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Trapezoidal back projection for positron emission tomography reconstruction.

Dóra Varnyú1,2, Krisztián Paczári3, László Szirmay-Kalos4

  • 1Mediso Medical Imaging Systems, Laborc u. 3., Budapest, 1037, Hungary. vdora@iit.bme.hu.

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Summary

A new deterministic trapezoidal back projection (TBP) algorithm significantly speeds up 3D PET reconstruction. TBP achieves low noise levels comparable to Monte Carlo methods but is 13 times faster, improving image quality and reducing scan times.

Keywords:
Back projectionGraphics processing unit (GPU)Maximum-likelihood expectation-maximization (ML-EM)Monte Carlo integrationPositron emission tomography (PET)

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Area of Science:

  • Medical Imaging
  • Computational Science

Background:

  • 3D PET reconstruction requires identifying all Lines of Responses (LORs) contributing to each voxel.
  • Standard Monte Carlo methods for LOR identification are computationally intensive due to extensive sampling.

Purpose of the Study:

  • To introduce a novel deterministic algorithm, trapezoidal back projection (TBP), for efficient 3D PET reconstruction.
  • To replace computationally expensive Monte Carlo sampling with a deterministic approach for accurate LOR identification and weighting.

Main Methods:

  • Developed the trapezoidal back projection (TBP) algorithm utilizing trapezoidal rasterization and a pre-computed look-up table.
  • Compared TBP's precision and speed against Monte Carlo back projection with varying sample numbers (1000, 10,000, 100,000).

Main Results:

  • TBP achieved a low noise level (2.5% STD uniformity) comparable to high-sample Monte Carlo methods.
  • TBP demonstrated a 13-fold speed increase, reducing reconstruction time from 31.3s to 2.3s on a NEMA NU 4-2008 phantom.

Conclusions:

  • The deterministic TBP algorithm offers a promising solution for 3D PET back projection, balancing low noise with short runtimes.
  • TBP's performance advantages can be leveraged to decrease reconstruction time, data acquisition duration, or image noise levels.