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Related Concept Videos

Computed Tomography01:10

Computed Tomography

Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
Imaging Studies III: Computed Tomography01:27

Imaging Studies III: Computed Tomography

DefinitionComputed Tomography (CT) of the genitourinary (GU) tract is a non-invasive imaging modality that utilizes X-rays and computer processing to generate detailed cross-sectional images of the urinary system, encompassing the kidneys, ureters, bladder, and adjacent structures such as the adrenal glands.PurposeCT scans of the GU tract serve several diagnostic and therapeutic purposes, including:Diagnosis of Urinary Tract Diseases: Detects kidney stones, tumors, cysts, and congenital...
Imaging Studies I: CT and MRI01:14

Imaging Studies I: CT and MRI

Introduction: MRI and CT scans are crucial advancements in medical imaging techniques, playing a vital role in diagnosing conditions related to the gastrointestinal (GI) system. Each scan serves distinct purposes, targets specific areas, and requires unique nursing duties.
Description of the Procedures
Computed Tomography (CT) scan:
Computed Tomography (CT) scans use X-ray technology to generate detailed images of bones, organs, and tissues. During the scan, the patient lies on a moving table...
Electron Microscope Tomography and Single-particle Reconstruction01:07

Electron Microscope Tomography and Single-particle Reconstruction

Transmission electron microscopy (TEM) can be used to determine the 3D structure of biological samples with the help of techniques such as electron microscope tomography and single-particle reconstruction. While single-particle reconstruction can examine macromolecules and macromolecular complexes in vitro conditions only, tomography permits the study of cell components or small cells in vivo.
Electron Tomography
Electron tomography can be performed either in TEM or STEM (scanning transmission...
Radiological Investigation II: MRI and Ventilation Perfusion Scan01:30

Radiological Investigation II: MRI and Ventilation Perfusion Scan

Description
Magnetic Resonance Imaging (MRI) and Ventilation Perfusion Scans are two radiological investigations that offer detailed diagnostic images of the body, particularly lung structures.
MRI
MRI uses magnetic fields and radiofrequency signals to distinguish between normal and abnormal tissues. This technology provides a more detailed diagnostic image than CT scans, enabling it to characterize pulmonary nodules, stage bronchogenic carcinoma, and evaluate inflammatory activity in...
Imaging Studies II: Positron Emission Tomography and Scintigraphy01:25

Imaging Studies II: Positron Emission Tomography and Scintigraphy

Positron Emission Tomography (PET) is a medical imaging technique that provides crucial insights into the body's physiological functions at a molecular level. It is an indispensable resource for diagnosing, staging, and monitoring various illnesses, notably cancer, neurological disorders, and cardiovascular conditions.
Fundamental Principles of PET

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Four-Dimensional CT Analysis Using Sequential 3D-3D Registration
05:05

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

Supplemental analysis on compressed sensing based interior tomography.

Hengyong Yu1, Jiansheng Yang, Ming Jiang

  • 1CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Virginia Tech, Blacksburg, VA 24061, USA. hengyong-yu@ieee.org

Physics in Medicine and Biology
|September 1, 2009
PubMed
Summary
This summary is machine-generated.

This study proves a key property for compressed sensing reconstruction: if an artifact is constant within a region of interest (ROI), it must be zero. This is crucial for accurate interior ROI reconstruction using total variation minimization.

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Area of Science:

  • Applied Mathematics
  • Signal Processing
  • Image Reconstruction

Background:

  • Compressed sensing enables signal reconstruction from limited measurements.
  • Total variation minimization is a powerful technique for image reconstruction.
  • Piecewise constant regions of interest (ROIs) are common in various imaging applications.

Purpose of the Study:

  • To rigorously prove a fundamental property used in compressed sensing reconstruction proofs.
  • To establish the mathematical basis for why constant artifacts within an ROI must be zero.
  • To support the exact reconstruction of interior ROIs in compressed sensing.

Main Methods:

  • Mathematical proof within the space of square-integrable functions.
  • Analysis of artifact image properties within a defined region of interest.
  • Leveraging principles of functional analysis.

Main Results:

  • Demonstrated that if an artifact image is constant within an ROI, that constant value must necessarily be zero.
  • Provided a formal proof for this property, previously used implicitly.
  • This property is essential for the success of total variation minimization in reconstructing interior ROIs.

Conclusions:

  • The proven property solidifies the theoretical underpinnings of compressed sensing reconstruction.
  • This work enhances the understanding of artifact behavior in signal and image processing.
  • It validates the use of total variation minimization for accurate interior ROI reconstruction in piecewise constant scenarios.