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Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate…
Iterative methods for tomographic image reconstruction have great potential for enabling high quality imaging from low-dose projection data. The computational burden of iterative reconstruction algorithms, however, has been an impediment in…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
Computer vision tasks require processing large amounts of data to perform image classification, segmentation, and feature extraction. Optical preprocessors can potentially reduce the number of floating point operations required by computer…
Most neoplastic tumors originate from a single cell, and their evolution can be genetically traced through lineages characterized by common alterations such as small somatic mutations (SSMs), copy number alterations (CNAs), structural…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
The traditional approaches to computerized tomography (CT) depend on the samples of Radon transform at multiple angles. In optics, the real time imaging requires the reconstruction of an object by the samples of Radon transform at a single…
Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce…
Radon transform is a type of transform which is used in image processing to transfer the image into intercept-slope coordinate. Its diagonal properties made it appropriate for some applications which need processes in different degrees.…
Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained. In general, approximate solutions can be obtained by…
Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models from hundreds of thousands of (noisy) two-dimensional…
Deep learning-based reconstruction of positron emission tomography(PET) data has gained increasing attention in recent years. While these methods achieve fast reconstruction,concerns remain regarding quantitative accuracy and the presence…
Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using…
A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of…
We propose a supervised machine learning approach for boosting existing signal and image recovery methods and demonstrate its efficacy on example of image reconstruction in computed tomography. Our technique is based on a local nonlinear…
Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…
We introduce the learned simultaneous iterative reconstruction technique (SIRT) for tomographic reconstruction. The learned SIRT algorithm is a deep learning based reconstruction method combining model knowledge with a learned component.…
Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and…
Magnetic particle imaging (MPI) is a medical imaging modality of recent origin, and it exploits the nonlinear magnetization phenomenon to recover the spatially dependent concentration of the nanoparticles. Currently, image reconstruction in…
Low-dose Proton Computed Tomography (pCT) is an evolving imaging modality that is used in proton therapy planning which addresses the range uncertainty problem. The goal of pCT is generating a 3D map of Relative Stopping Power (RSP)…