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Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
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.
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

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...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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...
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...

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Related Experiment Videos

Sparse approximation using M-term pursuit and application in image and video coding.

Adel Rahmoune1, Pierre Vandergheynst, Pascal Frossard

  • 1Signal Processing Laboratory (LTS2/LTS4), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland. adel.rahmoune@gmail.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|December 29, 2011
PubMed
Summary
This summary is machine-generated.

A new M-term pursuit (MTP) algorithm offers efficient sparse approximation by partitioning dictionaries and selecting multiple atoms per iteration. MTP achieves competitive performance with reduced computational complexity for signal processing applications.

Related Experiment Videos

Area of Science:

  • Signal Processing
  • Data Compression
  • Applied Mathematics

Background:

  • Sparse approximation is crucial for signal representation.
  • Existing methods like Matching Pursuit (MP) can be computationally intensive.
  • Redundant dictionaries offer flexibility but pose challenges for efficient decomposition.

Purpose of the Study:

  • Introduce the novel M-term pursuit (MTP) algorithm for sparse approximation.
  • Develop an adaptive signal representation method.
  • Evaluate MTP's performance and complexity against existing algorithms.

Main Methods:

  • Partitioning the dictionary into L quasi-disjoint subdictionaries.
  • Iteratively computing k-term signal approximations.
  • Selecting M atoms (M ≤ L) per iteration via thresholding.

Main Results:

  • MTP achieves competitive performance compared to the Matching Pursuit (MP) algorithm.
  • Significant reduction in computational complexity due to batch atom selection.
  • Demonstrated effectiveness in image and video compression applications.

Conclusions:

  • MTP provides an efficient and adaptive approach to sparse approximation.
  • The trade-off between MTP's suboptimal atom selection and reduced complexity is advantageous.
  • MTP shows promise for practical applications like signal compression.