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

Photon-counting computed tomography (PCCT) may dramatically benefit clinical practice due to its versatility such as dose reduction and material characterization. However, the limited number of photons detected in each individual energy bin can induce severe noise contamination in the reconstructed image. Fortunately, the notable low-rank prior inherent in the PCCT image can guide the reconstruction to a denoised outcome. To fully excavate and leverage the intrinsic low-rankness, we propose a novel reconstruction algorithm based on quaternion representation (QR), called low-rank quaternion reconstruction (LOQUAT). First, we organize a group of nonlocal similar patches into a quaternion matrix. Then, an adjusted weighted Schatten-p norm (AWSN) is introduced and imposed on the matrix to enforce its low-rank nature. Subsequently, we formulate an AWSN-regularized model and devise an alternating direction method of multipliers (ADMM) framework to solve it. Experiments on simulated and real-world data substantiate the superiority of the LOQUAT technique over several state-of-the-art competitors in terms of both visual inspection and quantitative metrics. Moreover, our QR-based method exhibits lower computational complexity than some popular tensor representation (TR) based counterparts. Besides, the global convergence of LOQUAT is theoretically established under a mild condition. These properties bolster the robustness and practicality of LOQUAT, facilitating its application in PCCT clinical scenarios. The source code will be available at https://github.com/linzf23/LOQUAT.