Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

860
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
860
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

434
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
434
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

423
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
423
Linearization and Approximation01:26

Linearization and Approximation

196
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
196
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

5.3K
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
5.3K
Methods of Medium Optimization01:28

Methods of Medium Optimization

53
Optimizing growth media enhances microbial proliferation and maximizes product yield. Statistical experimental design methodologies provide structured and reproducible approaches, offering progressively higher levels of robustness and efficiency.The One-Factor-at-a-Time (OFAT) MethodThe One-Factor-at-a-Time (OFAT) method involves adjusting a single variable while keeping all others constant. However, it cannot detect interactions between variables, often leading to suboptimal outcomes when...
53

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

IRG1/Itaconate Inhibits Microglial Senescence-Like Transition by Modulating Mitochondrial Dynamics through Rhoa Alkylation in Subarachnoid Hemorrhage.

Aging and disease·2026
Same author

Hyperpolarization of [1-<sup>13</sup>C]Ketoisocaproate-d<sub>2</sub> by Reversible Exchange with Parahydrogen Enables Profiling of Branched-Chain-Amino-Acid Metabolism in Cellulo and in Vivo.

Advanced science (Weinheim, Baden-Wurttemberg, Germany)·2026
Same author

A vendor-neutral functional MRI acquisition protocol for multi-site studies.

Aperture neuro·2026
Same author

Examining public acceptance intentions for government digital human through expectation confirmation and technology acceptance models.

Scientific reports·2026
Same author

A high-linearity, low-power 10-mm MEMS fast steering mirror with enhanced shock robustness for space laser communications.

Optics letters·2026
Same author

Boosting photoreduction of CO<sub>2</sub><i>via</i> synergistic Cu-Ag bimetallic sites on carbon nitride.

Chemical communications (Cambridge, England)·2026
Same journal

Multi-Contrast Human Brain CEST MRI at 11.7 T: First In Vivo Demonstration.

Magnetic resonance in medicine·2026
Same journal

Suppression of Oscillation and Ghosting in RF-Spoiled Gradient-Echo-Based Dynamic Imaging.

Magnetic resonance in medicine·2026
Same journal

A Simple, Dynamic Geometric Phantom for MRI and CT Reconstruction Pipelines: Beyond Shepp-Logan.

Magnetic resonance in medicine·2026
Same journal

7T 3D-EPI PCASL With High SNR Efficiency and Robustness to Through-Plane B<sub>0</sub> Field Gradients.

Magnetic resonance in medicine·2026
Same journal

A Comparison of Tissue Property Values Estimated Using Conventional Cardiac MRF and MT-Cardiac MRF.

Magnetic resonance in medicine·2026
Same journal

Dependence of the Extra-Cellular Diffusion Coefficient on the Fractions of Neurites and Cell Bodies in Gray Matter.

Magnetic resonance in medicine·2026
See all related articles

Related Experiment Video

Updated: Apr 6, 2026

Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles
11:54

Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles

Published on: March 13, 2017

9.9K

Trajectory optimization based on the signal-to-noise ratio for spatial encoding with nonlinear encoding fields.

Kelvin J Layton1, Stefan Kroboth1, Feng Jia1

  • 1Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany.

Magnetic Resonance in Medicine
|August 6, 2015
PubMed
Summary
This summary is machine-generated.

Optimized MRI trajectories using multiple nonlinear gradient fields enhance image resolution and reduce artifacts. This computer-based approach efficiently explores complex encoding spaces for improved medical imaging.

Keywords:
higher-dimensional encodingnonlinear encodingoptimizationsignal-to-noise ratiotrajectory design

More Related Videos

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

18.4K
Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

10.4K

Related Experiment Videos

Last Updated: Apr 6, 2026

Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles
11:54

Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles

Published on: March 13, 2017

9.9K
Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

18.4K
Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

10.4K

Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Medical Physics
  • Image Reconstruction

Background:

  • Multiple nonlinear gradient fields in MRI offer potential for faster imaging, reduced artifacts, and region-specific capabilities.
  • Designing optimal spatial encoding trajectories for these complex fields is a significant challenge.

Purpose of the Study:

  • To optimize MRI encoding trajectories for multiple nonlinear gradient fields.
  • To enhance image signal-to-noise ratio (SNR) through trajectory design.

Main Methods:

  • Utilized a Bayesian formulation to link image SNR to pixel covariance, calculated recursively.
  • Employed an evolutionary algorithm to minimize pixel covariance by optimizing high-dimensional trajectory projections.
  • Incorporated receive coil profiles, intravoxel dephasing, and reconstruction regularization into the optimization.

Main Results:

  • Optimized trajectories yielded images with superior resolution and fewer artifacts compared to conventional methods, especially under high undersampling conditions.
  • Simulations and experimental tests validated the performance of the developed trajectories.
  • Effectiveness of high-dimensional projection experiments relies on precise hardware calibration.

Conclusions:

  • Computer-based optimization is crucial for navigating the vast trajectory design space enabled by multiple nonlinear fields.
  • The presented optimization framework is essential for fully leveraging the benefits of nonlinear encoding fields in MRI.
  • This approach facilitates the development of advanced MRI techniques for improved diagnostic imaging.