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Related Experiment Videos

ML parameter estimation for Markov random fields with applications to Bayesian tomography.

S S Saquib1, C A Bouman, K Sauer

  • 1Polaroid Corp., Cambridge, MA 02139, USA. saquibs@polaroid.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 16, 2008
PubMed
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This study introduces efficient methods for estimating parameters in Markov random fields (MRFs), crucial for image reconstruction. The approach addresses challenges with parameter estimation when the true image is unknown, improving accuracy and reducing computation.

Area of Science:

  • Computational imaging
  • Statistical modeling
  • Image processing

Background:

  • Markov random fields (MRFs) are vital for Bayesian image reconstruction and restoration.
  • Estimating MRF parameters (hyperparameters) is challenging due to mathematical complexity and the unavailability of true image data.
  • Generalized Gaussian MRF (GGMRF) is a specific MRF model requiring parameter estimation.

Purpose of the Study:

  • To develop computationally efficient methods for estimating parameters in general MRF models.
  • To derive specific parameter estimation techniques for the Generalized Gaussian MRF (GGMRF).
  • To address the difficulties of direct parameter estimation and estimation without true image data.

Main Methods:

  • Derivation of direct estimation methods for scale and shape parameters in continuous-valued MRFs.

Related Experiment Videos

  • Development of a closed-form solution for the Maximum Likelihood (ML) estimate of the scale parameter (sigma) in GGMRF.
  • Efficient computation of the ML estimate for the shape parameter (p) in GGMRF using partition function dependence.
  • Application of the Expectation-Maximization (EM) algorithm with a fast simulation method for the E-step.
  • Implementation of a method to enhance parameter estimates from terminated simulations.

    • Main Results:

    • A computationally efficient scheme is proposed for general MRF parameter estimation.
    • Closed-form ML estimate for GGMRF scale parameter (sigma) is derived.
    • Efficient numerical computation for GGMRF shape parameter (p) ML estimate is presented.
    • Fast EM algorithm with improved simulation significantly reduces computation time.
    • Experimental results demonstrate good scale estimates for real tomographic data.

    Conclusions:

    • The proposed methods effectively address computational and data-availability challenges in MRF parameter estimation.
    • The developed algorithms offer substantial reductions in computation for image reconstruction and restoration tasks.
    • The techniques provide reliable parameter estimates, particularly for tomographic imaging applications.