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Piecewise Linear Slope Estimation.

A N Ingle1, W A Sethares2, T Varghese1

  • 1Depts. of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI, USA ; Depts. of Medical Physics, University of Wisconsin-Madison, Madison, WI, USA.

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Summary
This summary is machine-generated.

This study introduces a novel method for estimating slopes in noisy linear functions using a Markov structure. The approach efficiently identifies piecewise linear segments and estimates model parameters for applications like ultrasound imaging.

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Area of Science:

  • Signal Processing
  • Statistical Modeling
  • Applied Mathematics

Background:

  • Estimating parameters in noisy data is crucial for accurate analysis.
  • Piecewise linear functions are common in various scientific and financial domains.
  • Existing methods may struggle with noisy signals and complex structures.

Purpose of the Study:

  • To develop a direct slope estimation method for noisy piecewise linear functions.
  • To apply a Markov structure for robust parameter estimation.
  • To demonstrate the algorithm's efficacy in ultrasound shear wave imaging and financial data analysis.

Main Methods:

  • Formulating piecewise linear fitting as a maximum a posteriori estimation problem.
  • Employing a dynamic programming approach on a linearly growing trellis.
  • Utilizing an alternating maximization algorithm for model parameter estimation and convergence analysis.

Main Results:

  • Successfully developed a method for direct slope estimation in noisy piecewise linear functions.
  • Demonstrated efficient computation using dynamic programming and alternating maximization.
  • Validated the method's applicability in ultrasound shear wave imaging and financial interest rate shift estimation.

Conclusions:

  • The proposed method provides an efficient and robust way to estimate slopes in noisy piecewise linear data.
  • The Markov structure and dynamic programming offer significant advantages for this estimation task.
  • The algorithm's versatility is confirmed by its successful application in diverse fields.