Fully Constrained Least Squares Method

In this section, we elaborate on the Fully Constrained Least Squares (FCLS) method for mixed pixel decomposition in remote sensing imagery. The FCLS algorithm serves as a crucial technique in remote sensing image processing, specializing in decomposing and extracting various mixed pixels within images. This method implements two key constraints: the abundance sum-to-one constraint (where pixel component proportions must sum to 1) and the non-negativity constraint (ensuring all abundance values remain positive). Through the application of FCLS, we achieve more accurate analysis of different elements and features in remote sensing images, yielding richer and more detailed image information. The algorithm typically involves solving a quadratic optimization problem with linear constraints, often implemented using Lagrange multipliers or active set methods. Key computational steps include constructing the endmember matrix, formulating the constraint equations, and iteratively solving the optimization problem until convergence. Therefore, the Fully Constrained Least Squares method holds extensive applications and significant importance in remote sensing image processing and analysis, particularly in hyperspectral imagery where mixed pixels are prevalent. Implementation often utilizes matrix operations and optimization libraries in programming environments like MATLAB or Python with NumPy/SciPy.