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Statistical regularization in linearized microwave imaging through MRF-based MAP estimation: hyperparameter

Vito Pascazio1, Giancarlo Ferraiuolo

  • 1Inst. di Teoria e Tecnica delle Onde Elettromagnetiche, Univ. di Napoli Parthenope, Italy. vito.pascazio@uninav.it

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 2, 2008
PubMed
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This study introduces a Gaussian Markov random field (GMRF) method for microwave imaging. The approach efficiently estimates parameters using the expectation-maximization (EM) algorithm, improving image reconstruction accuracy.

Area of Science:

  • Electromagnetics and Imaging Science
  • Computational Mathematics and Statistics

Background:

  • Microwave imaging requires robust algorithms for accurate image reconstruction.
  • Conventional methods like Tikhonov regularization have limitations in handling complex image data.

Purpose of the Study:

  • To present a novel Maximum a posteriori (MAP) estimation method for microwave imaging using Gaussian Markov random fields (GMRF).
  • To demonstrate the well-posedness and efficiency of the proposed GMRF-MAP method.

Main Methods:

  • Application of a Gaussian Markov random field (GMRF) model for image prior.
  • Estimation of GMRF hyperparameters using an extended expectation-maximization (EM) algorithm for complex, nonhomogeneous images.
  • MAP estimation implemented via analytical gradient-based cost function minimization.

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Main Results:

  • The GMRF-MAP method ensures both well-posedness and computational efficiency due to the quadratic energy function.
  • Numerical simulations and real data experiments validate the method's good performance.
  • The proposed technique shows competitive or superior results compared to Tikhonov regularization.

Conclusions:

  • The GMRF-based MAP estimation provides an efficient and well-posed solution for microwave imaging.
  • The method demonstrates superior performance, particularly for complex and nonhomogeneous image reconstruction.
  • This approach offers a valuable advancement over conventional regularization techniques in microwave imaging.