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

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...
Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the key values are 3...
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...

You might also read

Related Articles

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

Sort by
Same author

SIRT7 Prevents Intervertebral Disc Degeneration by Inhibiting the NF-κB Pathway.

Frontiers in bioscience (Landmark edition)·2026
Same author

Tumor-Derived Exosomal PDLIM1 Promotes Angiogenesis and Tumor Progression in Papillary Thyroid Carcinoma: Insights From Integrated Single-Cell Transcriptomics and Exosomal Proteomics.

Cancer management and research·2026
Same author

Low-dose decitabine increases peripheral NKT-like cell proportions in patients with chronic myeloid neoplasms.

Cancer pathogenesis and therapy·2026
Same author

Preoperative CT-based topologically distinct intratumoral heterogeneity scores for predicting intratumoral tertiary lymphoid structures and outcomes in hepatocellular carcinoma: A multicenter study.

European journal of surgical oncology : the journal of the European Society of Surgical Oncology and the British Association of Surgical Oncology·2026
Same author

The suprapubic pseudosac crochet hook suspension technique in laparoscopic repair of direct inguinal hernia: An efficient alternative in pseudosac management.

American journal of surgery·2026
Same author

MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Model.

Proceedings of the ... IEEE International Conference on Acoustics, Speech, and Signal Processing. ICASSP (Conference)·2026

Related Experiment Videos

Nonlocal regularization of inverse problems: a unified variational framework.

Zhili Yang1, Mathews Jacob

  • 1Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14623, USA. yangwendy85@gmail.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 28, 2012
PubMed
Summary
This summary is machine-generated.

We propose a new energy minimization framework for inverse problems using nonlocal regularization. This method unifies existing techniques and offers a theoretical basis for iterative nonlocal schemes, improving image reconstruction quality.

Related Experiment Videos

Area of Science:

  • Image reconstruction
  • Computational imaging
  • Optimization theory

Background:

  • Current inverse problem regularization methods often use weighted sums of pixel differences.
  • Nonlocal regularization schemes are widely used but lack theoretical justification for iterative approaches.
  • Iterative nonlocal methods can suffer from alias amplification due to nonconvex penalties.

Purpose of the Study:

  • To introduce a unifying energy minimization framework for nonlocal regularization of inverse problems.
  • To provide theoretical justification for iterative nonlocal schemes.
  • To address and overcome alias amplification in iterative nonlocal methods.

Main Methods:

  • Developed an unweighted sum of inter-patch distances functional for regularization.
  • Utilized robust distance metrics to average similar image patches and penalize dissimilar ones.
  • Adapted and introduced fast optimization algorithms, including a continuation strategy to mitigate local minima convergence.

Main Results:

  • The first iteration of the proposed algorithm aligns with current nonlocal methods, providing theoretical grounding.
  • Demonstrated that alias amplification stems from convergence to local minima of nonconvex penalties.
  • Introduced efficient algorithms applicable to a broad range of distance metrics for nonlocal optimization.

Conclusions:

  • The proposed framework unifies nonlocal regularization for inverse problems.
  • The study offers theoretical insights into iterative nonlocal methods and their limitations.
  • Novel, efficient algorithms are presented for solving nonlocal optimization problems, enhancing image reconstruction.