High-order total variation minimization for interior SPECT.

Area of Science:

• Medical Imaging
• Image Reconstruction
• Computational Science

Background:

• Computed Tomography (CT) interior problems were previously solved using high-order total variation (HOT) minimization for piecewise polynomial regions-of-interest (ROIs).
• Extending these reconstruction techniques to other imaging modalities is crucial for broader applications.
• Existing HOT formulations lack explicit formulas for higher-order polynomial functions (n ≥ 2).

Purpose of the Study:

• To generalize the HOT minimization approach from CT to Single-Photon Emission Computed Tomography (SPECT) for ROI reconstruction.
• To prove the unique reconstructability of piecewise polynomial ROIs from SPECT data using HOT minimization.
• To develop a novel HOT formulation with an explicit formula for any n-order piecewise polynomial function.

Main Methods:

• Theoretical generalization of HOT minimization from CT to SPECT.
• Mathematical proof of unique reconstructability for piecewise polynomial ROIs in SPECT.
• Development of a new HOT formulation with explicit polynomial representation.

Main Results:

• The study proves that piecewise polynomial ROIs can be uniquely reconstructed from SPECT projection data using HOT minimization.
• A new HOT formulation is proposed, providing an explicit formula for n-order piecewise polynomial functions.
• Numerical simulations confirm the theoretical findings and demonstrate the method's efficacy.

Conclusions:

• The HOT minimization approach is effective for unique ROI reconstruction in SPECT for piecewise polynomial regions.
• The novel HOT formulation enhances applicability for higher-order polynomial functions in SPECT imaging.
• This work advances quantitative SPECT imaging and image reconstruction methodologies.