Multi-frequency Electrical Impedance Tomography Reconstruction with Multi-Branch Attention Image Prior

TL;DR

mfEIT reconstruction is challenged by dependence on training data in supervised MMV approaches. The authors propose a model-based unsupervised framework called MAIP, built on a Multi-Branch Attention Network that captures intra- and inter-frequency correlations without training data. MAIP employs a tensor-friendly forward model and a fusion-attention architecture to reconstruct all frequency images jointly, delivering competitive or superior results to state-of-the-art methods in simulations and real phantoms. The approach enhances robustness and generalization of mfEIT and opens pathways for practical deployment and extensions to 3D imaging.

Abstract

Multi-frequency Electrical Impedance Tomography (mfEIT) is a promising biomedical imaging technique that estimates tissue conductivities across different frequencies. Current state-of-the-art (SOTA) algorithms, which rely on supervised learning and Multiple Measurement Vectors (MMV), require extensive training data, making them time-consuming, costly, and less practical for widespread applications. Moreover, the dependency on training data in supervised MMV methods can introduce erroneous conductivity contrasts across frequencies, posing significant concerns in biomedical applications. To address these challenges, we propose a novel unsupervised learning approach based on Multi-Branch Attention Image Prior (MAIP) for mfEIT reconstruction. Our method employs a carefully designed Multi-Branch Attention Network (MBA-Net) to represent multiple frequency-dependent conductivity images and simultaneously reconstructs mfEIT images by iteratively updating its parameters. By leveraging the implicit regularization capability of the MBA-Net, our algorithm can capture significant inter- and intra-frequency correlations, enabling robust mfEIT reconstruction without the need for training data. Through simulation and real-world experiments, our approach demonstrates performance comparable to, or better than, SOTA algorithms while exhibiting superior generalization capability. These results suggest that the MAIP-based method can be used to improve the reliability and applicability of mfEIT in various settings.

Figures (10)

• Figure 1: Illustration of the imaging region discretization and the conversion between $\Delta\pmb{\sigma}_{f_{i}}$ and its corresponding rectangular image representation: The circular imaging region in ($\pmb{\textrm{a}}$) is discretized into an H-by-W mesh in ($\pmb{\textrm{b}}$), where each pink grid in the mesh represents a pixel and the green grids denote the void pixels. The pink grids are indexed and can be further arranged into a vector $\Delta\pmb{\sigma}_{f_{i}}$ ($\pmb{\textrm{c}}$). Conversely, $\Delta\pmb{\sigma}_{f_{i}}$ can be rearranged into its rectangular form.
• Figure 2: Schematic of the MAIP-based mfEIT reconstruction approach.
• Figure 3: The architecture of MBA-Net: a) the overall architecture; b) the Fusion Unit, used for multi-branch feature fusion; c) the structure of the Branch Attention module, detailing how attention mechanisms are applied, with the attention matrix $\mathbf{A}$ and the scaling vector $\mathbf{w}$ illustrating examples of their respective final values; and d) the architecture of the branch subnetwork, showing the configuration and connectivity of modules of our branch subnetwork.
• Figure 4: Real-world experiment phantoms: Phantom 1: apple flesh in a 15 mm 16-electrode EIT sensor; Phantom 2: sheep liver (top) and chicken skin slices (down) in a 10 mm 16-electrode EIT sensor; Phantom 3: two zebrafishes within the same sensor as phantom 2.
• Figure 5: Comparative results of the proposed MAIP algorithm and SOTA image reconstruction algorithms (i.e., ADMM-MMVb7, FISTA-Netb20, MoDLb19, MMV-Netb9, and DeepEITb18) in three simulated cases.