Related papers: Error analysis for filtered back projection recons…
We study optimal algorithms in adaptive sampling recovery of smooth functions defined on the unit $d$-cube ${\II}^d:= [0,1]^d$. The recovery error is measured in the quasi-norm $\|\cdot\|_q$ of $L_q := L_q(\II^d)$. For $B$ a subset in…
Digital aberration measurement and removal play a prominent role in computational imaging platforms aimed at achieving simple and compact optical arrangements. A recent important class of such platforms is Fourier ptychography, which is…
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement…
Proton computed tomography (pCT) is a novel imaging modality developed for patients receiving proton radiation therapy. The purpose of this work was to investigate hull-detection algorithms used for preconditioning of the large and sparse…
Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network…
Ultrasound imaging often suffers from image degradation stemming from phase aberration, which represents a significant contributing factor to the overall image degradation in ultrasound imaging. Frequency-space prediction filtering or FXPF…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
The celebrated universal approximation theorems for neural networks roughly state that any reasonable function can be arbitrarily well-approximated by a network whose parameters are appropriately chosen real numbers. This paper examines the…
Let $\mathbb{T}^d$ denote the $d$-dimensional torus. We consider the problem of optimally recovering a target function $f^*:\mathbb{T}^d\rightarrow \mathbb{C}$ from samples of its Fourier coefficients. We make classical smoothness…
The use of ray projections to reconstruct images is a common technique in medical imaging. Dealing with incomplete data is particularly important when a patient is vulnerable to potentially damaging radiation or is unable to cope with the…
The purpose of signal extrapolation is to estimate unknown signal parts from known samples. This task is especially important for error concealment in image and video communication. For obtaining a high quality reconstruction, assumptions…
A generalized cross-validation approach to estimate the reconstruction filter bandwidth in two-dimensional Filtered Backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form,…
Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP),…
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
Neural networks became the standard technique for image classification throughout the last years. They are extracting image features from a large number of images in a training phase. In a following test phase, the network is applied to the…
BV functions cannot be approximated well by piecewise constant functions, but this work will show that a good approximation is still possible with (countably) piecewise affine functions. In particular, this approximation is area-strictly…
We study the trapezoidal rule for periodic functions on uniform grids and show that the quadrature error exhibits a rich deterministic structure, beyond traditional asymptotic or statistical interpretations. Focusing on the prototype…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…