Impedance-optical Dual-modal Cell Culture Imaging with Learning-based Information Fusion

While Electrical Impedance Tomography (EIT) has found many biomedicine applications, a better resolution is needed to provide quantitative analysis for tissue engineering and regenerative medicine. This paper proposes an impedance-optical dual-modal imaging framework, which is mainly aimed at high-quality 3D cell culture imaging and can be extended to other tissue engineering applications. The framework comprises three components, i.e., an impedance-optical dual-modal sensor, the guidance image processing algorithm, and a deep learning model named multi-scale feature cross fusion network (MSFCF-Net) for information fusion. The MSFCF-Net has two inputs, i.e., the EIT measurement and a binary mask image generated by the guidance image processing algorithm, whose input is an RGB microscopic image. The network then effectively fuses the information from the two different imaging modalities and generates the final conductivity image. We assess the performance of the proposed dual-modal framework by numerical simulation and MCF-7 cell imaging experiments. The results show that the proposed method could significantly improve image quality, indicating that impedance-optical joint imaging has the potential to reveal the structural and functional information of tissue-level targets simultaneously

Networks for Nonlinear Diffusion Problems in Imaging

A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for applications where it is not apparent that convolutions are suited to capture the underlying physics. In this work we develop a network architecture based on nonlinear diffusion processes, named DiffNet. By design, we obtain a nonlinear network architecture that is well suited for diffusion related problems in imaging. Furthermore, the performed updates are explicit, by which we obtain better interpretability and generalisability compared to classical convolutional neural network architectures. The performance of DiffNet tested on the inverse problem of nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset. We obtain competitive results to the established U-Net architecture, with a fraction of parameters and necessary training data

Methods for the Electrical Impedance Tomography Inverse Problem: Deep Learning and Regularization with Wavelets

Electrical impedance tomography, also known as EIT, is a type of diffusive imaging modality that is non-invasive, radiation-free, and cost-effective for recovering electrical properties within a closed domain from surface measurements. The process involves injecting electrical current into a set of electrodes to measure the voltage on the smooth surface of the domain. The recovered EIT images show how well different materials or tissues within the domain conduct or impede electrical flow, which is helpful in detecting and locating anomalies. For the EIT inverse problem, it is challenging to recover reliable and resolvable electrical conductivity images since it is highly nonlinear and severely ill-posed, especially when the data is corrupted with noise. To address this issue, we propose (1) a wavelet-based modified Gauss-Newton (WGN) method that uses wavelets as a form of regularization and parameter reduction. In (1), we enforce regularization through the use of wavelet coefficients by projecting the original formulation to the wavelet domain and then only retaining the wavelet coefficients of highest power. The projected wavelet formulation is of a smaller dimension and, therefore, shows promise in improving the ill-posedness of the EIT inverse problem. Different wavelet families are implemented to capture localized features, smoothness, and irregularities within the domain. In addition, we also propose (2) a novel deep learning algorithm to solve the EIT inverse problem. In (2), we develop a deep neural network (DNN) with multiple transposed convolutional layers and activation functions to recover the EIT images. The DNN is first trained on a large set of EIT images and data, and then we recover EIT images in real-time from the trained DNN. We compare the image reconstructions from the DNN with a benchmark algorithm. For model validation, we employed a set of synthetic examples with various anomalies to test the performance and efficacy of both the DNN and WGN method. The results from both methods show promise in improving EIT image reconstructions

