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Related Concept Videos

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.
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Linear Approximation in Time Domain01:21

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For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Application of Linearization and Approximation01:29

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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...
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Related Experiment Video

Updated: Jul 7, 2026

Characterization of Anisotropic Leaky Mode Modulators for Holovideo
09:36

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

Published on: March 19, 2016

In-loop atom modulus quantization for matching pursuit and its application to video coding.

Christophe De Vleeschouwer1, Avideh Zakhor

  • 1Lab. de Telecommun., Univ. Catholique de Louvain, Belgium. devlees@tele.ucl.ac.be

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 2, 2008
PubMed
Summary
This summary is machine-generated.

This study optimizes matching pursuit (MP) coefficient quantization for video coding. An improved method enhances coding efficiency by carefully selecting atoms and quantizing their modulus, achieving significant bitrate improvements.

Related Experiment Videos

Last Updated: Jul 7, 2026

Characterization of Anisotropic Leaky Mode Modulators for Holovideo
09:36

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

Published on: March 19, 2016

Area of Science:

  • Signal Processing
  • Information Theory
  • Video Compression

Background:

  • Matching Pursuit (MP) is a signal decomposition algorithm.
  • Quantization of MP coefficients impacts coding efficiency.
  • Previous methods did not fully account for quantization error re-injection.

Purpose of the Study:

  • To analytically study the selection and modulus quantization of MP coefficients.
  • To achieve an optimal rate-distortion trade-off in MP-based coding.
  • To investigate the impact of in-loop quantization on quantizer design.

Main Methods:

  • Developing a quality-dependent threshold for atom selection.
  • Defining a modulus quantizer based on the selection threshold.
  • Analyzing quantization error re-injection within the MP atom computation loop.
  • Evaluating uniform and nonuniform quantization schemes.

Main Results:

  • Optimal rate-distortion trade-off achieved through threshold-based atom selection and modulus quantization.
  • In-loop quantization improves coding performance and influences optimal quantizer design.
  • Significant coding efficiency gains demonstrated in video coding applications.
  • Proposed nonuniform quantization yields 0.5-2 dB improvement at high bitrates.

Conclusions:

  • Precise understanding of atom selection and quantization is crucial for coding efficiency.
  • In-loop quantization offers benefits for both uniform and nonuniform schemes.
  • The proposed method provides superior performance in video compression.