Image Reconstruction Based on the Total Variation Model

This software package specializes in image reconstruction through the Total Variation (TV) model, which minimizes the L1-norm of image gradients to maintain sharp edges while reducing noise. The implementation includes three core functionalities: denoising through TV regularization that preserves structural boundaries, inpainting using partial differential equations to reconstruct missing regions, and deblurring via deconvolution algorithms combined with TV constraints. The underlying code typically utilizes gradient descent methods or primal-dual algorithms to solve the optimization problem efficiently. The referenced paper by Dahl et al. provides detailed mathematical formulations and computational strategies for these first-order methods, including convergence analysis and practical implementation considerations for large-scale image processing tasks. The software architecture likely modularizes each reconstruction task while sharing common optimization solvers and matrix operation routines for handling different types of degradation models.