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Related Experiment Video

Updated: Jun 20, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

Gradient Descent Provably Solves Nonlinear Tomographic Reconstruction.

Sara Fridovich-Keil1, Fabrizio Valdivia2, Gordon Wetzstein3

  • 1Department of Electrical Engineering and Computer Sciences at University of California, Berkeley, and the Department of Electrical Engineering at Stanford University. She is now with the School of Electrical and Computer Engineering at Georgia Institute of Technology.

IEEE Transactions on Information Theory
|June 19, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a direct nonlinear reconstruction method for computed tomography (CT) that bypasses problematic preprocessing steps. This approach reduces metal artifacts and improves image quality in CT scans.

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Last Updated: Jun 20, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

Area of Science:

  • Medical Imaging
  • Computational Imaging
  • Applied Mathematics

Background:

  • Computed tomography (CT) reconstruction typically involves linearizing the Beer-Lambert Law, which is sensitive to high-density materials like metal.
  • This nonlinear preprocessing step can lead to numerical instability and artifacts, particularly near metal implants.
  • Existing methods struggle with metal artifacts, impacting diagnostic accuracy in CT.

Purpose of the Study:

  • To develop and validate a direct nonlinear CT reconstruction method that avoids problematic preprocessing.
  • To demonstrate the provable convergence and efficiency of this direct nonlinear approach.
  • To reduce metal artifacts in CT reconstruction and improve image quality.

Main Methods:

  • Directly reconstructing CT data using the nonlinear forward model without intermediate linearization.
  • Applying gradient descent optimization to a nonconvex objective function, proving convergence to the global optimum.
  • Incorporating prior structural information via constraints for under-determined signal reconstruction.

Main Results:

  • Gradient descent provably converges to the global optimum at a geometric rate for direct nonlinear CT reconstruction.
  • The method achieves near-perfect signal reconstruction with a minimal number of measurements, even in under-determined cases.
  • Cone-beam CT experiments show significant reduction in metal artifacts compared to standard linear methods.

Conclusions:

  • Direct nonlinear CT reconstruction offers a more robust and artifact-free alternative to conventional methods.
  • The proposed technique effectively mitigates metal artifacts, enhancing the utility of CT imaging.
  • Logarithmic preprocessing itself can introduce artifacts, highlighting the benefits of direct nonlinear reconstruction.