Bias reduction for low-statistics PET: maximum likelihood reconstruction with a modified Poisson distribution

Area of Science:

• Medical Imaging
• Nuclear Medicine
• Image Reconstruction

Background:

• Positron emission tomography (PET) data reconstruction commonly uses Maximum Likelihood Expectation Maximization (MLEM).
• MLEM's non-negativity constraint introduces positive bias, problematic for tracer kinetic modeling.
• Filtered Backprojection (FBP) is an alternative, but bias characteristics differ.

Purpose of the Study:

• To present and compare two novel PET image reconstruction methods with bias reduction properties.
• To evaluate these methods against MLEM and FBP, focusing on bias and variance.
• To investigate the impact of randoms handling on reconstruction bias.

Main Methods:

• Introduced NEGML: an extension of existing methods replacing Poisson with Gaussian distribution for low-count data.
• Introduced AML: a simplified method with a negative lower bound for bias reduction.
• Compared NEGML, AML, MLEM, and FBP using various parameter settings and randoms handling strategies.

Main Results:

• Both NEGML and AML demonstrate bias reduction capabilities, particularly with larger parameter values.
• Bias-free reconstructions were achieved with NEGML and AML, approaching least squares algorithm behavior.
• NEGML and AML exhibited lower variance compared to FBP.
• Smoothed randoms handling resulted in lower bias than unsmoothed or precorrected randoms data.

Conclusions:

• NEGML and AML offer effective bias reduction in PET image reconstruction, crucial for accurate tracer kinetic modeling.
• These methods provide a viable alternative to MLEM, especially when bias is a concern.
• Optimized randoms handling is essential for minimizing bias in PET reconstructions.