Edge-preserving PET image reconstruction using trust optimization transfer.

Area of Science:

• Medical Imaging
• Computational Science
• Image Processing

Background:

• Iterative image reconstruction in positron emission tomography (PET) uses spatial regularization to enhance image quality.
• Quadratic penalties commonly used in PET reconstruction oversmooth edges, while nonquadratic penalties better preserve them.
• Existing algorithms like Expectation Maximization (EM) and Preconditioned Conjugate Gradient (PCG) are inefficient for edge-preserving regularizations.

Purpose of the Study:

• To develop a novel algorithm that accelerates edge-preserving image reconstruction in PET.
• To improve the efficiency and performance of PET image reconstruction, especially for nonquadratic regularization methods.
• To enhance the preservation of sharp edges and fine features in reconstructed PET images.

Main Methods:

• Proposed a new algorithm combining trust surrogate and optimization transfer descent strategies.
• Trust surrogate approximates the penalty with a smoother function, ensuring monotonic descent.
• Optimization transfer descent accelerates conventional methods using conjugate gradient and line search.

Main Results:

• The proposed algorithm demonstrates significantly faster convergence compared to conventional EM and PCG for smooth edge-preserving regularization.
• It shows greater efficiency than current state-of-the-art algorithms for nonsmooth L1 regularization.
• Simulations and real 3-D data validated the algorithm's superior performance.

Conclusions:

• The new algorithm effectively accelerates edge-preserving image reconstruction in PET.
• It offers improved efficiency and better feature preservation over existing methods, particularly for challenging regularization types.
• This advancement holds promise for higher quality and faster PET imaging.