ADMM-EM Method for L₁-Norm Regularized Weighted Least Squares PET Reconstruction

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• L1-norm regularization is crucial for noise reduction and edge preservation in Positron Emission Tomography (PET) reconstruction.
• Alternating Direction Method of Multipliers (ADMM) is effective for PET reconstruction but faces challenges with non-negative image updates and computational expense.

Purpose of the Study:

• To develop a new ADMM-based approach for L1-norm regularized weighted least squares PET reconstruction.
• To address the difficulties of non-negative image updates and reduce computational costs in ADMM for PET.

Main Methods:

• A novel iterative and monotonic image update strategy is derived, self-constraining the non-negativity region without a predetermined step size.
• Rigorous convergence proof is provided for the quadratic subproblem within the ADMM algorithm.
• A simplified ADMM version replaces function minima with a single decreasing iteration for computational efficiency.

Main Results:

• The proposed ADMM algorithm with greedy iterations demonstrates faster convergence than commonly used PET reconstruction methods.
• The simplified ADMM version achieves comparable reconstructed image quality at significantly lower computational costs.
• Experimental results validate the effectiveness and efficiency of the new approach.

Conclusions:

• The novel ADMM approach effectively handles non-negativity constraints and accelerates convergence in L1-norm regularized PET reconstruction.
• The simplified algorithm offers a practical and computationally efficient alternative for PET image reconstruction with comparable results.