Author: Eric Bezzam
Supervisors: Adrien Besson¹, Hanjie Pan², Dimitris Perdios¹, Prof. Jean-Philippe Thiran¹

¹Signal Processing Laboratory 5 (LTS5) at EPFL.
²Audiovisual Communications Laboratory (LCAV) at EPFL.

The full report and slides can be found on Infoscience (EPFL's platform for scientific publications and reports).

Questions/comments can be directed to: eric[dot]bezzam[at]epfl[dot]ch. Or feel free to create an issue up top!

The initial goal of this Master thesis was to reduce the sampling and thus data rate necessary for medical ultrasound imaging. To this end, we investigate how recent signal processing approaches in Finite Rate of Innovation (FRI) and Euclidean Distance Matrices (EDM) can be applied to the task of ultrasound imaging and localization.

For medical imaging, we identify a few practical limitations (e.g. sparsity under noise, zero-finding) that complicate the application of FRI techniques, in particular to achieve real-time imaging at sampling rates lower than the conventional approaches.

For the task of localization, we identify a suitable candidate for FRI and EDM techniques, most notably for the task of identifying a sparse number of bright reflectors. We consider an example of non-destructive evaluation (NDE) where we would like to identify a small amount of defects at rates lower than conventional methods.

If you use any code or results from here, please cite:

E. Bezzam, (2018). "Sampling at the rate of innovation for ultrasound imaging and localization," 2018,
Unpublished Master’s thesis, EPFL, Lausanne, Switzerland.

This software has been tested with a MacBook Pro running macOS Sierra (Version 10.12.6).

If you are using Anaconda, you can create the environment used in this project with the following command:

conda env create -f frius_env.yml

For activating the environment:

• Windows: activate frius
• macOS and Linux: source activate frius

If you are not using Anaconda, you can open the 'frius_env.yml' file to see which libraries were used (but perhaps not necessary). The essentials are:

1. Python 3.
2. numpy, scipy, matplotlib for standard scientific computing and plotting.
3. joblib for parallelizing some of the tests.
4. h5py for opening certain datasets.

In 'notebooks', we provide a couple tutorials that we hope will help the interested reader and hacker understand the core topics in this thesis. If you are not opting to download this repository, we recommend viewing the notebooks with nbviewer by entering the GitHub link to the corresponding notebook.

In 'frius' are the main utility functions for the work in this thesis:

1. 'us_utils': utilities for synthesizing ultrasound measurements and performing delay-and-sum (DAS) beamforming.
2. 'fri_utils': utilities for performing pulse stream recovery and evaluating the performance.
3. 'edm_utils': utilities for using EDMs to perform echo/time-of-flight matching.

In 'report_results' are various scripts for reproducing figures in the report. See below for more information.

Documentation is admittedly rough due to the short time frame of this project, but feel free to contact the author with any questions/comments!

All the figures in the report can be created by running:

python generate_figures.py

The PDF (and some PNG) files will be written to: 'report_results/FIGURES'.

For a particular figure, the image can be generated (and with modified parameters) by running the corresponding script 'report_results/figXpX*.py', e.g. 'report_results/fig1p6_pulse_shape.py' for Figure 1.6 in the report.

Note: this is only true for those figures that were generated with Python, e.g. simulations.

The source code is released under the MIT license. See the Licence file for more info.