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Wavelet based multiresolution expectation maximization image reconstruction algorithm for positron emission

A Raheja1, A P Dhawan

  • 1Department of Computer Science, Philadelphia University, Philadelphia, PA 19144, USA.

Computerized Medical Imaging and Graphics : the Official Journal of the Computerized Medical Imaging Society
|September 29, 2000
PubMed
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This study introduces a Wavelet-based Multiresolution EM (WMREM) algorithm for Positron Emission Tomography (PET) image reconstruction. WMREM enhances image quality and reduces iterations by utilizing wavelet transforms for multiresolution analysis.

Area of Science:

  • Medical Imaging
  • Signal Processing
  • Computational Science

Background:

  • Maximum Likelihood (ML) estimation based Expectation Maximization (EM) is a standard for Positron Emission Tomography (PET) image reconstruction.
  • Previous work introduced multigrid (MG) and multiresolution (MR) concepts to EM-based PET reconstruction.
  • Existing methods require significant computational resources and iterations for high-quality image reconstruction.

Purpose of the Study:

  • To develop a Wavelet-based Multiresolution EM (WMREM) algorithm for improved PET image reconstruction.
  • To leverage wavelet transform properties for efficient multiresolution analysis in both image and data spaces.
  • To design and evaluate customized biorthogonal wavelet filters for enhanced reconstruction.

Main Methods:

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  • The study transforms existing multigrid EM (MGEM) and multiresolution EM (MREM) algorithms into a WMREM framework.
  • A 2D-wavelet transform is applied to acquired PET data to create a multiresolution data space.
  • Wavelet transform is used for both multiresolution reconstruction and determining resolution switching criteria within the EM algorithm.

    • Main Results:

    • The WMREM algorithm effectively reconstructs PET images at varying spatial resolutions.
    • Wavelet transform's frequency and spatial localization properties are utilized to improve the EM estimation process.
    • The multiresolution approach recovers low-frequency image components at coarser resolutions, reducing overall iterations needed for high-frequency component recovery.

    Conclusions:

    • The WMREM algorithm offers an efficient and effective approach to PET image reconstruction.
    • The use of wavelet transforms in multiresolution EM significantly enhances reconstruction quality and computational efficiency.
    • Customized biorthogonal wavelet filters designed via the lifting method show promise for PET imaging applications.