Repository to solve the Helsinki Tomography Challenge 2022, while also exploring a wide range of optimization methods for inverse problems.
This was mainly done as part of the practical course "Applied Optimization Method for Inverse Problems" offered during the summer term 2023 at TUM.
The easiest and recommended way to install is using poetry (see
here). Once you've installed poetry,
run poetry install from the root directory.
Next, we miss the dependency on elsa (see
here), the tool for tomographic
reconstruction. First run poetry shell, which will activate the virtual
environment created by poetry, then clone elsa to a new directory,
move into the directory and run pip install . --verbose (the --verbose is
optional, but then you'll see the progress).
From now, you can either activate the virtual environment by running poetry shell,
or you run poetry run python myscript, which will activate the environment for
that single command.
If you do not want to use poetry, you can use virtual environments.
From the root directory of this repository run python -m venv /path/to/venv, activate
it using source /path/to/venv/bin/activate, and then install everything with
pip install --editable . (from the root directory). Feel free to use the requirement.txt file.
Then again you need to install elsa. Follow the steps described above in
the poetry section.
To get the dataset for the challenge, head over to
Zenodo and download the htc2022_test_data.zip. Extract it to a folder and
you should be good to go.
In the folder you will see a couple of different files.
.mat files contain the actual measurements/sinogram, which are needed for
reconstruction. There are the full measurements, one with limited number of
projections and example reconstructions of both. Further, there are segmented
files, which show the required binary thresholding segmentation done to
evaluate the score (again for full data and limited). However, for convenience the scoring is already implemented in
challenge/utils.py and can be used that way.
Finally, there are a couple of example images.
If you have trouble installing elsa , see the README
of elsa. If you use an Ubuntu based distro and want to use CUDA, you might
need to set CUDA_HOME, to wherever CUDA is installed.
Please note, that you do not need CUDA, but it might speed up your reconstructions quite dramatically.
For the challenge, I decided to focus my efforts initially on the phantom A with difficulty 7, look at the various angle cases and then try to apply the gained knowledge to the other phantoms. My procedure was basically the following:
- Determine best starting point with FBP (Filtered BackProjection)
- Choose promising formulations (Usually a linear system with some regularization)
- Determine formulation/algorithm combinations and optimizer setup
- Compare formulations and explore formulation parameters
- Trim combinations and formulations
- Extrapolate to other phantoms and Squeeze
My final best scores and their associated parameters are the following (Scores go from 0 to 1):
ARC: 360
| Phantom | Difficulty | Score | i | n_iter | Formulation | Method |
|---|---|---|---|---|---|---|
| a | 1 | 0.99911337 | 111 | 452 | LSDfRFormulation | optimized_gradient |
| a | 2 | 0.99836131 | 172 | 303 | LSDfRFormulation | optimized_gradient |
| a | 3 | 0.99871893 | 108 | 320 | LSDfRFormulation | optimized_gradient |
| a | 4 | 0.99780540 | 200 | 308 | LSDfRFormulation | optimized_gradient |
| a | 5 | 0.99710220 | 118 | 305 | LSDfRFormulation | optimized_gradient |
| a | 6 | 0.99777936 | 131 | 309 | LSDfRFormulation | optimized_gradient |
| a | 7 | 0.99592590 | 133 | 291 | LSDfRFormulation | optimized_gradient |
| b | 1 | 0.99889755 | 110 | 180 | LSDfRFormulation | optimized_gradient |
| b | 2 | 0.99765429 | 213 | 314 | LSDfRFormulation | optimized_gradient |
| b | 3 | 0.99780123 | 156 | 303 | LSDfRFormulation | optimized_gradient |
| b | 4 | 0.99709347 | 179 | 325 | LSDfRFormulation | optimized_gradient |
| b | 5 | 0.99710042 | 172 | 295 | LSDfRFormulation | optimized_gradient |
| b | 6 | 0.99804756 | 92 | 309 | LSDfRFormulation | optimized_gradient |
| b | 7 | 0.99701880 | 92 | 297 | LSDfRFormulation | optimized_gradient |
| c | 1 | 0.99832031 | 152 | 321 | LSDfRFormulation | optimized_gradient |
| c | 2 | 0.99895954 | 100 | 307 | LSDfRFormulation | optimized_gradient |
| c | 3 | 0.99808751 | 93 | 321 | LSDfRFormulation | optimized_gradient |
| c | 4 | 0.99817051 | 95 | 326 | LSDfRFormulation | optimized_gradient |
| c | 5 | 0.99698048 | 126 | 310 | LSDfRFormulation | optimized_gradient |
| c | 6 | 0.99749203 | 151 | 183 | LSDfRFormulation | optimized_gradient |
| c | 7 | 0.99792990 | 160 | 312 | LSDfRFormulation | optimized_gradient |
ARC: 90
| Phantom | Difficulty | Score | i | n_iter | Formulation | Method |
|---|---|---|---|---|---|---|
