Add 3 Methods and 1 Dataset

[paquiteau]

Hi,

This PR add 3 Method to solve the TV1D denoising problem: 1) The linear taut String method 2) A MM algorithm 3) A Group TV method (the L1 norm is replaced by a Group l1, similar to what Group LASSO is to LASSO). It is not strictly the TV problem, but is close enough to be integrated IMO.

Also I added a simulated dataset, which create a BOLD-fMRI times series (basically a block wise signal, convolve with an HRF). Note that linear operator is still the Identity, and the data-fit is restricted to quadratic.

Github does not support to embed HTML, so the results are here: https://perso.crans.org/comby/neurospin/benchmark_tv_1d_benchopt_run_2023-07-03_14h39m15.html

[paquiteau]

So the CI fails because the solver cannot be test with the test simulated dataset (they only work for A=Id in y = Ax +n ). In order to run the mm algorithm in the test I think that the following changes are required:

• add a A_type parameter in the dataset (similar to data_fit parameter)
• skip the MM algorithms for the `A_type != "identity"
• add A_type to all set_objective function in every solver (That would also be a good opportunity to add bibliographic references for all the solvers)

If you have a better solution for it I will be happy to implement it.

[agramfort]

the solvers can implement a skip method so its the responsibility of the solver to say they cannot do it.

Message ID: @.***>

[paquiteau]

Ready for merging ? :)