Simultaneous activity and attenuation estimation in TOF-PET with TV-constrained nonconvex optimization

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• The simultaneous estimation of activity and attenuation (SAA) is a critical inverse problem in time-of-flight positron emission tomography (TOF-PET).
• Maximum likelihood estimation (MLE) is often employed for SAA, but it can lead to nonsmooth biconvex optimization problems.
• Existing methods may require significant computational resources or yield suboptimal reconstructions.

Approach:

• A novel alternating direction method of multipliers (ADMM) framework is developed to address nonsmooth biconvex optimization in inverse imaging problems.
• The ADMM framework is specifically applied to MLE for SAA in TOF-PET, yielding the ADMM-SAA algorithm.
• Total variation (TV) constraints are incorporated into the ADMM-SAA algorithm, creating the ADMM-TVSAA algorithm for enhanced regularization of activity and attenuation maps.

Key Points:

• The proposed ADMM-SAA algorithm effectively handles the complexities of SAA in TOF-PET using MLE.
• The ADMM-TVSAA algorithm demonstrates improved performance by integrating TV constraints, leading to better-regularized activity and attenuation images.
• The performance is validated against the penalized maximum likelihood activity and attenuation estimation (P-MLAA) algorithm.

Conclusions:

• The developed ADMM framework provides an efficient and effective solution for SAA in TOF-PET.
• The incorporation of TV constraints in ADMM-TVSAA enhances image quality and reconstruction accuracy.
• This work offers a valuable advancement in TOF-PET image reconstruction techniques.