Related papers: Statistical microlocal analysis in two-dimensional…
Radio-Stereometric-Analysis and x-ray fluoroscopy are radiological techniques that require dedicated software to process data. The accurate calibration of these software is therefore critical. The aim of this work is to produce a protocol…
Local reconstruction analysis (LRA) is a powerful and flexible technique to study images reconstructed from discrete generalized Radon transform (GRT) data, $g=\mathcal R f$. The main idea of LRA is to obtain a simple formula to accurately…
We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…
In computed tomography (CT), the relative trajectories of a sample, a detector, and a signal source are traditionally considered to be known, since they are caused by the intentional preprogrammed movement of the instrument parts. However,…
Recent research in computational imaging largely focuses on developing machine learning (ML) techniques for image reconstruction, which requires large-scale training datasets consisting of measurement data and ground-truth images. However,…
Ultrafast electron beam X-ray computed tomography produces noisy data due to short measurement times, causing reconstruction artifacts and limiting overall image quality. To counteract these issues, two self-supervised deep learning methods…
We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photo- and thermoacoustic…
A mainstream type of the state of the arts (SOTAs) based on convolutional neural network (CNN) for real image denoising contains two sub-problems, i.e., noise estimation and non-blind denoising. This paper considers real noise approximated…
Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where $[f](x):=f(x+)-f(x-) \neq 0$. Our approach is based on two main aspects--localization using appropriate…
Purpose: Many useful image quality metrics for evaluating linear image reconstruction techniques do not apply to or are difficult to interpret for non-linear image reconstruction. The vast majority of metrics employed for evaluating…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
Computed tomography (CT) has become an essential part of modern science and medicine. A CT scanner consists of an X-ray source that is spun around an object of interest. On the opposite end of the X-ray source, a detector captures X-rays…
Inverse problems arise in many applications, especially tomographic imaging. We develop a Learned Alternating Minimization Algorithm (LAMA) to solve such problems via two-block optimization by synergizing data-driven and classical…
Nowadays, modern electron microscopes deliver images at atomic scale. The precise atomic structure encodes information about material properties. Thus, an important ingredient in the image analysis is to locate the centers of the atoms…
We study noise in iterative reconstruction from discrete noisy data of a generalized Radon transform in the plane. Our approach builds on Local Reconstruction Analysis (LRA), a framework for analyzing reconstructions at the native scale. We…
In x-ray computed tomography (CT) it is generally acknowledged that reconstruction methods exploiting image sparsity allow reconstruction from a significantly reduced number of projections. The use of such reconstruction methods is…