MULTI-FRAME SUPER-RESOLUTION MRI USING COUPLED LOW-RANK TUCKER APPROXIMATION

Copyright (c) 2022 Clemence Prevost, Freddy Odille
Contact: clemence.prevost@univ-lille.fr

This software reproduces the results from the following:

@unpublished{prevost:hal-03617754,
  TITLE = {{MULTI-FRAME SUPER-RESOLUTION MRI USING COUPLED LOW-RANK TUCKER APPROXIMATION}},
  AUTHOR = {Pr{\'e}vost, Cl{\'e}mence and ODILLE, F},
  URL = {https://hal.archives-ouvertes.fr/hal-03617754},
  NOTE = {working paper or preprint},
  YEAR = {2022},
  MONTH = Mar,
  PDF = {https://hal.archives-ouvertes.fr/hal-03617754/file/IRM_Tucker.pdf},
  HAL_ID = {hal-03617754},
  HAL_VERSION = {v1},
}

Link to the project

Content

• /demos : contains demo files that produce tables and figures
• /metrics : contains the metrics used to assess the quality of the reconstruction
• /src : contains helpful files to run the demos

Minimal requirements

In order to run the demo file demo.m, you will need to:

• Download and install Tensorlab 3.0: https://www.tensorlab.net
• Download the Sharpness Index toolbox: http://www.mi.parisdescartes.fr/~moisan/sharpness/
• Beltrami primal-dual solver: https://math.montana.edu/dzosso/code/

Please quote the corresponding papers if you decide to use these codes.

How it works

Generate coupled tensor model

In this software, we use the "MRI" dataset of MATLAB. The low-resolution observations are generated from the super-resolution image with manually-specified degradation matrices.

Run algorithms

In reconstruction.m, we showcase the performance of three algorithms:

• RICOTTA
• Block-RICOTTA (applies RICOTTA to corresponding subblocks of the observations)
• RICOTTA without regularization + 3D-Beltrami regularization (to highlight the importance of the Tikhonov regularization in the algorithm

The metrics and computation time are then displayed in a table. Slices of the reference and reconstructions are plotted in a figure.

Available demos

They are available in the /demos folder. The table below summarized what does what

Name	Content
reconstruction.m	Evaluates performance of the algorithms
choice_ranks.m	plots R-SNR, CC and RMSE as a function of the ranks
choice_regul.m	plots R-SNR, CC and RMSE as a function of the regul. parameter
choice_weights.m	plots R-SNR, CC and RMSE as a function of the weights lambda