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

Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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...
Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
Lagrange Multipliers: Problem Solving01:30

Lagrange Multipliers: Problem Solving

A silo with a cylindrical base, flat bottom, and hemispherical roof is a common design in agricultural and industrial storage due to its structural efficiency and ease of construction. Optimizing its dimensions to maximize storage capacity for a given amount of material—i.e., a fixed surface area—is a classic problem in applied calculus and engineering design. The key parameters are the radius r of the base and the height h of the cylindrical section.The total volume of the silo is obtained by...
Reconstruction of Signal using Interpolation01:10

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...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
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...

You might also read

Related Articles

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

Sort by
Same author

Nucleon mass from a covariant three-quark Faddeev equation.

Physical review letters·2010
Same author

Free-space optical collinear crossover interconnects.

Applied optics·2010
Same author

Fast digital optical multiplication using an array of binary symmetric logic counters.

Applied optics·2010
Same author

Optical higher-order symbolic recognition.

Applied optics·2010
Same author

Optical parallel register transfer microoperations using holographic symbolic substitutions.

Applied optics·2010
Same author

Liquid crystal TV-based white light optical tracking novelty filter.

Applied optics·2010
Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026
Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026
Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026
Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026
Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026
Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026
See all related articles

Related Experiment Video

Updated: Jun 14, 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

Superresolving image restoration using linear programming.

R Mammone, G Eichmann

    Applied Optics
    |April 8, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Superresolving image restoration (SIR) can now achieve finer detail, resolving sources one-tenth of the Rayleigh distance apart. This advancement is crucial for noisy images in fields like astronomy and medical diagnostics.

    More Related Videos

    Whole-cell Super-Resolution Imaging via DNA-PAINT on a Spinning Disk Confocal with Optical Photon Reassignment
    07:12

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

    Published on: January 6, 2026

    Related Experiment Videos

    Last Updated: Jun 14, 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

    Whole-cell Super-Resolution Imaging via DNA-PAINT on a Spinning Disk Confocal with Optical Photon Reassignment
    07:12

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

    Published on: January 6, 2026

    Area of Science:

    • Optics and Image Processing
    • Signal Processing

    Background:

    • Superresolving image restoration (SIR) aims to enhance image resolution beyond optical limits.
    • Existing SIR algorithms struggle with resolving closely spaced point sources, especially in noisy conditions.

    Purpose of the Study:

    • To demonstrate the feasibility of SIR for resolving two-point sources spaced at one-tenth of the Rayleigh distance.
    • To develop and validate methods for SIR in the presence of significant noise.

    Main Methods:

    • Utilized optimal data fitting techniques based on linear programming.
    • For noisy images, employed a combination of linear eigenvalue prefiltering and optimal data fitting.
    • Specifically designed techniques for impulsive-type images.

    Main Results:

    • Achieved SIR for two-point noncoherent sources spaced one-tenth of the Rayleigh distance apart.
    • Demonstrated successful SIR for diffraction-limited images of two-point sources (half Rayleigh distance) with significant noise.
    • Validated the effectiveness of linear programming and prefiltering for noisy SIR.

    Conclusions:

    • The developed methods significantly advance SIR capabilities, enabling finer resolution than previously possible.
    • These techniques have broad applicability in fields requiring high-resolution image deconvolution from noisy data.
    • The study highlights the potential of optimal data fitting and prefiltering for overcoming limitations in image restoration.