Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Methods of Medium Optimization

Methods of Medium Optimization

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...

Optimization Problems

Optimization Problems

Optimization problems often involve identifying maximum or minimum values under specific constraints. A well-known example is determining the longest horizontal pipe that can be moved around a right-angled corner, where a 3-meter-wide hallway meets a 2-meter-wide hallway. This scenario, common in architectural design and industrial transport, can be understood conceptually through geometric and trigonometric reasoning.To visualize the problem, consider the pipe as a straight line that touches...

Extraction: Partition and Distribution Coefficients

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...

Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

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 sampling...

Extraction: Advanced Methods

Extraction: Advanced Methods

Metal ions can be separated from one another by complexation with organic ligands–the chelating agent– to form uncharged chelates. Here, the chelating agent must contain hydrophobic groups and behave as a weak acid, losing a proton to bind with the metal. Since most organic ligands used in this process are insoluble or undergo oxidation in the aqueous phase, the chelating agent is initially added to the organic phase and extracted into the aqueous phase. The metal-ligand complex is formed in...

You might also read

Related Articles

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

Sort by

Same author

A benchmarking framework and dataset for learning to defer in human-AI decision-making.

Scientific data·2025

Same author

A Measure of Synergy Based on Union Information.

Entropy (Basel, Switzerland)·2024

Same author

Orders between Channels and Implications for Partial Information Decomposition.

Entropy (Basel, Switzerland)·2023

Same author

Nonnegative Blind Source Separation for Ill-Conditioned Mixtures via John Ellipsoid.

IEEE transactions on neural networks and learning systems·2020

Same author

A classification-based approach to semi-supervised clustering with pairwise constraints.

Neural networks : the official journal of the International Neural Network Society·2020

Same author

Nonlocal Sparse Tensor Factorization for Semiblind Hyperspectral and Multispectral Image Fusion.

IEEE transactions on cybernetics·2019

Search research articles

Related Experiment Video

Updated: Jun 14, 2026

Whole-cell Super-Resolution Imaging via DNA-PAINT on a Spinning Disk Confocal with Optical Photon Reassignment

Whole-cell Super-Resolution Imaging via DNA-PAINT on a Spinning Disk Confocal with Optical Photon Reassignment

Published on: January 6, 2026

Fast image recovery using variable splitting and constrained optimization.

Manya V Afonso¹, José M Bioucas-Dias, Mário A T Figueiredo

¹Instituto de Telecomunicações and the Department of Electrical and Computer Engineering, Instituto Superior Técnico, 1049-001 Lisboa, Portugal. mafonso@lx.it.pt

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|April 10, 2010

Summary

A new fast algorithm accelerates image restoration and reconstruction by employing variable splitting and an augmented Lagrangian method. This approach proves faster than existing state-of-the-art techniques for complex image processing tasks.

More Related Videos

3D Ultrasound Imaging: Fast and Cost-effective Morphometry of Musculoskeletal Tissue

3D Ultrasound Imaging: Fast and Cost-effective Morphometry of Musculoskeletal Tissue

Published on: November 27, 2017

Related Experiment Videos

Last Updated: Jun 14, 2026

Whole-cell Super-Resolution Imaging via DNA-PAINT on a Spinning Disk Confocal with Optical Photon Reassignment

Whole-cell Super-Resolution Imaging via DNA-PAINT on a Spinning Disk Confocal with Optical Photon Reassignment

Published on: January 6, 2026

3D Ultrasound Imaging: Fast and Cost-effective Morphometry of Musculoskeletal Tissue

3D Ultrasound Imaging: Fast and Cost-effective Morphometry of Musculoskeletal Tissue

Published on: November 27, 2017

Area of Science:

Image processing
Computational mathematics
Optimization

Background:

Image restoration and reconstruction are crucial in various scientific fields.
Standard formulations often involve complex optimization problems with nonsmooth regularizers.
Existing methods can be computationally intensive, limiting their application.

Purpose of the Study:

To develop a novel, fast algorithm for image restoration and reconstruction.
To address unconstrained optimization problems with L2 data-fidelity and nonsmooth regularization.
To provide a computationally efficient alternative to current state-of-the-art methods.

Main Methods:

Utilized variable splitting to transform the problem into a constrained optimization formulation.
Applied an augmented Lagrangian method to solve the constrained problem.
The algorithm is an instance of the alternating direction method of multipliers (ADMM), with proven convergence.

Main Results:

The proposed algorithm demonstrates significant speed improvements over existing methods.
Successfully applied to benchmark image restoration and reconstruction problems.
Convergence of the algorithm is theoretically guaranteed.

Conclusions:

The new algorithm offers a faster and efficient solution for image restoration and reconstruction.
Variable splitting combined with augmented Lagrangian methods is effective for this class of problems.
This advancement has the potential to enhance various image processing applications.