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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

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...
Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
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...
Discrete Fourier Transform01:15

Discrete Fourier Transform

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...
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...
Properties of DTFT II01:24

Properties of DTFT II

In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
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Related Experiment Video

Updated: May 30, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Efficient fringe image enhancement based on dual-tree complex wavelet transform.

Tai-Chiu Hsung1, Daniel Pak-Kong Lun, William W L Ng

  • 1Centre for Signal Processing, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, China.

Applied Optics
|July 21, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel image enhancement algorithm using the oriented two-dimensional dual-tree complex wavelet transform (DT-CWT) to denoise fringe images for optical phase shift profilometry (PSP). The method significantly improves the signal-to-noise ratio (SNR) for more accurate 3D modeling.

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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

Related Experiment Videos

Last Updated: May 30, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

Area of Science:

  • Optics and Photonics
  • Image Processing
  • Computer Vision

Background:

  • Optical Phase Shift Profilometry (PSP) enables real-time 3D modeling via fringe pattern projection and image capture.
  • Image noise in real-world PSP applications degrades the quality of reconstructed 3D models.

Purpose of the Study:

  • To develop a new image enhancement algorithm for denoising fringe images in optical PSP.
  • To improve the accuracy of 3D model reconstruction from noisy fringe data.

Main Methods:

  • Utilized the oriented two-dimensional dual-tree complex wavelet transform (DT-CWT) for sparse representation of fringe images.
  • Implemented a novel iterative regularization procedure with an enhanced initial guess for image denoising.
  • Applied the algorithm to enhance fringe images captured during optical PSP.

Main Results:

  • The proposed DT-CWT based algorithm achieved an average signal-to-noise ratio (SNR) improvement of 7.2 dB over traditional methods.
  • 3D model reconstruction accuracy improved by 6 to 20 dB in SNR when using the enhanced fringe images.

Conclusions:

  • The novel DT-CWT based enhancement algorithm effectively denoises fringe images in optical PSP.
  • This method significantly boosts the accuracy of 3D reconstruction, especially in the presence of image noise.