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

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

4.1K
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...
4.1K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

359
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....
359
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

347
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,...
347
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

9.1K
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...
9.1K
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

59
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...
59
Linearization and Approximation01:26

Linearization and Approximation

20
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...
20

You might also read

Related Articles

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

Sort by
Same author

Fourier Synchrosqueezed Transform for Shear Wave Speed Estimation in Crawling Wave Sonoelastography Approach.

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

Nonlinearity parameter estimation method from fundamental band signal depletion in pulse-echo using a dual-energy model.

The Journal of the Acoustical Society of America·2025
Same author

Proposal and comparison of quality measures in Crawling Waves Sonoelastography.

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

Spatially Weighted Fidelity and Regularization Terms for Attenuation Imaging.

IEEE transactions on ultrasonics, ferroelectrics, and frequency control·2025
Same author

Enhancing ultrasonic attenuation images through multi-frequency coupling with total nuclear variation.

The Journal of the Acoustical Society of America·2024
Same author

Sedation and Analgesia for Toxic Epidermal Necrolysis in the Intensive Care Unit: Few Certainties, Many Questions Ahead.

Journal of personalized medicine·2023

Related Experiment Video

Updated: Jan 18, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.0K

Regularized Joint Estimator of the Nonlinearity Parameter and Attenuation Coefficient Using a Nonlinear Least-Squares

Sebastian Merino1, Adriana Romero1, Roberto Lavarello1

  • 1Pontificia Universidad Católica del Perú, San Miguel, Lima, Peru.

Ultrasonic Imaging
|September 10, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new method, Gauss-Newton with total variation regularization (GNTV), to accurately estimate the acoustic nonlinearity parameter (B/A) and attenuation coefficient (AC). The GNTV method improves robustness and diagnostic capabilities in ultrasound imaging.

Keywords:
Gauss-Newton algorithmattenuation coefficientfrequency compoundingnonlinearity parametertotal variation regularization

More Related Videos

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
15:06

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

13.4K
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.1K

Related Experiment Videos

Last Updated: Jan 18, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.0K
Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
15:06

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

13.4K
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.1K

Area of Science:

  • Medical Imaging
  • Acoustics
  • Biophysics

Background:

  • The acoustic nonlinearity parameter (B/A) is crucial for enhancing diagnostic capabilities in ultrasonography and quantitative ultrasound for tissues and diseases.
  • Existing dual-energy models for B/A estimation rely on the depletion method, which requires prior knowledge of the attenuation coefficient (AC).
  • The simultaneous estimation of B/A and AC using the Gauss-Newton Levenberg-Marquardt (GNLM) algorithm is sensitive to initial guess values, limiting its robustness.

Purpose of the Study:

  • To develop a more robust method for simultaneously estimating the acoustic nonlinearity parameter (B/A) and attenuation coefficient (AC).
  • To improve the accuracy and reliability of quantitative ultrasound techniques for tissue and disease characterization.
  • To overcome the limitations of the GNLM method by enhancing its sensitivity to initial guess values.

Main Methods:

  • A novel approach combining the Gauss-Newton method with total variation regularization (GNTV) was developed for joint B/A and AC estimation.
  • The nonlinear model was expanded for pixel-wise parametric image analysis, moving beyond block-wise approaches.
  • Compounding data from multiple tone-burst transmissions at different center frequencies was utilized to enhance estimation accuracy.

Main Results:

  • The GNTV method demonstrated improved robustness compared to the GNLM approach.
  • Accurate estimation of B/A values was achieved in both uniform and nonuniform experimental phantoms, with a mean relative error below 18%.
  • Optimal B/A reconstruction performance was observed in sample media with a constant Gol'dberg number.

Conclusions:

  • The integration of total variation regularization and multi-frequency data significantly enhances the robustness of B/A and AC estimation.
  • The GNTV method offers a more reliable tool for quantitative ultrasound, improving diagnostic capabilities in medical imaging.
  • Further research can explore the application of GNTV in diverse biological tissues and disease states.