Noise properties of motion-compensated tomographic image reconstruction methods

Area of Science:

• Medical Imaging
• Image Reconstruction
• Signal Processing

Background:

• Motion artifacts degrade image quality in dynamic imaging, necessitating motion-compensated image reconstruction (MCIR) techniques.
• Existing MCIR methods, including motion-compensated temporal regularization (MTR), parametric motion model (PMM), and post-reconstruction motion correction (PMC), are well-studied individually but lack theoretical comparison.
• Understanding the theoretical noise properties of different MCIR approaches is crucial for optimizing image reconstruction.

Purpose of the Study:

• To theoretically compare the noise properties of three popular MCIR methods: MTR, PMM, and PMC.
• To analyze the relationship between these methods under penalized weighted least squares and Poisson models with quadratic regularizers.
• To provide a framework for comparing MCIR methods based on noise variance, regularizer effects, and motion influence.

Main Methods:

• Theoretical analysis of noise properties for MTR, PMM, and PMC under penalized weighted least squares and Poisson models.
• Derivation of accurate and fast variance prediction formulas using an analytical approach.
• Comparison of statistical weighting, matrix-weighted sums versus scalar-weighted sums, and the impact of motion Jacobian determinants.

Main Results:

• PMM and MTR are shown to be matrix-weighted sums, while PMC is a scalar-weighted sum of registered frames.
• Theoretical noise analyses reveal that PMM and MTR exhibit lower or comparable variances to PMC due to statistical weighting.
• Variance prediction formulas were derived, enabling detailed comparisons of MCIR methods and the influence of various factors like regularizers and motion.

Conclusions:

• PMM and MTR demonstrate superior or comparable noise performance to PMC in motion-compensated image reconstruction.
• The analytical approach provides a robust method for predicting noise variance and comparing different MCIR techniques.
• These theoretical insights are validated by 2D positron emission tomography simulations, supporting the selection of advanced MCIR methods for enhanced image quality.