Joint Sparsity With Partially Known Support and Application to Ultrasound Imaging

Adrien Besson¹, Dimitris Perdios¹, Yves Wiaux² and Jean-Philippe Thiran^1,3

¹Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland

²Institute of Sensors, Signals and Systems, Heriot-Watt University , UK

³Department of Radiology, University Hospital Center (CHUV), Switzerland

Code used to reproduce the results presented in this paper, submitted to the IEEE Signal Processing Letters

Abstract

We study the performance of joint-sparse algorithms when part of the unknown signal support is known. We demonstrate that such a prior knowledge is advantageous compared to rank-aware algorithms when the size of the known support is higher than the rank of the measurements. We suggest extensions of several joint-sparse recovery algorithms, e.g. multiple signal classification, rank-aware orthogonal recursive matching pursuit and simultaneous normalized iterative hard thresholding.

We describe a direct application of the proposed methods for compressive multiplexing of ultrasound (US) signals. The technique exploits the compressive multiplexer architecture for signal compression and relies on joint-sparsity of US signals in the frequency domain for signal reconstruction. Due to piezo-electric properties of transducer elements, accurate prior knowledge of the frequency support of US signals is available and can be used in joint-sparse algorithms.

We validate the proposed methods on numerical experiments and show their superiority against state-of-the-art approaches in rank-defective cases. We also demonstrate that the techniques lead to a significant increase of the image quality on in vivo carotid images compared to reconstruction without known support.

Requirements

• Python >=3.6 (Code tested with default Python 3.6.2 and Anaconda 4.3.21)
• git

Installation

1. Clone the repository

   git clone  https://github.com/AdriBesson/spl2018_joint_sparse.git

2. Enter in the spl2018_joint_sparse folder

   cd spl2018_joint_sparse

3. (Optional) Create a dedicated Python environment

   • Using Anaconda:

     conda create -n spl2018_joint_sparse python=3.6
     source activate spl2018_joint_sparse

   • Using pyenv:

     pyvenv /path/to/new/virtual/env . /path/to/new/virtual/env/bin/activate

4. Install Python dependencies from python_requirements.txt. Depending on your installation, pip may refer to Python 2 (you can verify with pip -V). In that case, use pip3 instead of pip.

   pip install --upgrade pip
   pip install -r python_requirements.txt

Usage

1. numerical_experiments.py provides a script to run the experiments to generate Figures 2-a to 2-f
2. numerical_experiments_supplementary.py provides a script to run the experiments to generate Figure 4 (in the supplementary material of the publication)
3. example_theorem2.pynb is an explicative notebook that illustrates the benefit of partial known support for rank-aware methods (Theorem 2)

Contact

Adrien Besson ([email protected])

License

The code in this repository is released under the terms of the MIT license.