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Related Concept Videos

Discrete Fourier Transform01:15

Discrete Fourier Transform

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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Fast Fourier Transform01:10

Fast Fourier Transform

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The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
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Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

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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...
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Discrete-time Fourier transform01:26

Discrete-time Fourier transform

343
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

280
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
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Deconvolution01:20

Deconvolution

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Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
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FEUSNet: Fourier Embedded U-Shaped Network for Image Denoising.

Xi Li1,2, Jingwei Han1, Quan Yuan2

  • 1School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.

Entropy (Basel, Switzerland)
|October 28, 2023
PubMed
Summary
This summary is machine-generated.

Fourier embedded U-shaped networks (FEUSNet) reduce image noise by analyzing Fourier coefficients. This novel deep learning approach effectively suppresses noise while preserving crucial image details.

Keywords:
Fourier coefficientsdeep convolution neural networkend-to-end denoising network mechanism

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Area of Science:

  • Computer Vision
  • Deep Learning
  • Image Processing

Background:

  • Deep convolution neural networks excel in computer vision tasks due to their learning capacity.
  • Image denoising is crucial for enhancing visual data quality.

Purpose of the Study:

  • To propose a novel end-to-end denoising network, the Fourier embedded U-shaped network (FEUSNet).
  • To leverage Fourier transform characteristics for improved noise reduction and detail preservation.

Main Methods:

  • Analyzing amplitude and phase spectrum of Fourier coefficients to distinguish image features from noise.
  • Embedding a learned Fourier feature prior module into a U-shaped network architecture.
  • Conducting ablation studies on network components and loss functions.

Main Results:

  • FEUSNet effectively suppresses noise while preserving multi-scale image structures.
  • Experimental results demonstrate superior performance compared to state-of-the-art denoising methods.
  • Ablation studies validate the effectiveness of the Fourier feature learning and network design.

Conclusions:

  • The proposed FEUSNet offers an effective approach for image denoising.
  • Integrating Fourier features enhances the network's ability to preserve fine details.
  • FEUSNet shows significant potential for advancing image denoising techniques.