Demystifying Lie Group Methods for Signal Processing: A Tutorial

Many problems in signal processing [e.g., filter bank design, independent component analysis (ICA), beamforming design, and neural network training] can be formulated as optimization over groups of transformations that depend continuously on real parameters (Lie groups). Such problems are usually tackled in two ways: using a constrained optimization procedure or using some parameterization to transform them into unconstrained problems.