Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method

Efficient L1 regularization-based reconstruction for fluorescent molecular tomography using restarted nonlinear conjugate gradient

For the ill-posed fluorescent molecular tomography (FMT) inverse problem, the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise. However, the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory, especially for large-scale problems. An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption. The reconstruction results from phantom experiments demonstrate that the proposed algorithm can obtain high spatial resolution and high signal-to-noise ratio, as well as high localization accuracy for fluorescence targets.

Hybrid multilevel sparse reconstruction for a whole domain bioluminescence tomography using adaptive finite element

Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed with in vivo experiments.

Comparative studies of l(p)-regularization-based reconstruction algorithms for bioluminescence tomography

Inverse source reconstruction is the most challenging aspect of bioluminescence tomography (BLT) because of its ill-posedness. Although many efforts have been devoted to this problem, so far, there is no generally accepted method. Due to the ill-posedness property of the BLT inverse problem, the regularization method plays an important role in the inverse reconstruction. In this paper, six reconstruction algorithms based on l(p) regularization are surveyed. The effects of the permissible source region, measurement noise, optical properties, tissue specificity and source locations on the performance of the reconstruction algorithms are investigated using a series of single source experiments. In order to further inspect the performance of the reconstruction algorithms, we present the double sources and the in vivo mouse experiments to study their resolution ability and potential for a practical heterogeneous mouse experiment. It is hoped to provide useful guidance on algorithm development and application in the related fields.

Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise

Bioluminescence Tomography attempts to quantify 3-dimensional luminophore distributions from surface measurements of the light distribution. The reconstruction problem is typically severely under-determined due to the number and location of measurements, but in certain cases the molecules or cells of interest form localised clusters, resulting in a distribution of luminophores that is spatially sparse. A Conjugate Gradient-based reconstruction algorithm using Compressive Sensing was designed to take advantage of this sparsity, using a multistage sparsity reduction approach to remove the need to choose sparsity weighting a priori. Numerical simulations were used to examine the effect of noise on reconstruction accuracy. Tomographic bioluminescence measurements of a Caliper XPM-2 Phantom Mouse were acquired and reconstructions from simulation and this experimental data show that Compressive Sensing-based reconstruction is superior to standard reconstruction techniques, particularly in the presence of noise.

Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.