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

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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.
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

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...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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, the...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Linearization and Approximation01:26

Linearization and Approximation

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...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...

You might also read

Related Articles

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

Sort by
Same author

TRAM-UNet: Transformer and Region Attention Module based U-Net for Breast Ultrasound Image Segmentation.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2025
Same author

Study about deep Bifurcation learning model for separation of ultrasound echo signals and tissue acoustic properties.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2025
Same author

Segmentation with Speckle Reduction and Superresolution by Deep Leaning for Human Ultrasonic Echo Image.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2021
Same author

Spatially variant regularization for tissue strain measurement and shear modulus reconstruction.

Journal of medical ultrasonics (2001)·2016
Same author

Shear modulus reconstruction by ultrasonically measured strain ratio.

Journal of medical ultrasonics (2001)·2016
Same author

Determining if the relative shear modulus or the inverse of the relative shear modulus should be imaged using axial strain ratios on agar phantoms.

Ultrasound in medicine & biology·2010

Related Experiment Video

Updated: Jun 13, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Determination of lateral modulation apodization functions using a regularized, weighted least squares estimation.

Chikayoshi Sumi1

  • 1Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University, 7-1 Kioi-Cho, Chiyoda-Ku, Tokyo 102-8554, Japan. c-sumi@sophia.ac.jp

International Journal of Biomedical Imaging
|May 15, 2010
PubMed
Summary

This study introduces a regularized, weighted minimum-norm least squares (WMNLSs) method for optimizing apodization functions in lateral cosine modulation (LCM) ultrasound imaging. This technique improves spatial resolution and displacement measurements in tissues.

More Related Videos

Pupillometry to Assess Auditory Sensation in Guinea Pigs
09:25

Pupillometry to Assess Auditory Sensation in Guinea Pigs

Published on: January 6, 2023

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Related Experiment Videos

Last Updated: Jun 13, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Pupillometry to Assess Auditory Sensation in Guinea Pigs
09:25

Pupillometry to Assess Auditory Sensation in Guinea Pigs

Published on: January 6, 2023

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Area of Science:

  • Ultrasound imaging
  • Biomedical engineering
  • Signal processing

Background:

  • Lateral cosine modulation (LCM) is a method for advanced ultrasound (US) echo imaging and tissue displacement vector/strain tensor measurements.
  • High lateral and axial spatial resolution are crucial for accurate US echo imaging.
  • Precise measurement of lateral and axial tissue displacements is essential for various biomedical applications.

Purpose of the Study:

  • To present a regularized, weighted minimum-norm least squares (WMNLSs) estimation method.
  • To optimize the determination of apodization functions for the LCM method.
  • To enhance the performance of LCM in ultrasound imaging and displacement measurements.

Main Methods:

  • Development and application of the regularized WMNLSs estimation method.
  • Simulation of Gaussian-type point spread functions (PSFs) with lateral modulation.
  • Comparison with Fraunhofer approximation and singular-value decomposition (SVD) methods.

Main Results:

  • The regularized WMNLSs estimation provides better approximations of designed PSFs compared to Fraunhofer and SVD methods.
  • Achieved wider lateral bandwidths in simulated PSFs.
  • Demonstrated the effectiveness of the WMNLSs method for apodization function determination.

Conclusions:

  • The regularized WMNLSs estimation is a valuable tool for optimizing apodization functions in LCM-based ultrasound applications.
  • This method enhances spatial resolution and accuracy in both echo imaging and displacement measurements.
  • The findings support the advancement of next-generation ultrasound technologies.