Yang Fugang, Yao Ruoyang, Ozturk Mehmet, Faulkner Denzel, Qu Qinglan, Intes Xavier
School of Information and Electronic Engineering, Shandong Institute of Business and Technology, Yantai 264005, China.
Department of Biomedical Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA.
Biomed Opt Express. 2018 May 23;9(6):2765-2778. doi: 10.1364/BOE.9.002765. eCollection 2018 Jun 1.
Mesoscopic fluorescence molecular tomography (MFMT) is a novel imaging technique capable of obtaining 3-D distribution of molecular probes inside biological tissues at depths of a few millimeters with a resolution up to ~100 μm. However, the ill-conditioned nature of the MFMT inverse problem severely deteriorates its reconstruction performances. Furthermore, dense spatial sampling and fine discretization of the imaging volume required for high resolution reconstructions make the sensitivity matrix (Jacobian) highly correlated, which prevents even advanced algorithms from achieving optimal solutions. In this work, we propose two computational methods to respectively increase the incoherence of the sensitivity matrix and improve the convergence rate of the inverse solver. We first apply a compressed sensing (CS) based preconditioner on either the whole sensitivity matrix or sub sensitivity matrices to reduce the coherence between columns of the sensitivity matrix. Then we employed a regularization method based on the weight iterative improvement method (WIIM) to mitigate the ill-condition of the sensitivity matrix and to drive the iterative optimization process towards convergence at a faster rate. We performed numerical simulations and phantom experiments to validate the effectiveness of the proposed strategies. In both and cases, we were able to improve the quality of MFMT reconstructions significantly.
介观荧光分子断层扫描（MFMT）是一种新型成像技术，能够在几毫米深度的生物组织内获取分子探针的三维分布，分辨率高达约100μm。然而，MFMT反问题的不适定性严重恶化了其重建性能。此外，高分辨率重建所需的成像体积的密集空间采样和精细离散化使得灵敏度矩阵（雅可比矩阵）高度相关，这使得即使是先进的算法也无法获得最优解。在这项工作中，我们提出了两种计算方法，分别提高灵敏度矩阵的非相干性和提高反解算器的收敛速度。我们首先在整个灵敏度矩阵或子灵敏度矩阵上应用基于压缩感知（CS）的预处理器，以降低灵敏度矩阵列之间的相干性。然后，我们采用基于权重迭代改进方法（WIIM）的正则化方法来减轻灵敏度矩阵的病态，并以更快的速度推动迭代优化过程收敛。我们进行了数值模拟和模型实验，以验证所提出策略的有效性。在这两种情况下，我们都能够显著提高MFMT重建的质量。
