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The recent application of Fourier Based Iterative Reconstruction Method (FIRM) has made it possible to achieve high-quality 2D images from a fan beam Computed Tomography (CT) scan with a limited number of projections in a fast manner. The…
This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…
Computed tomography (CT) is a widely used medical imaging technique to scan internal structures of a body, typically involving collimation and mechanical rotation. Compton scatter tomography (CST) presents an interesting alternative to…
An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior…
Many clinical applications depend critically on the accurate differentiation and classification of different types of materials in patient anatomy. This work introduces a unified framework for accurate nonlinear material decomposition and…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
The cone beam computed tomography (CBCT) technique was first inserted in dental imaging 15 years ago. Due to this technique 3D imaging in dentistry has been excessively changed. The purpose beyond using CBCT instead of computed tomography…
Cone-beam CT (CBCT) is installed in the treatment room to facilitate online clinical applications, including image guidance in radiation and surgery. Half-fan and short-can are the commonly used modes in clinical applications to expand the…
Three-dimensional (3D) reconstruction of head Computed Tomography (CT) images elucidates the intricate spatial relationships of tissue structures, thereby assisting in accurate diagnosis. Nonetheless, securing an optimal head CT scan…
Proton computed tomography (pCT) is an image modality that will improve treatment planning for patients receiving proton radiation therapy compared with the current treatment techniques, which are based on X-ray CT. Reconstruction of a pCT…
Recently, a number of approaches to low-dose computed tomography (CT) have been developed and deployed in commercialized CT scanners. Tube current reduction is perhaps the most actively explored technology with advanced image reconstruction…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both sampling models lack flexibility for various circumstances in…
A new concept, decomposition-unstable (DU) variety of a parametric polynomial system, is introduced in this paper and the stabilities of several triangular decomposition methods, such as characteristic set decomposition, relatively…
Computed tomography (CT) involves a patient's exposure to ionizing radiation. To reduce the radiation dose, we can either lower the X-ray photon count or down-sample projection views. However, either of the ways often compromises image…
Cone-beam computed tomography (CBCT) is widely used for image-guided radiotherapy (IGRT). It provides real time visualization at low cost and dose. However, photon scattering and beam hindrance cause artifacts in CBCT. These include…
The concept of comprehensive triangular decomposition (CTD) was first introduced by Chen et al. in their CASC'2007 paper and could be viewed as an analogue of comprehensive Grobner systems for parametric polynomial systems. The first…
We provide a fast and accurate scatter artifacts correction algorithm for cone beam CT (CBCT) imaging. The method starts with an estimation of coarse scatter profile for a set of CBCT images. A total-variation denoising algorithm designed…
Nowadays, the field computed tomography (CT) encompasses a large variety of settings, ranging from nanoscale to meter-sized objects imaged by different kinds of radiation in various acquisition modes. This experimental diversity challenges…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…