Object dependency of resolution in reconstruction algorithms with interiteration filtering applied to PET data

Area of Science:

• Medical Imaging
• Image Reconstruction
• Signal Processing

Background:

• Resolution properties are crucial for accurate image reconstruction in Positron Emission Tomography (PET).
• Interiteration filtering in algorithms like MLEM can lead to spatially varying and object-dependent resolution.
• This non-uniformity arises from the interaction between filtering and Poisson noise models.

Purpose of the Study:

• To analyze the resolution properties of iterative image reconstruction algorithms with interiteration filtering.
• To develop methods for achieving uniform and object-independent resolution in PET imaging.
• To evaluate proposed regularization techniques on simulated PET data.

Main Methods:

• Derivation of analytic approximations for the linearized local impulse response (LLIR) for filtered gradient descent algorithms.
• Development of three distinct regularization approaches: pixel-based filter coefficients and preconditioner selection.
• Testing and evaluation of these methods using filtered Maximum-Likelihood Expectation Maximization (MLEM) and filtered separable paraboloidal surrogates (SPS) on simulated data.

Main Results:

• Analytic expressions reveal that interiteration filtering typically results in spatially varying, object-dependent, and asymmetric resolution.
• Non-regularized and post-filtered MLEM achieve near-uniform resolution upon convergence.
• Proposed regularization methods demonstrate the ability to yield nearly object-independent and uniform resolution.

Conclusions:

• Interiteration filtering introduces significant non-uniformities in image resolution due to its interaction with Poisson noise.
• The proposed regularization strategies effectively address these non-uniformities, leading to improved resolution characteristics.
• These findings offer a pathway to more consistent and reliable image quality in PET reconstruction.