Reproducible 4D Electrical Capacitance Tomography Research Pipeline

This repository contains a staged MATLAB implementation for synthetic four-dimensional electrical capacitance tomography (4D ECT): sensor preparation, dynamic phantom simulation, FEM forward modeling, measurement-error generation, linear and nonlinear reconstruction, motion compensation, confirmatory validation, robustness controls, and inverse-grid convergence analysis.

The numbered directory names encode both execution order and scientific purpose. MATLAB function names retain their original ect4d_stepXX_* identifiers to preserve provenance and make outputs traceable to the corresponding study stage.

Repository map

Stage	Directory	Scientific role
01	step_01_sensor_model_and_geometry	Load and validate the 32-electrode 3D FEM sensor model
02	step_02_static_phantom_definition	Define static tetrahedral permittivity phantoms
03	step_03_dynamic_phantom_sequence	Generate moving-object ground-truth sequences
04	step_04_fem_forward_simulation	Solve electrostatic fields and capacitance measurements
05	step_05_measurement_noise_and_model_error	Add acquisition/model error and estimate covariance
06	step_06_spatiotemporal_visualization	Visualize 3D+time sequences and space–time maps
07	step_07_dataset_export_and_ml_interface	Export MATLAB, HDF5, CSV, and metadata datasets
08	step_08_independent_and_causal_3d_reconstruction	Independent and causal dynamic 3D reconstruction
09	step_09_centered_multiframe_4d_reconstruction	Centered multiframe 4D method based on the 2009 formulation
10	step_10_validation_and_hyperparameter_tuning	Independent calibration, validation-only tuning, and test reporting
11	step_11_multiphantom_benchmark	Multi-phantom benchmark and aggregate comparison
12	step_12_nonlinear_4d_aem_and_motion_compensation	Nonlinear 4D reconstruction with AEM and transport regularization
13	step_13_quick_v2_motion_compensation_study	Quick-v2 motion-compensation study
14	step_14_quick_v3_confirmatory_validation	Frozen quick-v3 development/validation/test protocol
15	step_15_publication_robustness_and_replication	Numerical controls, ablation, and independent replication
16	step_16_inverse_grid_density_and_convergence	Inverse-grid density, memory, PCG, and convergence study

Requirements

• MATLAB R2022b or newer; development and large-scale runs used MATLAB R2024b.
• 64-bit operating system.
• At least 64 GB RAM for the complete study; Step 16 may require substantial SSD workspace.
• The supplied 3DECTworkspace.mat file in the repository root.
• Python 3 with numpy and h5py only for the optional Step 07 HDF5 interface.

Reference single-workstation computations were performed on a PC equipped with an AMD Ryzen 9 5950X CPU, 64 GB RAM, and an NVIDIA RTX A6000 GPU with 48 GB VRAM. The baseline MATLAB implementation remains CPU-dominant unless a stage explicitly selects GPU-enabled operations.

The base Steps 01–16 do not require a live ECT acquisition system because the study is built on synthetic FEM data. The supplied workspace contains the sensor/mesh state required by the code.

Initial setup

Start MATLAB in the repository root and run:

stageDirectories = setup_ect4d_paths(pwd);

The helper verifies that exactly one descriptive directory exists for every stage and adds stages in ascending order. Later stages receive higher path precedence because they may contain corrected versions of shared reconstruction functions.

Recommended execution strategy

1. Run each stage self-test before a long experiment.
2. Use the demonstration scripts for Steps 01–13.
3. Follow RUN_IN_ORDER.md exactly in Steps 14–16.
4. Do not edit frozen-stage source files after a SHA-256 protocol has been created.
5. Keep generated .mat, logs, tables, and figures outside version control unless they are intentionally released as archival research outputs.

Reproducibility conventions

• Development, historical validation, fresh test, and independent replication sets are explicitly separated.
• Random seeds and scenario catalogs are stored in result files.
• Expensive phases support checkpoint/resume.
• Step 14 and later use SHA-256 fingerprints to detect source or protocol changes.
• Step 16 evaluates every inverse grid against the same native tetrahedral FEM truth and the same measurement bank.
• Function and result-file names retain ect4d_stepXX prefixes even though directories are descriptive.

Source-code fingerprint compatibility

Renaming the directories required updating the internal path-discovery helpers. Consequently, frozen .mat protocols created from an earlier directory layout may fail their source-code SHA-256 checks. For a clean public replication, regenerate the relevant freeze phase with this repository revision and retain the generated protocol together with the commit identifier.

Citation

The centered multiframe reconstruction in Step 09 follows the formulation introduced in:

M. Soleimani, C. N. Mitchell, R. Banasiak, R. Wajman, and A. Adler, “Four-Dimensional Electrical Capacitance Tomography Imaging Using Experimental Data,” Progress In Electromagnetics Research, vol. 90, pp. 171–186, 2009.

When publishing results from this repository, cite both the research article and the archived repository release/DOI associated with the exact commit used for computation.