Tv warmstart

[MargaretDuff]

Describe your changes

Added warm start functionality to the CIL total variation function

Describe any testing you have performed

Please add any demo scripts to CIL-Demos/misc/

Testing script added here https://github.com/TomographicImaging/CIL-Demos/blob/main/misc/testing_TV_warmstart.ipynb
Here you can see that:

• Using TV with a warm start led to a speed-up in performing implicit PDHG with TV regularisation due to reduced inner iterations required.

• PDHG regularised TV with and without warm start converged to a similar reconstructed image.
  

• PDHG regularised by TV with warm start was able to converge to a lower objective function value than without warm start (see e.g. https://link.springer.com/article/10.1007/s10589-022-00410-x)
  

• Changing the number of warm start iterations changes the speed of convergence:
  

• Over the iterations of PDHG, the calculated proximal by TV warm start converges to that of the calculated proximal by the CCPi regulariser
  

Link relevant issues

supersedes #1201
closes #1200

Checklist when you are ready to request a review

• I have performed a self-review of my code
• I have added docstrings in line with the guidance in the developer guide
• I have implemented unit tests that cover any new or modified functionality
• CHANGELOG.md has been updated with any functionality change
• Request review from all relevant developers
• Change pull request label to 'Waiting for review'

Contribution Notes

Please read and adhere to the developer guide and local patterns and conventions.

• The content of this Pull Request (the Contribution) is intentionally submitted for inclusion in CIL (the Work) under the terms and conditions of the Apache-2.0 License.
• I confirm that the contribution does not violate any intellectual property rights of third parties

[MargaretDuff]

Thanks for your comments @paskino, I have updated the PR and the experiments are still giving similar results.

Also for smaller regularisation parameter and more realistic solutions:

[paskino]

It looks good, however the setter for self.p2 should be changed. This should be discussed with @gfardell

[MargaretDuff]

Thanks @paskino! I will make those changes and we can chat with @gfardell.

[paskino]

@MargaretDuff can you comment about the speed of convergence in terms of wall clock?

[MargaretDuff]

Without warm start (100 inner iterations):

With warm start (5 inner iterations):

Using the CCPi TV regulariser (100 inner iterations):

[gfardell]

It's looking good. Can you remove the comments referencing the lines in the algorithm from the paper. It's useful to include the link to the paper in the docstring but the code may not always line for line reflect the paper. Comments are much less likely to be updated when we do make code changes so could end up confusing things more as they get out of date.

Edo and I chatted, and I've made some changes and scrapped the property and setter and incorporated the changes in to the code. Properties have their place, but I would avoid using them when the call is a much higher cost than the user would expect. I think the user shouldn't be surprised by unintended consequences when from their pov they are just accessing a class member.

Lastly, we need to implement some unit tests and we're good to go!

[paskino]

Please update warmstart to warm_start.

[MargaretDuff]

Please update warmstart to warm_start.

Done!

[MargaretDuff]

@paskino and @gfardell: Thanks for all your comments, think that I have resolved everything and the documentation looks like it has rendered properly