SVD for imaging systems with discrete rotational symmetry

Area of Science:

• Medical Imaging
• Computational Science
• Linear Algebra

Background:

• Singular Value Decomposition (SVD) is crucial for tomographic imaging systems.
• High dimensionality of system matrices makes SVD computationally intensive and resource-demanding.
• Current limitations hinder SVD analysis on standard desktop computers.

Purpose of the Study:

• To develop a dimension reduction method for SVD in tomographic imaging.
• To make SVD computations tractable for standard computing resources.
• To enable advanced analysis of imaging system characteristics.

Main Methods:

• Developed a novel mathematical method to reduce SVD problem dimensionality.
• Leveraged discrete rotational symmetry in tomographic systems.
• Validated the method against standard SVD analysis for accuracy.

Main Results:

• Demonstrated significant dimension reduction in SVD computations.
• Achieved reduction factor equal to the number of collection angles.
• Confirmed identical results compared to traditional SVD methods.
• Successfully applied the technique to a clinical CT system's sensitivity matrix.

Conclusions:

• The developed method makes full SVD analysis accessible on standard computers.
• Enables computation of singular value spectra and vectors for tomographic systems.
• Will facilitate future advancements in system characterization, image quality assessment, and reconstruction techniques.