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Related Concept Videos

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...
Linear Approximations01:23

Linear Approximations

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...
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...
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.
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

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Related Experiment Video

Updated: Jun 22, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

SAR image regularization with fast approximate discrete minimization.

Loïc Denis1, Florence Tupin, Jérôme Darbon

  • 1Institut TELECOM, TELECOM ParisTech, GET/Télécom Paris, France.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|June 2, 2009
PubMed
Summary
This summary is machine-generated.

Synthetic aperture radar (SAR) images contain speckle noise. A novel graph-cut algorithm efficiently reduces this noise in SAR images, improving interpretation for remote sensing applications.

Related Experiment Videos

Last Updated: Jun 22, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Area of Science:

  • Remote Sensing
  • Image Processing
  • Computational Imaging

Background:

  • Synthetic Aperture Radar (SAR) images are prone to speckle noise, hindering automatic interpretation and requiring effective noise reduction for subsequent algorithms.
  • Markov Random Field (MRF) models and Total Variation (TV) minimization are established methods for speckle noise filtering, balancing data fidelity with image regularization and edge preservation.
  • Existing MRF-based speckle reduction methods, particularly alpha-expansion, face computational challenges and memory constraints for large-scale remote sensing SAR images.

Purpose of the Study:

  • To develop an efficient and computationally feasible algorithm for speckle noise reduction in SAR images.
  • To address the limitations of existing methods, especially for large images and joint regularization tasks.
  • To improve the quality and interpretability of SAR images for remote sensing applications.

Main Methods:

  • Utilized a graph-cut-based approach for minimizing non-convex energy functions arising from MRF modelization of speckle noise.
  • Introduced a novel algorithm employing combinatorial exploration of large trial moves for approximate minimization, overcoming the computational burden of traditional alpha-expansion.
  • Applied the developed method to the joint regularization of amplitude and interferometric phase in urban area SAR images.

Main Results:

  • The proposed graph-cut algorithm achieves satisfying speckle noise reduction in SAR images within a few iterations.
  • The method demonstrates computational efficiency and feasibility for large remote sensing images, unlike exact minimization techniques.
  • Successful joint regularization of amplitude and interferometric phase was achieved, enhancing the utility of SAR data for urban area analysis.

Conclusions:

  • The developed graph-cut-based algorithm offers an efficient solution for speckle noise reduction in SAR images.
  • This approach effectively handles the challenges associated with large image sizes and joint regularization tasks in remote sensing.
  • The improved image quality facilitates more accurate automatic interpretation and analysis of SAR data, particularly in complex urban environments.