TR2016-109

Minimizing Isotropic Total Variation without Subiterations

    •  Kamilov, U., "Minimizing Isotropic Total Variation without Subiterations", International Traveling Workshop on Interactions Between Sparse Models and Technology (iTWIST), August 2016.
      BibTeX TR2016-109 PDF
      • @inproceedings{Kamilov2016aug2,
      • author = {Kamilov, Ulugbek},
      • title = {Minimizing Isotropic Total Variation without Subiterations},
      • booktitle = {International Traveling Workshop on Interactions Between Sparse Models and Technology (iTWIST)},
      • year = 2016,
      • month = aug,
      • url = {https://www.merl.com/publications/TR2016-109}
      • }
  • Research Area:

    Computational Sensing

Abstract:

Total variation (TV) is one of the most popular regularizers in the context of ill-posed image reconstruction problems. Due to its particular structure, minimization of a TV-regularized function with a fast iterative shrinkage/thresholding algorithm (FISTA) requires additional sub-iterations, which may lead to a prohibitively slow reconstruction when dealing with very large scale imaging problems. In this work, we introduce a novel variant of FISTA for isotropic TV that circumvents the need for subiterations. Specifically, our algorithm replaces the exact TV proximal with a componentwise thresholding of the image gradient in a way that ensures the convergence of the algorithm to the true TV solution with arbitrarily high precision.