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

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...
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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.
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...

You might also read

Related Articles

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

Sort by
Same author

Lighting effects on optimal facial regions for remote heart rate measurement.

NPJ cardiovascular health·2026
Same author

EventTracer: Fast Path Tracing-Based Event Stream Rendering.

IEEE transactions on visualization and computer graphics·2026
Same author

Seasonal Divergence between Microbiomes on Microplastics and Natural Particles Increases with Rising Water Temperatures in Urban Rivers.

Environmental science & technology·2026
Same author

Roadmap of remote photoplethysmography from heart rate measurement toward clinical translation.

NPJ digital medicine·2026
Same author

Dark-EvGS: Event Camera as an Eye for Radiance Field in the Dark.

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

Adaptive physiology-informed correction for reliable remote photoplethysmography heart-rate monitoring.

NPJ digital medicine·2026

Related Experiment Video

Updated: Jun 13, 2026

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline
09:27

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline

Published on: January 30, 2019

Image Restoration Learning via Noisy Supervision in Fourier Domain.

Haosen Liu, Jiahao Liu, Shan Tan

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |June 11, 2026
    PubMed
    Summary

    This study introduces a new deep learning approach for image restoration using noisy data. By utilizing the Fourier domain, it effectively handles complex noise patterns, improving image quality in various applications.

    Related Experiment Videos

    Last Updated: Jun 13, 2026

    Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline
    09:27

    Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline

    Published on: January 30, 2019

    Area of Science:

    • Computer Vision
    • Signal Processing
    • Machine Learning

    Background:

    • Noisy supervision trains models with corrupted data, reducing collection burdens but facing challenges with correlated noise and limited pixel-wise supervision.
    • Real-world imaging (low-light, remote sensing) often involves spatially correlated noise, hindering current deep learning restoration methods.
    • Existing pixel-wise loss functions provide insufficient guidance for complex image restoration tasks like deblurring and super-resolution.

    Purpose of the Study:

    • To develop novel deep learning frameworks for image restoration that effectively handle noisy supervision and complex noise patterns.
    • To overcome the limitations of existing methods in addressing long-range correlated noise and weak supervision signals.
    • To enhance the practical applicability of deep learning for image restoration in challenging real-world scenarios.

    Main Methods:

    • Leveraging the Fourier domain for image restoration, exploiting noise sparsity and global information captured by Fourier coefficients.
    • Proving the convergence of Fourier coefficients of various noise types to a Gaussian distribution.
    • Establishing statistical equivalence between learning with clean and noisy targets in the Fourier domain.
    • Developing a weakly supervised framework for image restoration with noisy targets.
    • Constructing a fully unsupervised denoising method specifically for stripe-wise noise.

    Main Results:

    • The proposed methods demonstrate superior performance in quantitative metrics and perceptual quality compared to existing approaches.
    • Effective handling of noise with long-range correlations, a common issue in real-world imaging.
    • Stronger supervision signals derived from the Fourier domain enhance image restoration accuracy.
    • Successful application in both weakly supervised and fully unsupervised image denoising scenarios.

    Conclusions:

    • The Fourier domain offers a powerful tool for addressing limitations in noisy supervision for deep learning-based image restoration.
    • The developed frameworks provide effective solutions for handling complex noise and improving image quality in practical applications.
    • This research advances the field of image restoration by enabling more robust and efficient deep learning models under noisy conditions.