Machine learning aided bioimpedance tomography for tissue engineering

In tissue engineering, miniature Electrical Impedance Tomography (mEIT) (or bioimpedance tomography), is an emerging tomographic modality that contributes to non-destructive and label-free imaging and monitoring of 3-D cellular dynamics. The main challenge of mEIT comes from the nonlinear and ill-posed image reconstruction problem, leading to the increased sensitivity to imperfect measurement signals. Physical model-based image reconstruction methods have been successfully applied to conventional setups, but are less satisfying for the mEIT setup regarding image quality, conductivity retrieval and computational efficiency. Data-driven or learning-based methods have recently become a new frontier for tomographic image reconstruction, particularly for medical imaging modalities, e.g., Computed Tomography (CT), Positron Emission Tomography (PET), and Magnetic Resonance Imaging (MRI). However, the study of learning-based image reconstruction methods in challenging micro-scale sensor setups and the seamless integration of such algorithms with the tomography instrument remains a gap. This thesis aims to develop 2-D and 3-D imaging platforms integrating multi-frequency EIT and machine learning-based image reconstruction algorithms to extract spectroscopic electrical properties of 3-D cultivated cells under in vitro conditions, in a non-destructive, robust, and computation-efficient manner. Recent advances in deep learning have pointed out a promising alternative for EIT image reconstruction. However, it is still challenging to image multiple objects with varying conductivity levels with a single neural network. A deep learning and group sparsity regularization-based hybrid image reconstruction framework was proposed to enable high-quality cell culture imaging with mEIT. A deep neural network was proposed to estimate the structural information in binary masks, given the limited number of data sets. Then the structural information is encoded in group sparsity regularization to obtain the final conductivity estimation. We validated our approach by imaging 3D cancer cell spheroids (MCF-7). Our method can be readily translated to spheroids, organoids, and cell culture in scaffolds of biomaterials. As the measured conductivity is a proxy for cell viability, mEIT has excellent potential to enable non-invasive, real-time, long-term monitoring of 3D cell growth, opening new avenues in regenerative medicine and drug testing. Deep learning provides binary structural information in the above-mentioned hybrid learning approach, whereas the regularization algorithm determines conductivity contrasts. Despite the advancement of structure distribution, the exact conductivity values of different objects are less accurately estimated by the regularization-based framework, which essentially prevents EIT’s transition from generating qualitative images to quantitative images. A structure-aware dual-branch deep learning method was proposed to further tackle this issue to predict structure distribution and conductivity values. The proposed network comprises two independent branches to encode the structure and conductivity features, respectively, and the two branches are joined later to make final predictions of conductivity distributions. Numerical and experimental evaluation results on MCF-7 human breast cancer cell spheroids demonstrate the superior performance of the proposed method in dealing with the multi-level, continuous conductivity reconstruction problem. Multi-frequency Electrical Impedance Tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods suffer from low spatial resolution, unconstrained frequency correlation and high computational cost. Most existing learning-based approaches deal with the single-frequency setup, which is inefficient and ineffective when extended to the multi-frequency setup. A Multiple Measurement Vector (MMV) model-based learning algorithm named MMV-Net was proposed to solve the mfEIT image reconstruction problem. MMV-Net considers the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers for the MMV problem (MMV-ADMM). The nonlinear shrinkage operator associated with the weighted l_{1,2} regularization term of MMV-ADMM is generalized in MMV-Net with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to capture intra- and inter-frequency dependencies better. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. The results show superior image quality, convergence performance, noise robustness and computational efficiency against the conventional MMV-ADMM and the state-of-the-art deep learning methods. Finally, few work on image reconstruction for Electrical Impedance Tomography (EIT) focuses on 3D geometries. Existing reconstruction algorithms adopt voxel grids for representation, which typically results in low image quality and considerable computational cost, and limits their applicability to real-time applications. In contrast, point clouds are a more efficient format for 3D surfaces, and such representation can naturally handle 3D shapes of arbitrary topologies with fine-grained details. Therefore, a learning-based 3D EIT reconstruction algorithm with efficient 3D representations (i.e., point cloud) was proposed to achieve higher image accuracy, spatial resolution and computational efficiency. A transformer-like point cloud network is adopted for 3D image reconstruction. This network simultaneously recovers the 3D coordinates of points to adaptively portray the objects' surface and predicts each point's conductivity. The results show that point cloud provides more efficient fine-shape descriptions and effectively alleviates computational costs. In summary, the work demonstrated in this thesis addressed the research void in tissue imaging with bioimpedance tomography by developing learning-based imaging approaches. The results achieved in this thesis could promote bioimpedance tomography as a robust, intelligent imaging technique for tissue engineering applications

FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging

Inverse problems are essential to imaging applications. In this paper, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) and strong regularization and tuning-free advantages of the data-driven neural network. By unfolding the FISTA into a deep network, the architecture of FISTA-Net consists of multiple gradient descent, proximal mapping, and momentum modules in cascade. Different from FISTA, the gradient matrix in FISTA-Net can be updated during iteration and a proximal operator network is developed for nonlinear thresholding which can be learned through end-to-end training. Key parameters of FISTA-Net including the gradient step size, thresholding value and momentum scalar are tuning-free and learned from training data rather than hand-crafted. We further impose positive and monotonous constraints on these parameters to ensure they converge properly. The experimental results, evaluated both visually and quantitatively, show that the FISTA-Net can optimize parameters for different imaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT). It outperforms the state-of-the-art model-based and deep learning methods and exhibits good generalization ability over other competitive learning-based approaches under different noise levels.Comment: 11 pages