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README.md

Fast Total Variation Proximal

** EXPERIMENTAL CODE: may or may not work on your computer **

ftvp is a CUDA library dedicated to the computation of the proximal operator of the isotropic Total Variation in 2D and 3D on Nvidia GPU. This repository includes examples of use in C, along with bindings for Python. It is licensed under the New BSD licence, see LICENSE file.

Status

ftvp is currently under active development, and the API is susceptible to change at any time. At the moment, the following features are available:

  • 2D (exact/smoothed)-isotropic TV with different optimization schemes (Newton descent, Gradient descent, primal-dual scheme) in B/W or color.
  • fast CPU implementation in a single file.
  • Performs on float arrays only.
  • Python 3 bindings available.

Basic use

The library is at the moment splitted in two part libftvp for B/W images and libftvp-color for color images.

For the sake of conciseness, we exemplify the use of the library for the B/W version only. If u is float array of size nxm, the call to

prox_tv(n, m, 1, u, lambda, 100, 16, 2, 1, 0.25, OE_SPLIT_NEWTON, 0);

will compute the TV regularization of u in place with regularization parameter lambda, for 100 global iterations, with GPU blocks of size 16, with 2 inner iterations, testing the gap each iterations, stopping when the gap factor is less than 0.25, where the inner iteration are given by a Newton scheme and with standard over-relaxation parameter.

If one wants to perform the smoothed (Huber-like) TV regularization with the same parameter, the following call should be used:

prox_tv(n, m, 1, u, lambda, epsilon 100, 16, 2, 1, 0.25, OE_SPLIT_NEWTON, 0);

A more low-level call is possible in order to control the memory on GPU if necessary, for instance using prox_tv as a inner iteration in a first-order method for inverse problems. We refer to init_memory and prox_tv_eps_2d_noalloc for more information.

On contrary, for the standard user, the number of parameter can be overwhelming. In this case, we refer the user to the python 3 binding where a similar call is done by executing

prox_tv(u, lambda, epsilon=epsilon)

Please see the examples directory for more examples.

Build instructions

You will need CUDA tools >= 5.5 installed to compile this library. On most systems you can build the library using the following commands

$ cd ftvp
$ make

To install the library you can use the following command with the appropriate permissions

$ make install

ftvp has been successfully tested on a Jetson TK1 Embedded Development Kit (NVIDIA Tegra K1) on Linux 3.10.24 with CUDA 6.0.1, and on a Amazon EC2 g2.2xlarge instance on Linux Ubuntu Server 14.04 LTS with CUDA 6.5. Please report any issues with your configuration on the GitHub Issues page.

References

If you use this library for academic work, please cite the following paper and/or preprint

[1] Chambolle, A., & Pock, T. (2015). A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions. SMAI Journal of Computational Mathematics, 1, 29-54.

[2] Chambolle, A., Tan, P., & Vaiter S. (2016). Accelerated Alternating Descent Methods for Dykstra-like problems. arXiV preprint.

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