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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
  1. Activate the environment
$ conda activate PsiDONet_tf_env
  1. 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
  1. 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
  1. Activate the environment
$ conda activate PsiDONet_torch_env
  1. 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
  1. Add the pytorch wavelet package with pip.
$ git clone https://github.com/fbcotter/pytorch_wavelets
$ cd pytorch_wavelets
$ pip install .
  1. 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.