An Unrolled Half-Quadratic Approach for Sparse Signal Recovery in Spectroscopy

• Publication: This is the source repository of the following work

  Mouna Gharbi, Emilie Chouzenoux, Jean-Christophe Pesquet. An Unrolled Half-Quadratic Approach for Sparse Signal Recovery in Spectroscopy. Inria Saclay. 2023. ⟨hal-04229774⟩

• Instituition: Centre de Vision Numérique, CentraleSupélec, Inria, Université Paris-Saclay

• Email: mouna.gharbi@centralesupelec.fr

How to run

Make sure that PyTorch is available in your Python environment. The code has been tested with Python 3.8.5 and PyTorch 1.8.0. All of the following commands are assumed to be run in the root directory of the repository.

In order to create data for training, please refer to the .csv file and use create_data.py. To create a dataset named Dataset1 with specified train, validation and test sizes run:

python ./Datasets/Create_Data.py --Dataset Dataset1 --set_size_training 900 --set_size_validation 100 --set_size_test 100

In case the exact datasets used in the paper are required, please contact me via email.

In order to run an experiment with the generated datasets, execute the respective Python scripts. For example, to train unrolled half-quadratic (U-HQ)

python ./Unrolled_methods/U_HQ/runfile.py --Dataset Dataset1 --function train --architectre_lambda lamda_Acrh2_overparam

To see the exact command-line parameters available for each method check the corresponding files:

Method	Script to run
Iterative Half-Quadratic	Iterative_methods/HQ.py
Unrolled Half-Quadratic	Unrolled_methods/U_HQ/runfile.py
Unrolled ISTA	Unrolled_methods/U_ISTA/runfile.py
Unrolled PD	Unrolled_methods/U_PD/runfile.py
FCNet	Deep_learning_methods/FCNet_AE/FCNet_AE.py
ResUNet	Deep_learning_methods/ResUNet/ResUNet.py

Detailed Files organization

The repository is organized as follows:

• Datasets

  • MSdata.csv: contains original Mass Spectrometry data.
  • Create_Data.py: creates datasets with different blur kernels and noise levels. A Dataset folder contains respectively training, validation and test subfolders. Each of these folders contains a Groundtruth, Degraded, Degraded2000 and H folders. To reproduce Dataset1 from the paper, create respectively $900$, $100$ and $100$ training, validation and test samples. Groundtruth signals $\overline{x}$ (of size $n=2000$) have a monoisotopic mass-to-charge ratio $m/z$ between $0$ and $200$ ppm. Degraded signals $y$ (of size m=2049) are created through a convolution (mode=Full) with a varying Ricker kernel H with spreading factor unifromly between $0.25$ and $1$. Finally, a standrad Gaussian noise, with a noise variance uniformly sampled between $0$ amd $0.5$ is added. Degraded is used for unrolled, FCNet and AE trainings. Degraded2000 (convolution mode=same) is used for ResUNet training. Dataset2 contains respectively $900$, $100$ and $100$ training, validation and test samples. Groundtruth signals $\overline{x}$ (of size $n=2000$) have a monoisotopic mass-to-charge ratio $m/z$ between $0$ and $200$ ppm. Degraded signals $y$ (of size m=2049) are created through a convolution (mode=Full) with a varying Ricker kernel H with spreading factor unifromly between $0.25$ and $1$. Finally, a standrad Gaussian noise, with a noise variance uniformly sampled between $0.5$ amd $1$ is added. Degraded is used for unrolled, FCNet and AE trainings. Degraded2000 (convolution mode=same) is used for ResUNet training.Dataset3 contains respectively $900$, $100$ and $100$ training, validation and test samples. Groundtruth signals $\overline{x}$ (of size $n=2000$) have a monoisotopic mass-to-charge ratio $m/z$ between $0$ and $200$ ppm. Degraded signals $y$ (of size m=2049) are created through a convolution (mode=Full) with a varying Fraser Suzuki kernel H with spreading factor unifromly between $0.25$ and $1$ and an asymmetry factor between $0.2$ and $0.6$. Finally, a standrad Gaussian noise, with a noise variance uniformly sampled between $0$ amd $0.5$ is added. Degraded is used for unrolled, FCNet and AE trainings. Degraded2000 (convolution mode=same) is used for ResUNet training.

• Deep_Learning_Methods

  • FCNet_AE: trains and tests fully connected and autoencoder-like architectures.
  • ResUNet: trains and tests a residual UNet architecture as in the code in this repository .

• Iterative methods:

  • `HQ.py: performs grid search and tests Half-Quadratic variants HQ-SC and HQ-ES.

• Unrolled methods:

  • U_HQ: trains and tests all variants of the unrolled Half-Quadratic paradigm: U-HQ-DE, U-HQ-FixS, U-HQ-FixN and U-HQ-FixN-Over-P.
  • U_PD: trains and tests unrolled primal-dual algorithm.
  • U_ISTA: trains and tests unrolled iterative soft thresholding algorithm.

• Chromatography_Toolbox: This is a tool that allows us to build simulated chromatographic datasets. This tool was not used in the experiments of the aforementioned paper but it can be useful to provide simulated datasets for the user. For more information please check the description

Acknowledgements

The comparisons with the ResUNet method are based on the code of Conor C. Horgan (see github repo) and all experiments are run on mass spectrometry data from MassBank.

This work has been supported by the ITN-ETN project TraDE-OPT funded by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 861137 and by the European Research Council Starting Grant MAJORIS ERC-2019-STG850925.