Code and data for: Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms

Data and code that support findings of the article "Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms" (https://arxiv.org/abs/2506.11291) <br>

<b>Getting started</b><br>

You can find the required packages in 'requirementsDIP.txt' or use the conda environment 'DIP.yaml'.<br>

<b>Tikhonov regularization in Banach spaces</b><br>

The codes for the dual method (Tikhonov regularization in Banach spaces) can be found in the directory ```Tikhonov```.
The files '_rec_Tikhonov_dynamic/static' construct the phantoms, data and reconstructions. The files '_error_plot_Tikhonov_dynamic/static'
construct the figures using the data in 'results'.<br>

<b>Temporal variational regularization</b><br>

The codes for temporal variational regularization can be found in the directory 'TemporalVariationalRegularization'.
As before the files starting with '_Reconstruct...' construct phantoms, data and reconstructions for the time or intensity preserving phantom or the emoji data.
The files starting with '_error_plot...' produce the figures using the data in 'results'.<br>

For the emoji data, we first need to do preprocessing in matlab to start with the original data from https://fips.fi/open-datasets/x-ray-tomographic-datasets/tomographic-x-ray-data-of-a-time-dependent-emoji-phantom/ . This is done by 'DataToParallel.m'.