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.
Newton’s Method01:30

Newton’s Method

Newton’s Method is a powerful iterative technique for approximating the roots of real-valued, differentiable functions, particularly when analytical solutions are impractical. This approach is widely used in scientific computing, engineering, and finance, where equations may be too complex for traditional algebraic methods to handle. The method relies on an iterative process that refines an initial estimate using the function’s derivative to approach the true solution progressively.
Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
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...
Derivatives of Inverse Trigonometric Functions01:30

Derivatives of Inverse Trigonometric Functions

A ship tracking an approaching aircraft relies on geometric measurements to find out the aircraft’s position relative to the observer. By measuring the slant distance to the aircraft and the angle of elevation, the horizontal and vertical components of the distance can be obtained using trigonometric relationships. This geometric approach provides a basis for analyzing how the observed angle changes as the aircraft moves closer to the ship.To examine the mathematical behavior of the angle of...
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...

You might also read

Related Articles

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

Sort by
Same author

Bimodal PET/MRI generative reconstruction based on VAE architectures.

Physics in medicine and biology·2024
Same author

Reconstruction of vascular blood flow in a vessel from tomographic projections.

Biomedical physics & engineering express·2021
Same author

Registration of phase-contrast images in propagation-based X-ray phase tomography.

Journal of microscopy·2017
Same author

Cortical bone elasticity measured by resonant ultrasound spectroscopy is not altered by defatting and synchrotron X-ray imaging.

Journal of the mechanical behavior of biomedical materials·2017
Same author

Multiscale and multimodality computed tomography for cortical bone analysis.

Physics in medicine and biology·2016
Same author

Characterizing microcrack orientation distribution functions in osteonal bone samples.

Journal of microscopy·2016
Same journal

Denoising algorithm of Φ-OTDR systems based on adaptive fractional wavelet transform denoising.

Optics express·2026
Same journal

Millisecond photon-to-photon latency and high-speed volumetric projection system for optogenetics.

Optics express·2026
Same journal

Polarization-encoded coaxial structured light for high-precision 3D surface profilometry.

Optics express·2026
Same journal

Discrete freeform optical design based on collaborative optimization of point cloud and local normals.

Optics express·2026
Same journal

Ultrafast ghost imaging with 25 GHz speckle switching and wavelength-division multiplexing.

Optics express·2026
Same journal

Atomic vapor cells fabricated by femtosecond laser welding of standard-optical-quality glass.

Optics express·2026
See all related articles

Related Experiment Video

Updated: May 27, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Non-linear iterative phase retrieval based on Frechet derivative.

V Davidoiu1, B Sixou, M Langer

  • 1CREATIS, CNRS UMR5220, Inserm U630, INSA-Lyon, Universite Lyon 1, Universite de Lyon, F-69621 Villeurbanne Cedex, France. valentina.davidoiu@creatis.insa-lyon.fr

Optics Express
|November 24, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel non-linear iterative phase retrieval method for in-line phase tomography. The approach enhances accuracy with noisy data and is efficient for large datasets.

More Related Videos

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

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Related Experiment Videos

Last Updated: May 27, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

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

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Area of Science:

  • Optics and Photonics
  • Image Reconstruction
  • Computational Imaging

Background:

  • Linearized methods for in-line phase tomography face limitations with complex phase shifts.
  • Accurate phase retrieval is crucial for quantitative phase imaging and materials science.

Purpose of the Study:

  • To develop and evaluate a non-linear iterative phase retrieval method for in-line phase tomography.
  • To improve phase retrieval accuracy, especially in the presence of noise.
  • To create a computationally efficient method for large experimental datasets.

Main Methods:

  • Utilized a non-linear iterative approach based on the Frechet derivative of recorded intensity.
  • Employed a Landweber type iterative method with analytically calculated Frechet derivative adjoint.
  • Regularized the inverse problem using the smoothing L₂ norm of the phase gradient.

Main Results:

  • The proposed non-linear method outperforms linear methods on simulated noisy data.
  • Demonstrated robustness against high noise levels.
  • The analytical calculation enables efficient processing of large experimental image datasets.

Conclusions:

  • The non-linear iterative phase retrieval method offers superior performance compared to linear approaches.
  • The method is well-suited for processing large-scale experimental data in phase tomography.
  • This advancement has implications for quantitative phase imaging and material analysis.