Alternating direction method of multiplier for tomography with nonlocal regularizers

Area of Science:

• Medical Imaging
• Computational Science
• Image Reconstruction

Background:

• Ordered Subset Expectation Maximization (OSEM) is used for fast image reconstruction in SPECT, PET, and CT.
• OSEM struggles to accelerate reconstruction with computationally intensive regularizers like patch-based nonlocal (NL) regularizers.

Purpose of the Study:

• To develop a faster image reconstruction algorithm for penalized emission tomography.
• To address the limitations of OSEM with complex regularizers.

Main Methods:

• Proposed a variable splitting technique to separate likelihood and regularizer terms.
• Optimized the problem using the alternating direction method of multipliers (ADMM).
• Developed a fast algorithm for ADMM parameter optimization based on convergence rate analysis.

Main Results:

• The proposed ADMM scheme enabled more sub-iterations for the likelihood term.
• Demonstrated substantial improvement in convergence speed for 3-D SPECT image reconstruction.
• Outperformed existing methods including gradient descent, EM, and OSEM with De Pierro's approach, and L-BFGS.

Conclusions:

• The novel ADMM approach significantly enhances the speed of penalized emission tomographic image reconstruction.
• This method is particularly effective with patch-based nonlocal regularizers.
• Offers a promising alternative for accelerating complex image reconstruction tasks in medical imaging.