TotalVariationImageFiltering.jl

TotalVariationImageFiltering.jl is a Julia package for total-variation (TV) denoising and reconstruction on N-dimensional arrays.

It currently provides:

• ROF denoising (L2 + TV) via a Chambolle-style dual projected-gradient algorithm.
• PDHG / Chambolle-Pock for L2 + TV and Poisson KL + TV.
• PDHG primal constraints: non-negativity and box constraints.
• Isotropic and anisotropic TV.
• Single-image and batched solves.
• Automatic lambda selection for ROF (discrepancy principle and MC-SURE).
• Optional CUDA acceleration via package extension.

Core models:

\[\min_u \frac{1}{2}\|u-f\|_2^2 + \lambda\,\mathrm{TV}(u)\]

\[\min_u \sum_i \left(u_i - f_i \log(u_i)\right) + \lambda\,\mathrm{TV}(u)\]

Documentation Guide

• Installation
• Quick Start
• Problem & API
• ROF Solver
• PDHG Solver
• Lambda Selection
• Batch & CUDA
• Benchmarking
• API Reference
• References

Notes

• This manual consolidates and expands content from the repository README.md, benchmark/README.md, source code, and docstrings.
• For the latest benchmark runs, see the benchmark scripts and generated CSVs in the repository.