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Related Concept Videos

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...
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...
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...
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.
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Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Transformations of Functions III01:20

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

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Related Experiment Video

Updated: Jul 15, 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

On rate-distortion models for natural images and wavelet coding performance.

Nima Sarshar1, Xiaolin Wu

  • 1Faculty of Engineering, University of Regina, Regina, SK S4S 2A0 Canada. nima.sarshar@uregina.ca

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|May 12, 2007
PubMed
Summary

This study explains why natural images compressed with wavelet coders follow a power-law rate-distortion (RD) function, unlike traditional models. Using fractional Brownian motion (fBm), it shows both theoretical and operational RD functions exhibit this power-law behavior.

Related Experiment Videos

Last Updated: Jul 15, 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

Area of Science:

  • Image compression
  • Information theory
  • Signal processing

Background:

  • State-of-the-art wavelet coders compress natural images with power-law rate-distortion (RD) functions (D ∝ R⁻γ).
  • This deviates from the exponential RD function (D ∝ 2⁻ˣⁱᴿ) typical for bandlimited stationary processes.
  • Natural images often exhibit nonstationary behaviors, necessitating advanced source modeling.

Purpose of the Study:

  • To explain the power-law behavior of operational RD functions for natural images during wavelet compression.
  • To investigate the theoretical and operational RD characteristics of natural image compression.
  • To provide theoretical support for wavelet compression of self-similar processes.

Main Methods:

  • Modeling natural images using fractional Brownian motion (fBm) to capture nonstationary characteristics.
  • Establishing the theoretical RD function for 1-D and 2-D fBm processes.
  • Deriving the operational RD function for fBm processes using wavelet encoding and the water-filling principle.

Main Results:

  • The theoretical RD function of the fBm process demonstrates a power-law relationship (D ∝ R⁻γ).
  • The operational RD function of the wavelet-encoded fBm process also follows a power law (D ∝ R⁻γ).
  • For natural images, the exponent γ is observed to be distributed around 1.

Conclusions:

  • The power-law behavior of operational RD functions in wavelet compression of natural images is theoretically supported by the fBm model.
  • Wavelet compression is effective for self-similar processes, including natural images modeled by fBm.
  • Findings can aid in predicting the performance of rate-distortion optimized image coders.