Related papers: Error analysis for filtered back projection recons…
This paper studies function approximation in Gaussian Sobolev spaces over the real line and measures the error in a Gaussian-weighted $L^p$-norm. We construct two linear approximation algorithms using $n$ function evaluations that achieve…
The observations in many applications consist of counts of discrete events, such as photons hitting a dector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model.…
Optimization algorithms such as projected Newton's method, FISTA, mirror descent, and its variants enjoy near-optimal regret bounds and convergence rates, but suffer from a computational bottleneck of computing ``projections'' in…
Classical neural network approximation results take the form: for every function $f$ and every error tolerance $\epsilon > 0$, one constructs a neural network whose architecture and weights depend on $\epsilon$. This paper introduces a…
X-ray phase-contrast imaging has the potential to improve image contrast with lower dose by probing an object's refractive properties as well as its absorptive properties. To reconstruct a phase-contrast image from a raw dataset, a phase…
The great success of Deep Neural Networks (DNNs) has inspired the algorithmic development of DNN-based Fixed-Point (DNN-FP) for computer vision tasks. DNN-FP methods, trained by Back-Propagation Through Time or computing the inaccurate…
The study of the Cosmic Microwave Background (CMB) lensing potential has established itself by now as a robust way of probing the physics of large-scale structure growth. The most common estimators of the lensing potential are derived under…
Coded aperture is a promising approach for capturing the 4-D light field (LF), in which the 4-D data are compressively modulated into 2-D coded measurements that are further decoded by reconstruction algorithms. The bottleneck lies in the…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
This paper studies the problem of how efficiently functions in the Sobolev spaces $\mathcal{W}^{s,q}([0,1]^d)$ and Besov spaces $\mathcal{B}^s_{q,r}([0,1]^d)$ can be approximated by deep ReLU neural networks with width $W$ and depth $L$,…
Coordinate networks like Multiplicative Filter Networks (MFNs) and BACON offer some control over the frequency spectrum used to represent continuous signals such as images or 3D volumes. Yet, they are not readily applicable to problems for…
State-of-the-art face recognition systems are based on deep (convolutional) neural networks. Therefore, it is imperative to determine to what extent face templates derived from deep networks can be inverted to obtain the original face…
Computed Tomography is one of the efficient and vital modalities of non-destructive techniques (NDT). Various factors influence the CT reconstruction result, including limited projection data, detector electronics optimization, background…
Recovery of sparse signals from compressed measurements constitutes an l0 norm minimization problem, which is unpractical to solve. A number of sparse recovery approaches have appeared in the literature, including l1 minimization…
This paper is concerned with the convergence and the error analysis for the feedback particle filter (FPF) algorithm. The FPF is a controlled interacting particle system where the control law is designed to solve the nonlinear filtering…
Imaging objects with high relative permittivity and large electrical size remains a challenging problem in the field of inverse scattering. In this work we present a phaseless inverse scattering method that can accurately image and…
Phase aberration is an inherent side effect of ultrasound imaging due to the speed of sound inhomogeneity nature of human tissues, resulting in focusing error and reduced image contrast. This work introduces a phase aberration correction…
Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired…
This paper explores the use of "generated sets" $\{ \{ k \boldsymbol{\zeta} \} : k = 1, \ldots, n \}$ for function approximation in reproducing kernel Hilbert spaces which consist of multi-dimensional functions with an absolutely convergent…
The back-propagation algorithm has long been the de-facto standard in optimizing weights and biases in neural networks, particularly in cutting-edge deep learning models. Its widespread adoption in fields like natural language processing,…