PsiDONet

Convolutional neural network for limited-angle tomographic reconstruction inspired by pseudodifferential operators

• License: GNU General Public License v3.0
• Author: Mathilde Galinier
• Institution: Università degli studi di Modena e Reggio Emilia
• Doctoral programme: INdAM Doctoral Programme in Mathematics and Applications Cofunded by Marie Sklodowska-Curie Actions (INdAM-DP-COFUND-2015)
• Email: [email protected]
• Related publication: https://arxiv.org/abs/2006.01620
• Please use the following citation:

  T. A. Bubba, M. Galinier, M. Lassas, M. Prato, L. Ratti, and S. Siltanen. 'Deep neural networks for inverse problems with pseudodifferential operators: an ap-plication to limited-angle tomography'. To appear in SIAM Journal on Imaging Sciences (SIIMS), 2020.

Installation of the Tensorflow environment

1. Install anaconda.
2. Create an environment with python version 3.6.9.

$ conda create -n PsiDONet_tf_env python=3.6.9

3. Activate the environment

$ conda activate PsiDONet_tf_env 

4. Inside this environment install the following packages.

$ conda install -c anaconda numpy=1.14.6 
$ conda install -c conda-forge matplotlib=3.2.1 scikit-image=0.17.2 pywavelets=1.1.1
$ conda install tensorflow-gpu=1.13.1 
$ conda install -c astra-toolbox astra-toolbox=1.8.3
$ conda install -c odlgroup odl=0.7.0

5. Use the demo notebook to train and test PsiDONet models.

(alternative) Installation of the PyTorch environment

1. Install anaconda.
2. Create an environment with python version 3.6.9.

$ conda create -n PsiDONet_torch_env python=3.6.9

3. Activate the environment

$ conda activate PsiDONet_torch_env 

4. Inside this environment install the following packages.

$ conda install -c anaconda numpy=1.14.6 
$ conda install -c conda-forge matplotlib=3.2.1 scikit-image=0.17.2 pywavelets=1.1.1
$ conda install pytorch=1.0.0 torchvision=0.2.1 cuda80 -c pytorch
$ conda install -c astra-toolbox astra-toolbox=1.8.3
$ conda install -c odlgroup odl=0.7.0

5. Add the pytorch wavelet package with pip.

$ git clone https://github.com/fbcotter/pytorch_wavelets
$ cd pytorch_wavelets
$ pip install .

6. Use the demo notebook to train and test PsiDONet models.

File organisation:

• Tensorflow: Contains the tensorflow version of PsiDONet files

  • fundamental_functions: Contains PsiDONet files
    • Train_Test_PsiDONet.py: Contains the training and testing functions of PsiDONet
    • utils_learning.py: Includes the definition of the PsiDONet unrolled iterations
    • utils_bowtie.py: Contains functions for filter computation
    • tools.py: Includes loading and quality evalutation functions
    • auxiliary_functions.py: Contains some useful side functions
    • tf_wavelets.py: Contains wavelet transform functions
    • haar_psi.py: Contains the implementation of HaarPSI (code from http://www.haarpsi.org/)
  • demo.ipynb: shows how to train and test PsiDONet with the tensorflow implementation

• PyTorch: Contains the PyTorch version of PsiDONet files (only PsiDONetO and PsiDONetO+ are implemented)

  • fundamental_functions: Contains PsiDONet files
    • Train_Test_PsiDONet.py: Contains the training and testing functions of PsiDONet
    • model.py: Includes the definition of the layers in PsiDONet
    • modules.py: Contains useful functions employed in PsiDONet
    • tools.py: Includes loading and quality evalutation functions
    • auxiliary_functions.py: Contains some useful side functions
    • haar_psi.py: Contains the implementation of HaarPSI
  • PyTorch_ssim: forward and backward functions to use SSIM as the training loss, (code from https://github.com/Po-Hsun-Su/pytorch-ssim)
  • demo.ipynb: shows how to train and test PsiDONet with the PyTorch implementation

• Ellipses_Datasets: Datasets of ellipse images

  • Size_128: Dataset of 128x128 images
    • train: Training set
      • Images: Contains 10000 ground truth ellipse images
      • Sinograms: Contains 10000 complete-angle sinograms
    • val: Validation set
      • Images: Contains 500 ground truth ellipse images
      • Sinograms: Contains 500 complete-angle sinograms
    • test: Test set
      • Images: Contains 500 ground truth ellipse images
      • Sinograms: Contains 500 complete-angle sinograms

The ground truth images and the sinograms were simulated with Matlab. The sinograms were corrupted by gaussian noise and generated according to a procedure that avoids inverse crime.

Thank you for using our code, kindly report any suggestion to the corresponding author.