TV Regularization Deconvolution: An Iteratively Reweighted Norm Approach for L2-TV and L1-TV Problems

TV regularization deconvolution is an Iteratively Reweighted Norm algorithm designed to solve generalized TV functionals, encompassing both L2-TV and L1-TV problems. This approach first constrains solution smoothness through regularization terms, then performs reconstruction via deconvolution. The algorithm's robustness is enhanced through iterative reweighting of norms - in each iteration, weights derived from the current solution update the regularization term, which then refines the solution in subsequent iterations. From an implementation perspective, the core algorithm typically involves: 1. Initializing with a naive deconvolution result 2. Calculating weight matrices based on current gradient magnitudes 3. Solving weighted regularization problems using optimization methods like conjugate gradient or Cholesky decomposition 4. Iterating until convergence criteria are met This method is particularly valuable in image processing applications for restoring degraded images and removing noise, where it effectively preserves edges while smoothing homogeneous regions. The L2-TV variant handles Gaussian noise efficiently, while L1-TV demonstrates superior performance for impulse noise and sparse artifacts.