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Estimation and model selection in constrained deconvolution

D Verotta1

  • 1Department of Pharmacy and Pharmaceutical Chemistry, University of California San Francisco 94143-0446.

Annals of Biomedical Engineering
|November 1, 1993
PubMed
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This study estimates system input A(t) from noisy measurements using spline functions and linear regression. It compares nonparametric regression methods and proposes model selection criteria for accurate system identification.

Area of Science:

  • Statistics
  • System Identification
  • Applied Mathematics

Background:

  • Accurate system input estimation is crucial in various scientific fields.
  • Noisy measurements complicate the estimation of the underlying system response.
  • The unit impulse response function (K(t)) is known, but the system input (A(t)) is unknown.

Purpose of the Study:

  • To develop and evaluate methods for estimating an unknown system input A(t) from noisy measurements.
  • To compare different nonparametric regression techniques for this estimation problem.
  • To propose and assess statistically based model selection criteria for choosing the best spline function.

Main Methods:

  • The unknown function A(t) is represented using spline functions.
  • The estimation problem is reformulated as inequality-constrained linear regression.

Related Experiment Videos

  • Nonparametric regression methods and statistical selection criteria are compared via simulations.

    • Main Results:

    • Spline-based methods provide a robust approach to system input estimation.
    • Simulation results guide the selection of appropriate nonparametric regression techniques.
    • Modified selection criteria are suggested for improved performance in this specific estimation context.

    Conclusions:

    • The study offers a comprehensive framework for system input estimation using splines.
    • The findings are applicable to both simulated and real-world data, including pharmacokinetics.
    • The research contributes to improved signal processing and system identification methodologies.