Feasibility of tomography with unknown view angles.

Area of Science:

• Medical Imaging
• Computational Imaging
• Applied Mathematics

Background:

• Standard 2-D parallel beam tomography assumes known projection angles.
• Previous work demonstrated unique angle recovery from projection data under mild conditions.

Purpose of the Study:

• To assess the reliability and stability of recovering unknown view angles in 2-D parallel beam tomography.
• To analyze the impact of noise and shifts on angle recovery accuracy.
• To develop a feasible algorithm for angle recovery in practical scenarios.

Main Methods:

• Utilized moments of projection data to analyze the angle recovery problem.
• Determined Cramer-Rao lower bounds for angle estimation variance under Gaussian noise.
• Investigated joint estimation of angles and projection shifts.
• Developed a simplified algorithm approximating the Maximum Likelihood (ML) estimator.

Main Results:

• Angle recovery solutions are unique and stable under mild conditions, even with data perturbations.
• Cramer-Rao lower bounds quantify estimation variance for noisy projections.
• Joint estimation of angles and shifts is feasible.
• Simulations show the developed algorithm performs excellently at low to moderate noise levels, nearing theoretical bounds.

Conclusions:

• Recovering view angles from projection data in 2-D parallel beam tomography is a reliable and stable problem.
• The proposed algorithm offers a feasible solution for angle recovery in noisy imaging conditions.
• The findings support the practical application of automated angle recovery in tomographic reconstruction.