Least-squares and maximum-likelihood in computed tomography.

Area of Science:

• Medical Imaging
• Computational Science
• Optimization Theory

Background:

• Existing maximum-likelihood (ML) methods in computed tomography (CT) are computationally intensive and often limited to simplified noise models.
• There's a need for general, rapid ML methods that accurately incorporate specific experimental noise characteristics.

Purpose of the Study:

• To investigate a mathematical-computational procedure for developing constrained quadratic optimization (CQO) reconstruction algorithms.
• To create rapid ML methods for CT that precisely account for arbitrary noise models, offering high-fidelity reconstructions with reduced computational resources.

Main Methods:

• Developed a systematic procedure to generate CQO methods maximizing tomogram likelihood under diverse noise models.
• Applied the procedure to mixed Poisson-Gaussian noise and Poisson noise with invertible linear transformations.
• Performed tomographic reconstructions on a 2D phantom, comparing speed and fidelity against conventional quadratic metrics.

Main Results:

• CQO methods demonstrated significantly greater reconstruction fidelity compared to untuned quadratic metrics.
• These systematically produced methods required less computation than conventional approaches while maintaining high fidelity.
• Reconstructions showed comparable performance to least-squares iterative methods with improved efficiency.

Conclusions:

• CQO methods provide a practical approximation for high-fidelity CT reconstruction across various noise models.
• These methods are computationally efficient, explicit, and tunable for specific experimental noise characteristics.
• Preliminary results are promising for widespread application, though further research is needed to explore their full potential.