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Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a…
Physics-guided deep learning is an important prevalent research topic in scientific machine learning, which has tremendous potential in various complex applications including science and engineering. In these applications, data is expensive…
Deep learning has been widely employed to solve the Electrical Impedance Tomography (EIT) image reconstruction problem. Most existing physical model-based and learning-based approaches focus on 2D EIT image reconstruction. However, when…
Latent diffusion models have established a new state-of-the-art in high-resolution visual generation. Integrating Vision Foundation Model priors improves generative efficiency, yet existing latent designs remain largely heuristic. These…
Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization…
Electrical Impedance Tomography (EIT) provides a non-invasive, portable imaging modality with significant potential in medical and industrial applications. Despite its advantages, EIT encounters two primary challenges: the ill-posed nature…
This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and…
This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to…
Domain Generalized Semantic Segmentation (DGSS) focuses on training a model using labeled data from a source domain, with the goal of achieving robust generalization to unseen target domains during inference. A common approach to improve…
Electrical Impedance Tomography (EIT) systems are becoming popular because they present several advantages over competing systems. However, EIT leads to images with very low resolution. Moreover, the nonuniform sampling characteristic of…
Electrical Impedance Tomography (EIT) is a powerful tool for non-destructive evaluation, state estimation, and process tomography - among numerous other use cases. For these applications, and in order to reliably reconstruct images of a…
Variational autoencoders (VAEs) typically encode images into a compact latent space, reducing computational cost but introducing an optimization dilemma: a higher-dimensional latent space improves reconstruction fidelity but often hampers…
The vast applications of deep generative models are anchored in three core capabilities -- generating new instances, reconstructing inputs, and learning compact representations -- across various data types, such as discrete text/protein…
Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
Determining physical properties inside an object without access to direct measurements of target regions can be formulated as a specific type of \textit{inverse problem}. One of such problems is applied in \textit{Electrical Impedance…
In this work, we propose a denoising diffusion generative model (DDGM) trained with healthy electrocardiogram (ECG) data that focuses on ECG morphology and inter-lead dependence. Our results show that this innovative generative model can…
Electrical impedance tomography (EIT) plays a crucial role in non-invasive imaging, with both medical and industrial applications. In this paper, we present three data-driven reconstruction methods for EIT imaging. These three approaches…
Electrical Impedance Tomography (EIT) is a noninvasive imaging technique that does not use ionizing radiation, with application both in environmental sciences and in health. Image reconstruction is performed by solving an inverse problem…
Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…