Here, we provide an implementation of the network described in our work
"Deep Supervised Dictionary Learning by Algorithm Unrolling - Application to Fast 2D Dynamic MR Image Reconstruction"
by A. Kofler, M.C. Pali, T. Schaeffter and C. Kolbitsch.
The method is a so-called physics-informed neural network that implements an algorithm that approaches the solution of the problem
by alternating minimization. The weights of the network - i.e. the atoms of the dictionary and the regularization parameters and
- can be trained in a supervised and physics-informed way.
By running the files dlmri_reco_example.py and dlmri_denoising_example.py you can get familiar with how to apply the networks to an undersampled MRI reconstruction problem and a image denoising problem.
The main results of the paper are the following:
First, we have observed that reconstructing images with the dictionary obtained by training it via algorithm unrolling yields superior results compared to the dictionary obtained by decoupled pre-training, i.e. using the LASSO algorithm to solve a sparse approximation problem to obtain the dictionary.
Second, we have introduced a 2D spatio-temporal dictionary that yields superior results compared to the standard choice of the 3D dictionary.
The following shows a comparison of an image obtained using the 3D dictionary pre-trained by employing the LASSO algorithm and an image obtained with the proposed 2D spatio-temporal dictionary that was trained usin by algorithm unrolling, both results are shown for a dictionary of shape with
.
From left to right:
Zero-Filled Recon - 3D dictionary with patch-size (4,4,6) - 2D dictionary with shape (4,1,16) - Target image, for .
The following shows the decay of the mean squared error (MSE) over 16 iterations that were used reconstruct the images shown above.
The paper (open-access) is available under
https://aapm.onlinelibrary.wiley.com/doi/10.1002/mp.16182
For citing this work, please use
@article{kofler2023end2end_dlmri, title={Deep supervised dictionary learning by algorithm unrolling—Application to fast 2D dynamic {MR} image reconstruction}, author={Kofler, Andreas and Pali, Marie-Christine and Schaeffter, Tobias and Kolbitsch, Christoph}, journal={Medical Physics}, volume={50}, number={5}, pages={2939--2960}, year={2023}, publisher={Wiley Online Library} }