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

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

15.5K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
15.5K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

13.7K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
13.7K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

501
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....
501
Linearization and Approximation01:26

Linearization and Approximation

231
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...
231
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

7.1K
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...
7.1K
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

192
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...
192

You might also read

Related Articles

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

Sort by
Same author

Recurrent and metastatic osteoclast-like giant cell tumor of the liver revealed by FDG PET/CT.

Clinical nuclear medicine·2012
Same author

Case-control study of single nucleotide polymorphisms of PSCA and MUC1 genes with gastric cancer in a Chinese.

Asian Pacific journal of cancer prevention : APJCP·2012
Same author

Significance of Aspergillus spp. isolation from lower respiratory tract samples for the diagnosis and prognosis of invasive pulmonary aspergillosis in chronic obstructive pulmonary disease.

Chinese medical journal·2012
Same author

Stage-specific gender differences in cognitive and neuropsychiatric manifestations of vascular dementia.

American journal of Alzheimer's disease and other dementias·2012
Same author

Oncolytic virus-mediated tumor radiosensitization in mice through DNA-PKcs-specific shRNA.

Translational cancer research·2012
Same author

A label-free electrochemiluminescence aptasensor for thrombin based on novel assembly strategy of oligonucleotide and luminol functionalized gold nanoparticles.

Biosensors & bioelectronics·2012
Same journal

Mask-guided Asymmetric Contrastive and Semantic Alignment for Unsupervised Person Re-Identification.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Hyperbolic Cycle Alignment for Infrared-Visible Image Fusion.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Learning Gaze Synthesizer via 3D-eye Controlled Diffusion and Cross-domain Feature Alignment.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Underlying Semantic Diffusion for Effective and Efficient In-Context Learning.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

DiffRES: Unleashing Text-to-Image Diffusion Models for Generative Referring Expression Segmentation without Information Leakage.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Location Matters: Frequency-Spatial Dual Space Adaptation for Cross-Domain Few-Shot Segmentation.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
See all related articles

Related Experiment Video

Updated: Apr 25, 2026

Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
07:05

Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters

Published on: June 18, 2021

2.0K

A universal variational framework for sparsity-based image inpainting.

Fang Li, Tieyong Zeng

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |August 15, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces advanced numerical algorithms for image inpainting, improving restoration quality for damaged images. The new methods offer superior performance in various image restoration tasks.

    Related Experiment Videos

    Last Updated: Apr 25, 2026

    Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
    07:05

    Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters

    Published on: June 18, 2021

    2.0K

    Area of Science:

    • Computer Vision
    • Image Processing
    • Numerical Analysis

    Background:

    • Image inpainting aims to reconstruct missing or corrupted parts of an image.
    • Existing variational frameworks often require complex numerical solutions.

    Purpose of the Study:

    • To extend a universal variational framework for image inpainting with novel numerical algorithms.
    • To enhance the efficiency and effectiveness of image restoration techniques.

    Main Methods:

    • Minimization of the l(p) norm (p=0,1) of a regularization operator Φ applied to the latent image.
    • Operator splitting technique to approximate the original problem with an auxiliary variable.
    • Alternating minimization method to decompose the problem into two solvable subproblems.

    Main Results:

    • Demonstrated superior performance in diverse image inpainting tasks, including scratch/text removal and random pixel filling.
    • The framework allows flexible choices for the regularization operator Φ (e.g., gradient, wavelet, framelet).
    • The approach can be decoupled into independent denoising and linear combination steps, allowing integration of methods like BM3D filter.

    Conclusions:

    • The proposed numerical algorithms significantly improve image inpainting results.
    • The theoretical convergence of the developed algorithms is rigorously proven.
    • The flexible and efficient framework is suitable for a wide range of image restoration applications.