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A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods.

Kihwan Choi1, Ruijiang Li, Haewon Nam

  • 1Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA. Department of Radiation Oncology, Stanford University, Stanford, CA 94305, USA. Medical System Laboratory, Samsung Advanced Institute of Technology (SAIT), Suwon, Gyeonggi, 443-803, Korea.

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This study introduces a Fourier-based scaling technique to accelerate first-order methods for computed tomography (CT) image reconstruction. The novel approach enhances convergence speed and image quality compared to existing compressed sensing (CS) methods.

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Area of Science:

  • Medical Imaging
  • Computational Imaging
  • Image Reconstruction

Background:

  • First-order methods are effective for large-scale computed tomography (CT) image reconstruction due to their fast convergence.
  • However, CT system matrices with high condition numbers can impede convergence speed, limiting practical applications.
  • Existing methods often struggle with convergence limitations in complex CT geometries.

Purpose of the Study:

  • To develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods in CT image reconstruction.
  • To improve the overall image quality and computational efficiency of CT reconstruction algorithms.
  • To address the limitations posed by ill-conditioned system matrices in CT imaging.

Main Methods:

  • A Fourier-based scaling technique was developed, transforming projection data into Fourier space for a data fidelity model.
  • An optimization problem was formulated using weighted least-squares in Fourier space and total-variation (TV) regularization in image space.
  • The optimization problem was solved using a fast iterative shrinkage-thresholding algorithm with GPU-accelerated projection/backprojection.

Main Results:

  • The proposed Fourier-based compressed sensing (CS) method demonstrated significant improvements in both image quality and convergence rate.
  • Performance was validated through digital simulations and experimental phantom studies across various CT geometries (parallel-beam, fan-beam, cone-beam).
  • Compared to existing TV-regularized techniques and algebraic reconstruction, the new method showed superior results.

Conclusions:

  • The Fourier-based scaling technique effectively enhances the convergence speed of first-order methods for CT image reconstruction.
  • This approach offers a significant advancement over current compressed sensing techniques, providing better image quality and faster reconstruction.
  • The method is robust and applicable to diverse CT imaging scenarios, paving the way for more efficient and accurate CT imaging.