IRLS Algorithm - Iteratively Reweighted Least Squares Algorithm

The IRLS algorithm, known as Iteratively Reweighted Least Squares, serves as an effective tool for compressed sensing and adaptive filtering applications.

IRLS is an iterative optimization algorithm based on the least squares principle. Its applications in compressed sensing and adaptive filtering have been extensively researched and implemented. The algorithm operates through an iterative process that continuously adjusts weighting coefficients to gradually converge toward the optimal least squares solution. In compressed sensing applications, IRLS can reconstruct signals from undersampled measurements, enabling effective signal compression and recovery. For adaptive filtering, IRLS facilitates signal filtering operations that achieve signal smoothing and noise reduction. The algorithm typically implements weight updates using a reweighting function that penalizes large residuals, often employing a p-norm minimization approach where the weights are iteratively recalculated based on residual magnitudes. Key implementation aspects include setting appropriate convergence thresholds and selecting robust weighting functions to handle outliers. In summary, IRLS demonstrates significant potential across various signal processing domains due to its robust convergence properties and flexibility in handling different optimization scenarios.