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

Distance Corrections01:15

Distance Corrections

18
To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
18
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

1.2K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
1.2K
Second Order systems II01:18

Second Order systems II

62
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
62
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

53
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,...
53
Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

233
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
233
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

195
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
195

You might also read

Related Articles

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

Sort by
Same author

PhotIQA: A photoacoustic image data set with image quality ratings.

Scientific data·2026
Same author

Real-time CBCT reconstructions using Krylov solvers in repeated scanning procedures.

Physics in medicine and biology·2026
Same author

Hierarchical Multiscale Structure-Function Coupling for Brain Connectome Integration.

ArXiv·2026
Same author

Celcomen: spatial causal disentanglement for single-cell and tissue perturbation modeling.

Nature communications·2026
Same author

Computational 3D multispectral fluorescence lifetime microscopy.

Optics express·2026
Same author

Neural Fields for Highly Accelerated 2D Cine Phase Contrast MRI.

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

Subspace Method of Moments for <i>Ab Initio</i> 3-D Single Particle Cryo-EM Reconstruction.

SIAM journal on imaging sciences·2026
Same journal

Smooth optimization using global and local low-rank regularizers.

SIAM journal on imaging sciences·2026
Same journal

A Common Lines Approach for Ab Initio Modeling of Molecules with Tetrahedral and Octahedral Symmetry.

SIAM journal on imaging sciences·2025
Same journal

A Wasserstein-Type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis.

SIAM journal on imaging sciences·2025
Same journal

Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit.

SIAM journal on imaging sciences·2024
Same journal

A Majorization-Minimization Algorithm for Neuroimage Registration.

SIAM journal on imaging sciences·2024
See all related articles

Related Experiment Video

Updated: May 7, 2025

Bringing the Visible Universe into Focus with Robo-AO
10:35

Bringing the Visible Universe into Focus with Robo-AO

Published on: February 12, 2013

19.3K

On Learned Operator Correction in Inverse Problems.

Sebastian Lunz1, Andreas Hauptmann2, Tanja Tarvainen3

  • 1University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Cambridge.

SIAM Journal on Imaging Sciences
|January 1, 2025
PubMed
Summary
This summary is machine-generated.

This study explores learning data-driven model corrections for inverse problems, proposing a forward-adjoint correction method. This approach enables regularized reconstructions within variational frameworks, showing convergence to correct operator solutions.

Keywords:
47A5265F2265K1094A08deep learninginverse problemsmodel correctionoperator learningphotoacoustic tomographyvariational methods

More Related Videos

Operation of the Collaborative Composite Manufacturing CCM System
10:09

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

6.5K
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

8.6K

Related Experiment Videos

Last Updated: May 7, 2025

Bringing the Visible Universe into Focus with Robo-AO
10:35

Bringing the Visible Universe into Focus with Robo-AO

Published on: February 12, 2013

19.3K
Operation of the Collaborative Composite Manufacturing CCM System
10:09

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

6.5K
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

8.6K

Area of Science:

  • Applied Mathematics
  • Image Reconstruction
  • Computational Imaging

Background:

  • Inverse problems are central to many scientific and engineering fields.
  • Variational methods are widely used for regularized solutions in inverse problems.
  • Explicitly learning model errors offers a path to improved reconstruction accuracy.

Purpose of the Study:

  • To investigate the feasibility of learning data-driven explicit model corrections for inverse problems.
  • To develop a variational framework incorporating learned model corrections for regularized reconstructions.
  • To analyze the convergence properties of solutions obtained with learned corrections.

Main Methods:

  • A novel forward-adjoint correction is proposed, acting in both data and solution spaces.
  • Conditions for convergence of variational solutions with learned corrections to true solutions are derived.
  • The method is applied to limited view photoacoustic tomography.

Main Results:

  • The proposed forward-adjoint correction effectively addresses model deficiencies in inverse problems.
  • Convergence of the learned correction approach to solutions with the correct operator is demonstrated under specific conditions.
  • The method shows competitive performance compared to the Bayesian approximation error method in photoacoustic tomography.

Conclusions:

  • Learning data-driven model corrections is a viable strategy for enhancing inverse problem solutions.
  • The proposed forward-adjoint correction offers a robust framework for regularized reconstructions.
  • This work advances the state-of-the-art in model-based iterative reconstruction techniques.