Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ℓ1-regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ℓ1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai–Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ℓ1 minimization method in both spatial aggregation and location accuracy.
As an important optical molecular imaging technique, bioluminescence tomography (BLT) offers an inexpensive and
sensitive means for non-invasively imaging a variety of physiological and pathological activities at cellular and
molecular levels in living small animals. The key problem of BLT is to recover the distribution of the internal
bioluminescence sources from limited measurements on the surface. Considering the sparsity of the light source
distribution, we directly formulate the inverse problem of BLT into an l0-norm minimization model and present a
smoothed l0-norm (SL0) based reconstruction algorithm. By approximating the discontinuous l0 norm with a suitable
continuous function, the SL0 norm method solves the problem of intractable computational load of the minimal l0 search as well as high sensitivity of l0-norm to noise. Numerical experiments on a mouse atlas demonstrate that the proposed
SL0 norm based reconstruction method can obtain whole domain reconstruction without any a priori knowledge of the
source permissible region, yielding almost the same reconstruction results to those of l1 norm methods.
The diffusion approximation of the radiative transport equation is the most widely used model in current researches on fluorescence molecular tomography (FMT), which is limited in some low or zero scattering regions. Recently, the simplified spherical harmonics equations (SPN) model has attracted much attention in modeling the light propagation in small tissue geometries at visible and near-infrared wavelengths. In this paper, we report an efficient numerical method for FMT that combines the advantage of SPN model and hp-FEM. For comparison purposes, hp-FEM and h-FEM are respectively applied in the reconstruction process with diffusion model and SPN model. Simulation experiments on a 3D digital mouse atlas are designed to evaluate the reconstruction methods in terms of the location and the reconstructed fluorescent yield. The experimental results demonstrate that hp-FEM with SPN model, yield more accurate results than h-FEM with DA model does. And the reconstructed results show the potential and feasibility of the proposed approach.
As a novel optical molecular imaging modality, Bioluminescence Tomography (BLT) aims at quantitative reconstruction
of the bioluminescent source distribution inside the biological tissue from the optical signals measured on the living
animal surface, which is a highly ill-posed inverse problem. In this paper, with the finite element method solving the
diffusion equation, an iterative regularization algorithm, referred to as least square QR-factorization (LSQR), is applied
to the inverse problem in BLT. The affect of the preconditioning strategy on the LSQR method (PLSQR) for BLT is also
investigated. The Simulations with a heterogeneous mouse chest phantom demonstrate that by incorporating a priori
knowledge of the permissible source region, the LSQR method can reconstruct the source accurately and stably.
Moreover, by employing preconditioning strategy, PLSQR outperforms LSQR in terms of source power density and