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Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates…
Latent generative models have emerged as a leading approach for high-quality image synthesis. These models rely on an autoencoder to compress images into a latent space, followed by a generative model to learn the latent distribution. We…
Electrical Impedance Tomography (EIT) is a promising noninvasive imaging technique that reconstructs the spatial conductivity distribution from boundary voltage measurements. However, it poses a highly nonlinear and ill-posed inverse…
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…
Self-supervised image denoising methods have garnered significant research attention in recent years, for this kind of method reduces the requirement of large training datasets. Compared to supervised methods, self-supervised methods rely…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…
Dense depth and surface normal predictors should possess the equivariant property to cropping-and-resizing -- cropping the input image should result in cropping the same output image. However, we find that state-of-the-art depth and normal…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
Image Dehazing (ID) aims to produce a clear image from an observation contaminated by haze. Current ID methods typically rely on carefully crafted priors or extensive haze-free ground truth, both of which are expensive or impractical to…
Image normalization, the correction for intra-volume inhomogeneities in magnetic resonance imaging (MRI) data has little significance for visual diagnosis, but is a crucial step before automated radiotherapy solutions. There are several…
Spiking neural networks are a promising approach towards next-generation models of the brain in computational neuroscience. Moreover, compared to classic artificial neural networks, they could serve as an energy-efficient deployment of AI…
Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of…
The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…
Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present…
Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks…
Convolutional Neural Networks (CNNs) work very well for supervised learning problems when the training dataset is representative of the variations expected to be encountered at test time. In medical image segmentation, this premise is…
Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between…
Deep learning has emerged as a technique of choice for rapid feature extraction across imaging disciplines, allowing rapid conversion of the data streams to spatial or spatiotemporal arrays of features of interest. However, applications of…
Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such…