MATLAB Code for Minimum L1 Norm Optimization

This MATLAB code implements the minimum L1 norm optimization problem, solving the model: min lambda*||x||_1 + ||A*x - y||_2. The term ||x||_1 represents the L1-norm (sum of absolute values), while ||*||_2 denotes the L2-norm (Euclidean norm). This formulation is particularly valuable in sparse component analysis and compressed sensing applications where sparsity-promoting regularization is essential. The implementation typically involves convex optimization approaches, potentially using techniques like proximal gradient methods, ADMM (Alternating Direction Method of Multipliers), or specialized solvers for L1-regularized problems. Key computational considerations include handling the non-differentiable L1-norm through subgradient methods or transformation to linear programming formulations. For deeper understanding of the underlying theory and applications, consider these references: - "L1-Magic: Recovery of Sparse Signals via Convex Programming" by E. Candès - "Compressive Sensing" by W. Bajwa et al. - "Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing" edited by M. Elad The code structure would typically include matrix operations for A*x-y computation, efficient L1-norm calculation using sum(abs(x)), and optimization loops with convergence criteria for the regularized objective function.