LOQUAT: Low-Rank Quaternion Reconstruction for Photon-Counting CT

Area of Science:

• Medical Imaging
• Image Reconstruction
• Computational Imaging

Background:

• Photon-counting computed tomography (PCCT) offers clinical benefits like dose reduction and material characterization.
• Image noise is a significant challenge in PCCT due to limited photon detection.
• Low-rank properties in PCCT images can be leveraged for denoising.

Purpose of the Study:

• To introduce a novel low-rank quaternion reconstruction (LOQUAT) algorithm for PCCT.
• To address noise contamination in PCCT images by exploiting inherent low-rankness.
• To improve the quality of reconstructed PCCT images.

Main Methods:

• Utilizing quaternion representation (QR) to organize nonlocal similar image patches into matrices.
• Introducing an adjusted weighted Schatten-p norm (AWSN) to enforce low-rank properties.
• Developing an AWSN-regularized model solved via an alternating direction method of multipliers (ADMM) framework.

Main Results:

• LOQUAT demonstrates superior performance over state-of-the-art methods in visual and quantitative evaluations.
• The quaternion-based approach offers lower computational complexity compared to tensor representation methods.
• Theoretical global convergence of the LOQUAT algorithm is established.

Conclusions:

• LOQUAT provides a robust and practical solution for denoising PCCT images.
• The algorithm's efficiency and effectiveness support its potential clinical application.
• The developed method enhances the utility of PCCT in medical diagnostics.