Algorithms and software for total variation image reconstruction via first-order methods. This paper describes new algorithms and related software for total variation (TV) image reconstruction, more specifically: denoising, inpainting, and deblurring. The algorithms are based on one of Nesterov’s first-order methods, tailored to the image processing applications in such a way that, except for the mandatory regularization parameter, the user needs not specify any parameters in the algorithms. The software is written in C with interface to Matlab (version 7.5 or later), and we demonstrate its performance and use with examples. (netlib numeralgo na28)

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  1. Mead, J.: ( \chi^2) test for total variation regularization parameter selection (2020)
  2. Barbero, Álvaro; Sra, Suvrit: Modular proximal optimization for multidimensional total-variation regularization (2018)
  3. Antil, Harbir; Bartels, Sören: Spectral approximation of fractional PDEs in image processing and phase field modeling (2017)
  4. Gu, Shuhang; Xie, Qi; Meng, Deyu; Zuo, Wangmeng; Feng, Xiangchu; Zhang, Lei: Weighted nuclear norm minimization and its applications to low level vision (2017)
  5. Li, Yusheng; Xie, Xinchang; Yang, Zhouwang: Alternating direction method of multipliers for solving dictionary learning models (2015)
  6. Zhang, Benxin; Zhu, Zhibin: A modified quasi-Newton diagonal update algorithm for total variation denoising problems and nonlinear monotone equations with applications in compressive sensing. (2015)
  7. Chen, K.; Loli Piccolomini, E.; Zama, F.: An automatic regularization parameter selection algorithm in the total variation model for image deblurring (2014)
  8. Ayvaci, Alper; Raptis, Michalis; Soatto, Stefano: Sparse occlusion detection with optical flow (2012)
  9. Bonettini, Silvia; Ruggiero, Valeria: On the convergence of primal-dual hybrid gradient algorithms for total variation image restoration (2012)
  10. Chung, Julianne; Chung, Matthias; O’leary, Dianne P.: Optimal filters from calibration data for image deconvolution with data acquisition error (2012)
  11. Jensen, T. L.; Jørgensen, J. H.; Hansen, P. C.; Jensen, S. H.: Implementation of an optimal first-order method for strongly convex total variation regularization (2012)
  12. Becker, Stephen; Bobin, Jérôme; Candès, Emmanuel J.: NESTA: A fast and accurate first-order method for sparse recovery (2011)
  13. Bonettini, S.; Ruggiero, V.: An alternating extragradient method for total variation-based image restoration from Poisson data (2011)
  14. Dahl, Joachim; Hansen, Per Christian; Jensen, Søren Holdt; Jensen, Tobias Lindstrøm: Algorithms and software for total variation image reconstruction via first-order methods (2010)
  15. Hansen, Per Christian: Discrete inverse problems. Insight and algorithms. (2010)
  16. Yu, Gaohang; Qi, Liqun; Dai, Yuhong: On nonmonotone Chambolle gradient projection algorithms for total variation image restoration (2009) ioport