Improving mesoscopic fluorescence molecular tomography via preconditioning and regularization

Abstract

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.

System configuration optimization for mesoscopic fluorescence molecular tomography

“…(2) as a convex quadratic problem with linear inequality constraints. The equivalent quadratic program can be solved by interior-point methods [25,27]. For each of the following simulations and experiment cases, we employed the same inverse solution methodology proposed in [25].…”

“…The equivalent quadratic program can be solved by interior-point methods [25,27]. For each of the following simulations and experiment cases, we employed the same inverse solution methodology proposed in [25]. The optimal regularization parameter λ can be chosen through L-curve analysis for different Jacobian matrix [31].…”

“…To perform comparison fairly for different scenarios, these metrics are normalized so that they produce values between 0 (for two absolute different results) and 1 (for two totally coincident results). The adopted metrics here provide a comprehensive evaluation in term of similarity (normalized sum of square of the differences, nSSD), displacement of mass center (normalized sum of the absolute differences, nSAD), determination of spatial alignment (normalized correlation, nR), and disparity (normalized disparity, nD) [25]:…”

“…Last, we test the best optical configuration experimentally using our previously reported platform [25]. Hence, the scanning spots and 2D detectors array are respectively set to 31×31 and 7×7 and with coupled scanning mode.…”

“…Hence, its imaging performances are highly dependent on the selection of an appropriate forward model, dense spatial measurements and a dedicated inverse solver. To this end, we have developed efficient Monte Carlo tools to model accurately the sub-diffuse and diffuse regime [21,22], compressive sensing based inverse solvers [23], pre-conditioning techniques to reduce the ill-posedness of the sensitivity matrix [24,25], and data reduction techniques to facilitate the computation of the inverse problem [26]. However, it is well known that the intrinsic properties of the Jacobian such as sparsity, condition number, and redundancy have a significant effect on the accuracy of the reconstruction [27].…”