Related papers: Error analysis for filtered back projection recons…
Let $X_n = \{x^j\}_{j=1}^n$ be a set of $n$ points in the $d$-cube $[0,1]^d$, and $\Phi_n = \{\varphi_j\}_{j =1}^n$ a family of $n$ functions on $[0,1]^d$. We consider the approximate recovery functions $f$ on $[0,1]^d$ from the sampled…
Sampling-based alpha matting methods have traditionally followed the compositing equation to estimate the alpha value at a pixel from a pair of foreground (F) and background (B) samples. The (F,B) pair that produces the least reconstruction…
Artificial vision models are often evaluated against the human visual cortex by measuring how accurately their internal representations predict brain responses. However, prediction accuracy alone does not indicate which dimensions of the…
Fluorescence molecular tomography (FMT) is an emerging powerful tool for biomedical research. There are two factors that influence FMT reconstruction most effectively. The first one is the regularization techniques. Traditional methods such…
English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods…
Deep neural networks with rectified linear units (ReLU) are getting more and more popular due to their universal representation power and successful applications. Some theoretical progress regarding the approximation power of deep ReLU…
In recent years, machine learning (ML) based reconstruction has been widely investigated and employed in cardiac magnetic resonance (CMR) imaging. ML-based reconstructions can deliver clinically acceptable image quality under substantially…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
In the past few years, significant advancements were made in reconstruction of observed natural images from fMRI brain recordings using deep-learning tools. Here, for the first time, we show that dense 3D depth maps of observed 2D natural…
Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…
Upcoming ground-based cosmic microwave background experiments will provide CMB maps with high sensitivity and resolution that can be used for high fidelity lensing reconstruction. However, the sky coverage will be incomplete and the noise…
This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective…
A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…
This paper concerns iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with the Total Variation (TV) penalty. We propose a very fast iterative algorithm to solve this problem. The algorithm…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Electron tomographic reconstruction is a method for obtaining a three-dimensional image of a specimen with a series of two dimensional microscope images taken from different viewing angles. Filtered backprojection, one of the most popular…
In this study, we present a large-scale earth surface reconstruction pipeline for linear-array charge-coupled device (CCD) satellite imagery. While mainstream satellite image-based reconstruction approaches perform exceptionally well, the…
A CT image can be well reconstructed when the sampling rate of the sinogram satisfies the Nyquist criteria and the sampled signal is noise-free. However, in practice, the sinogram is usually contaminated by noise, which degrades the quality…
While model-based reconstruction methods have been successfully applied to flat-panel cone-beam CT (FP-CBCT) systems, typical implementations ignore both spatial correlations in the projection data as well as system blurs due to the…
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…