperspectral cameras, which capture high spectral resolution images, are used for material identification and have applications in various fields such as earth observation, remote sensing, food safety, and pharmaceutical quality control. The unmixing process involves separating pixel spectra into constituent spectra (endmembers) and fractional abundances, which can be challenging due to model inaccuracies, noise, and environmental conditions. The paper discusses linear and nonlinear mixing models, highlighting the simplicity and effectiveness of linear models. Linear mixing occurs when light interacts with materials in a macroscopic way, while nonlinear mixing involves interactions at classical or microscopic levels. The authors describe various unmixing algorithms, including geometrical, statistical, and sparse regression approaches. Geometrical methods exploit the simplex set property of linearly mixed vectors, while statistical methods use parameter estimation techniques. Sparse regression approaches formulate unmixing as a linear sparse regression problem, similar to compressive sensing. The paper also covers signal subspace identification, which is crucial for reducing dimensionality and improving computational efficiency. Techniques such as principal component analysis (PCA), singular value decomposition (SVD), and maximum noise fraction (MNF) are discussed. The authors emphasize the importance of projecting data onto the signal subspace to reduce noise and improve SNR. Finally, the paper presents experimental results from simulated and real datasets, demonstrating the effectiveness of different unmixing algorithms. The discussion concludes with a summary and future directions in hyperspectral unmixing research.The paper provides an overview of hyperspectral unmixing methods, focusing on linear and nonlinear mixing models. Hyperspectral cameras, which capture high spectral resolution images, are used for material identification and have applications in various fields such as earth observation, remote sensing, food safety, and pharmaceutical quality control. The unmixing process involves separating pixel spectra into constituent spectra (endmembers) and fractional abundances, which can be challenging due to model inaccuracies, noise, and environmental conditions. The paper discusses linear and nonlinear mixing models, highlighting the simplicity and effectiveness of linear models. Linear mixing occurs when light interacts with materials in a macroscopic way, while nonlinear mixing involves interactions at classical or microscopic levels. The authors describe various unmixing algorithms, including geometrical, statistical, and sparse regression approaches. Geometrical methods exploit the simplex set property of linearly mixed vectors, while statistical methods use parameter estimation techniques. Sparse regression approaches formulate unmixing as a linear sparse regression problem, similar to compressive sensing. The paper also covers signal subspace identification, which is crucial for reducing dimensionality and improving computational efficiency. Techniques such as principal component analysis (PCA), singular value decomposition (SVD), and maximum noise fraction (MNF) are discussed. The authors emphasize the importance of projecting data onto the signal subspace to reduce noise and improve SNR. Finally, the paper presents experimental results from simulated and real datasets, demonstrating the effectiveness of different unmixing algorithms. The discussion concludes with a summary and future directions in hyperspectral unmixing research.