Chapter 14: Sparse Reconstruction for RF Imaging

Learning Objectives

• Apply the LASSO and Basis Pursuit to the RF sensing matrix and select the regularization parameter via cross-validation, SURE, and the discrepancy principle
• Implement FISTA and ADMM solvers for imaging-specific sensing matrices with debiasing on the estimated support
• Formulate group sparsity and MMV problems for multi-frequency RF imaging using the mixed $\ell_{2,1}$-norm and the Pesavento compact formulation
• Apply total variation regularization for piecewise-constant scenes via ADMM, and compare isotropic TV, anisotropic TV, and TGV
• Implement OMP, CoSaMP, and IHT for the RF sensing matrix and understand when greedy methods outperform convex relaxation
• Formulate super-resolution via atomic norm minimization and SPARROW for off-grid scatterer recovery