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We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a…

Quantitative susceptibility mapping (QSM) inevitably suffers from streaking artifacts caused by zeros on the conical surface of the dipole kernel in k-space. This work proposes a novel and accurate QSM reconstruction method based on a…

Abnormal iron accumulation in the brain subcortical nuclei has been reported to be correlated to various neurodegenerative diseases, which can be measured through the magnetic susceptibility from the quantitative susceptibility mapping…

We propose a new framework for processing Fringe Patterns (FP). Our novel approach builds upon the hypothesis that the denoising and normalisation of FPs can be learned by a deep neural network if enough pairs of corrupted and ideal FPs are…

Deep Matching (DM) is a popular high-quality method for quasi-dense image matching. Despite its name, however, the original DM formulation does not yield a deep neural network that can be trained end-to-end via backpropagation. In this…

Neural networks are known to be vulnerable to adversarial attacks -- slight but carefully constructed perturbations of the inputs which can drastically impair the network's performance. Many defense methods have been proposed for improving…

In recent years, with the development of quantum machine learning, quantum neural networks (QNNs) have gained increasing attention in the field of natural language processing (NLP) and have achieved a series of promising results. However,…

The precision anticipated from next-generation cosmic microwave background (CMB) surveys will create opportunities for characteristically new insights into cosmology. Secondary anisotropies of the CMB will have an increased importance in…

Adversarial examples have shown that albeit highly accurate, models learned by machines, differently from humans, have many weaknesses. However, humans' perception is also fundamentally different from machines, because we do not see the…

Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…

Text-guided image generation and editing using diffusion models have achieved remarkable advancements. Among these, tuning-free methods have gained attention for their ability to perform edits without extensive model adjustments, offering…

Compressed sensing (CS) leverages the sparsity prior to provide the foundation for fast magnetic resonance imaging (fastMRI). However, iterative solvers for ill-posed problems hinder their adaption to time-critical applications. Moreover,…

Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model…

Hyperspectral image is unique and useful for its abundant spectral bands, but it subsequently requires extra elaborated treatments of the spatial-spectral correlation as well as the global correlation along the spectrum for building a…

MRI is an inherently slow process, which leads to long scan time for high-resolution imaging. The speed of acquisition can be increased by ignoring parts of the data (undersampling). Consequently, this leads to the degradation of image…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Filter-decomposition-based group equivariant convolutional neural networks (CNNs) have shown promising stability and data efficiency for 3D image feature extraction. However, these networks, which rely on parameter sharing and discrete…

Multi-image super-resolution, which aims to fuse and restore a high-resolution image from multiple images at the same location, is crucial for utilizing satellite images. The satellite images are often occluded by atmospheric disturbances…

Deep neural networks have emerged as effective tools for computational imaging including quantitative phase microscopy of transparent samples. To reconstruct phase from intensity, current approaches rely on supervised learning with training…

Deep neural networks (DNN) have achieved great success in image restoration. However, most DNN methods are designed as a black box, lacking transparency and interpretability. Although some methods are proposed to combine traditional…