MA - Compressed Sensing for Efficient Data Acquisition in Electrical Impedance Tomography

Entwicklung eines Robotersystems für die Synchronisation und Datenmanagement von EIT- und Dopplermessungen

Compressed Sensing for Efficient Data Acquisition in Electrical Impedance Tomography

General Setting

Electrical Impedance Tomography (EIT) is a non-invasive imaging technology based where a conductivity profile inside a medium is reconstructed based on voltage measurements on its boundary. At iMEK, within the context of the Collaborative Research Center CRC1615, a 3D EIT system to monitor chemical processes is being developed. In order to bring bubble size distributions in the reactor together with electrical measurements this work aims to couple those measurements and automize the control of the system and the storage of the derived data.

1. Project Objective

The goal of this project is to investigate and implement alternatives to the Fourier Transform and corresponding phase and amplitude transmission of signals in the time-domain. Compressed Sensing (CS) techniques offer an approach to develop alternative ways to compress time-resolved signals. The final system will consist of a physical EIT measurement setup (including a signal generator and impedance analyzer), a signal compression framework using sparse representations (e.g., wavelets, shearlets), and a reconstruction algorithm adapted to work with compressed data.

2. Motivation and Background

EIT is a non-invasive imaging technique used to reconstruct the internal conductivity distribution of an object. It relies on injecting current through electrodes and measuring resulting voltages. A major challenge is the large number of measurements required, which slows down data acquisition and increases hardware complexity.

Compressed sensing offers a solution by allowing reconstruction from fewer measurements, provided the signal is sparse in some domain. Recent studies have shown that temporal and spatial sparsity in EIT measurements can be exploited using transforms such as wavelets, curvelets, and shearlets. This project will leverage these ideas to build a real-time or near-real-time EIT system with reduced data overhead.

3. Methodology

Step 1: Literature Review & Theoretical Foundation

• Investigate sparsifying transforms for EIT signals (wavelets, shearlets, discrete cosine transform, etc.).

• Study previous applications of CS in compression of timely resolved signals

• Understand theoretical guarantees of recovery (RIP, incoherence, etc.).

Step 2: Experimental Setup

• Build or obtain a cylindrical EIT test cell

• Integrate a signal generator (to inject known current patterns) and an impedance analyzer (to measure voltage responses)

Step 3: Signal Compression Framework

• Acquire full measurement data as a baseline for different excitation signal shapes

• Apply selected sparsifying transforms (e.g., for example wavelet transform, shearlet transform of timely resolved signals).

• Implement compressed sensing recovery algorithms such as:

  • Basis Pursuit

  • Orthogonal Matching Pursuit (OMP)

  • Iterative Shrinkage-Thresholding Algorithm (ISTA/FISTA)

• Compare compression rates and reconstruction quality.

Step 4: Image Reconstruction

• Modify or extend existing EIT inverse solvers (e.g., GREIT, EIDORS) to work with compressed data.

• Compare reconstruction from derived compressed reconstruction with standard methods.

• Analyze tradeoffs in speed, accuracy, and stability.

Step 5: Evaluation

• Quantitative metrics: RMSE, SSIM, PSNR.

• Qualitative analysis of reconstructed conductivity distributions.

• Sensitivity to noise and electrode misplacements.

• Compare results across different transforms and sampling strategies.

4. Expected Outcomes

• A working hardware setup for EIT measurements.

• A compressive sensing framework tailored for EIT data.

• Comparative analysis of different sparsity domains (wavelet, shearlet, etc.).

• A prototype using the compressed sensing for reconstructing EIT images.

Zeitplanung:

start asap

Checklist

• Introduction / tour in M4

• Urheberrechtsvereinbarung signed

• if applicable: signed confidential agreement

• official registration

Helpful links:

• Thesis Work / Studentische Arbeiten 

• Criteria for the evaluation of Bachelor's and Master's theses, handout version

• Laborordnung

• Spotlights / Kurzvorträge

• Templates (Latex, ppt etc.)

Document Upload Final Thesis / Dokumentenabgabe Abschlussdokument

File of final presentation / Dokumentenabgabe Abschlusspräsentation

Link for further files / Link für weitere Dokumente