| a | 1 | 0.98315684 | 0 | 48 | LassoFormulation | optimized_proximal_gradient |
| a | 2 | 0.97160876 | 110 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 3 | 0.94341835 | 412 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 4 | 0.95396707 | 124 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 5 | 0.94761390 | 467 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 6 | 0.88822590 | 490 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 7 | 0.88385510 | 421 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 1 | 0.95903665 | 130 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 2 | 0.95546577 | 125 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 3 | 0.92124738 | 0 | 50 | LassoFormulation | optimized_proximal_gradient |
| b | 4 | 0.85531617 | 105 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 5 | 0.93823663 | 434 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 6 | 0.83720253 | 528 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 7 | 0.87818244 | 142 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 1 | 0.95233803 | 108 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 2 | 0.95991236 | 0 | 49 | LassoFormulation | optimized_proximal_gradient |
| c | 3 | 0.91283543 | 454 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 4 | 0.93823993 | 108 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 5 | 0.87203141 | 483 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 6 | 0.93357335 | 120 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 7 | 0.94400170 | 107 | 1000 | LSDfRFormulation | optimized_gradient |
ARC: 60
| Phantom | Difficulty | Score | i | n_iter | Formulation | Method |
|---|---|---|---|---|---|---|
| a | 1 | 0.97581547 | 0 | 43 | LassoFormulation | optimized_proximal_gradient |
| a | 2 | 0.94439732 | 428 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 3 | 0.86466503 | 495 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 4 | 0.81652094 | 617 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 5 | 0.86991124 | 523 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 6 | 0.86431890 | 437 | 1000 | LSDfRFormulation | optimized_gradient |
| a | 7 | 0.84978890 | 506 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 1 | 0.92504951 | 507 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 2 | 0.89841847 | 534 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 3 | 0.78610247 | 491 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 4 | 0.78565684 | 428 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 5 | 0.86656066 | 523 | 1000 | LSDfRFormulation | optimized_gradient |
| b | 6 | 0.79117909 | 0 | 43 | LassoFormulation | optimized_proximal_gradient |
| b | 7 | 0.75971128 | 540 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 1 | 0.89991305 | 538 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 2 | 0.86561725 | 609 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 3 | 0.86056884 | 432 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 4 | 0.78753502 | 488 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 5 | 0.83520899 | 0 | 48 | LassoFormulation | optimized_proximal_gradient |
| c | 6 | 0.86982834 | 451 | 1000 | LSDfRFormulation | optimized_gradient |
| c | 7 | 0.87492935 | 512 | 1000 | LSDfRFormulation | optimized_gradient |
ARC: 30
| Phantom | Difficulty | Score | i | n_iter | Formulation | Method |
|---|---|---|---|---|---|---|
| a | 1 | 0.97522754 | 2 | 66 | TVRegularizationFormulation | admm |
| a | 2 | 0.86904071 | 3 | 66 | TVRegularizationFormulation | admm |
| a | 3 | 0.82638661 | 4 | 573 | ElasticNetFormulation | admm |
| a | 4 | 0.78936320 | 4 | 66 | TVRegularizationFormulation | admm |
| a | 5 | 0.85047692 | 3 | 539 | ElasticNetFormulation | admm |
| a | 6 | 0.81374212 | 3 | 67 | TVRegularizationFormulation | admm |
| a | 7 | 0.80093117 | 4 | 66 | TVRegularizationFormulation | admm |
| b | 1 | 0.90751182 | 6 | 66 | TVRegularizationFormulation | admm |
| b | 2 | 0.86670303 | 4 | 540 | ElasticNetFormulation | admm |
| b | 3 | 0.74334419 | 4 | 574 | ElasticNetFormulation | admm |
| b | 4 | 0.65569374 | 4 | 67 | TVRegularizationFormulation | admm |
| b | 5 | 0.84435297 | 3 | 66 | TVRegularizationFormulation | admm |
| b | 6 | 0.78933489 | 3 | 67 | TVRegularizationFormulation | admm |
| b | 7 | 0.74354104 | 4 | 66 | TVRegularizationFormulation | admm |
| c | 1 | 0.80041927 | 4 | 66 | TVRegularizationFormulation | admm |
| c | 2 | 0.84188645 | 3 | 142 | ElasticNetFormulation | admm |
| c | 3 | 0.81581281 | 4 | 66 | TVRegularizationFormulation | admm |
| c | 4 | 0.67804736 | 3 | 66 | TVRegularizationFormulation | admm |
| c | 5 | 0.82568818 | 4 | 66 | TVRegularizationFormulation | admm |
| c | 6 | 0.77035164 | 4 | 67 | TVRegularizationFormulation | admm |
| c | 7 | 0.76017163 | 4 | 66 | TVRegularizationFormulation | admm |
And finally, the associated reconstructions compared to ground truth:
