Total variation regularization for bioluminescence tomography with the split Bregman method

Efficient FMT reconstruction based on L1-αL2 regularization via half-quadratic splitting and a two-probe separation light source strategy

Fluorescence molecular tomography (FMT) can achieve noninvasive, high-contrast, high-sensitivity three-dimensional imaging in vivo by relying on a variety of fluorescent molecular probes, and has excellent clinical transformation prospects in the detection of tumors in vivo. However, the limited surface fluorescence makes the FMT reconstruction have some ill-posedness, and it is difficult to obtain the ideal reconstruction effect. In this paper, two different emission fluorescent probes and L 1-L 2 regularization are combined to improve the temporal and spatial resolution of FMT visual reconstruction by introducing the weighting factor α and a half-quadratic splitting alternating optimization (HQSAO) iterative algorithm. By introducing an auxiliary variable, the HQSAO method breaks the sparse FMT reconstruction task into two subproblems that can be solved in turn: simple reconstruction and image denoising. The weight factor α (α>1) can increase the weight of nonconvex terms to further promote the sparsity of the algorithm. Importantly, this paper combines two different dominant fluorescent probes to achieve high-quality reconstruction of dual light sources. The performance of the proposed reconstruction strategy was evaluated by digital mouse and nude mouse single/dual light source models. The simulation results show that the HQSAO iterative algorithm can achieve more excellent positioning accuracy and morphology distribution in a shorter time. In vivo experiments also further prove that the HQSAO algorithm has advantages in light source information preservation and artifact suppression. In particular, the introduction of two main emission fluorescent probes makes it easy to separate and reconstruct the dual light sources. When it comes to localization and three-dimensional morphology, the results of the reconstruction are much better than those using a fluorescent probe, which further facilitates the clinical transformation of FMT.

Multi-target reconstruction strategy based on blind source separation of surface measurement signals in FMT

Fluorescence molecular tomography (FMT) is a promising molecular imaging technique for tumor detection in the early stage. High-precision multi-target reconstructions are necessary for quantitative analysis in practical FMT applications. The existing reconstruction methods perform well in retrieving a single fluorescent target but may fail in reconstructing a multi-target, which remains an obstacle to the wider application of FMT. In this paper, a novel multi-target reconstruction strategy based on blind source separation (BSS) of surface measurement signals was proposed, which transformed the multi-target reconstruction problem into multiple single-target reconstruction problems. Firstly, by multiple points excitation, multiple groups of superimposed measurement signals conforming to the conditions of BSS were constructed. Secondly, an efficient nonnegative least-correlated component analysis with iterative volume maximization (nLCA-IVM) algorithm was applied to construct the separation matrix, and the superimposed measurement signals were separated into the measurements of each target. Thirdly, the least squares fitting method was combined with BSS to determine the number of fluorophores indirectly. Lastly, each target was reconstructed based on the extracted surface measurement signals. Numerical simulations and in vivo experiments proved that it has the ability of multi-target resolution for FMT. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.

Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study

SIGNIFICANCE

Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons.

AIM

The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry.

APPROACH

The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method.

RESULTS

3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object.

CONCLUSIONS

Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.

Multi-scale thermal radiation effects correction via a fast surface fitting with Chebyshev polynomials

In an uncooled infrared imaging system, thermal radiation effects are caused by the heat source from the target or the detection window, which affects the ability of target detection, tracking, and recognition seriously. To address this problem, a multi-scale correction method via a fast surface fitting with Chebyshev polynomials is proposed. A high-precision Chebyshev polynomial surface fitting is introduced into thermal radiation bias field estimation for the first time, to the best of our knowledge. The surface fitting in the gradient domain is added to the thermal radiation effects correction model as a regularization term, which overcomes the ill-posed matrix problem of high-order bivariate polynomials surface fitting, and achieves higher accuracy under the same order. Additionally, a multi-scale iterative strategy and vector representation are adopted to speed up the iterative optimization and surface fitting, respectively. Vector representation greatly reduces the number of basis function calls and achieves fast surface fitting. In addition, split Bregman optimization is used to solve the minimization problem of the correction model, which decomposes the multivariable optimization problem into multiple univariate optimization sub-problems. The experimental results of simulated and real degraded images demonstrate that our proposed method performs favorably against the state of the art in thermal radiation effects correction.

A review of advances in imaging methodology in fluorescence molecular tomography

Objective. Fluorescence molecular tomography (FMT) is a promising non-invasive optical molecular imaging technology with strong specificity and sensitivity that has great potential for preclinical and clinical studies in tumor diagnosis, drug development and therapeutic evaluation. However, the strong scattering of photons and insufficient surface measurements make it very challenging to improve the quality of FMT image reconstruction and its practical application for early tumor detection. Therefore, continuous efforts have been made to explore more effective approaches or solutions in the pursuit of high-quality FMT reconstructions. Approach. This review takes a comprehensive overview of advances in imaging methodology for FMT, mainly focusing on two critical issues in FMT reconstructions: improving the accuracy of solving the forward physical model and mitigating the ill-posed nature of the inverse problem from a methodological point of view. More importantly, numerous impressive and practical strategies and methods for improving the quality of FMT reconstruction are summarized. Notably, deep learning methods are discussed in detail to illustrate their advantages in promoting the imaging performance of FMT thanks to large datasets, the emergence of optimized algorithms and the application of innovative networks. Main results. The results demonstrate that the imaging quality of FMT can be effectively promoted by improving the accuracy of optical parameter modeling, combined with prior knowledge, and reducing dimensionality. In addition, the traditional regularization-based methods and deep neural network-based methods, especially end-to-end deep networks, can enormously alleviate the ill-posedness of the inverse problem and improve the quality of FMT image reconstruction. Significance. This review aims to illustrate a variety of effective and practical methods for the reconstruction of FMT images that may benefit future research. Furthermore, it may provide some valuable research ideas and directions for FMT in the future, and could promote, to a certain extent, the development of FMT and other methods of optical tomography.

Sparse-graph manifold learning method for bioluminescence tomography

In preclinical researches, bioluminescence tomography (BLT) has widely been used for tumor imaging and monitoring, imaged-guided tumor therapy, and so forth. For these biological applications, both tumor spatial location and morphology analysis are the leading problems needed to be taken into account. However, most existing BLT reconstruction methods were proposed for some specific applications with a focus on sparse representation or morphology recovery, respectively. How to design a versatile algorithm that can simultaneously deal with both aspects remains an impending problem. In this study, a Sparse-Graph Manifold Learning (SGML) method was proposed to balance the source sparseness and morphology, by integrating non-convex sparsity constraint and dynamic Laplacian graph model. Furthermore, based on the nonconvex optimization theory and some iterative approximation, we proposed a novel iteratively reweighted soft thresholding algorithm (IRSTA) to solve the SGML model. Numerical simulations and in vivo experiments result demonstrated that the proposed SGML method performed much superior to the comparative methods in spatial localization and tumor morphology recovery for various source settings. It is believed that the SGML method can be applied to the related optical tomography and facilitate the development of optical molecular tomography.

Back-propagation neural network-based reconstruction algorithm for diffuse optical tomography

Diffuse optical tomography (DOT) is a promising noninvasive imaging modality and is capable of providing functional characteristics of biological tissue by quantifying optical parameters. The DOT image reconstruction is ill-posed and ill-conditioned, due to the highly diffusive nature of light propagation in biological tissues and limited boundary measurements. The widely used regularization technique for DOT image reconstruction is Tikhonov regularization, which tends to yield oversmoothed and low-quality images containing severe artifacts. It is necessary to accurately choose a regularization parameter for Tikhonov regularization. To overcome these limitations, we develop a noniterative reconstruction method, whereby optical properties are recovered based on a back-propagation neural network (BPNN). We train the parameters of BPNN before DOT image reconstruction based on a set of training data. DOT image reconstruction is achieved by implementing a single evaluation of the trained network. To demonstrate the performance of the proposed algorithm, we compare with the conventional Tikhonov regularization-based reconstruction method. The experimental results demonstrate that image quality and quantitative accuracy of reconstructed optical properties are significantly improved with the proposed algorithm.

Recent methodology advances in fluorescence molecular tomography

Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.

Bayesian sparse-based reconstruction in bioluminescence tomography improves localization accuracy and reduces computational time

Bioluminescence tomography (BLT) provides fundamental insight into biological processes in vivo. To fully realize its potential, it is important to develop image reconstruction algorithms that accurately visualize and quantify the bioluminescence signals taking advantage of limited boundary measurements. In this study, a new 2-step reconstruction method for BLT is developed by taking advantage of the sparse a priori information of the light emission using multispectral measurements. The first step infers a wavelength-dependent prior by using all multi-wavelength measurements. The second step reconstructs the source distribution based on this developed prior. Simulation, phantom and in vivo results were performed to assess and compare the accuracy and the computational efficiency of this algorithm with conventional sparsity-promoting BLT reconstruction algorithms, and results indicate that the position errors are reduced from a few millimeters down to submillimeter, and reconstruction time is reduced by 3 orders of magnitude in most cases, to just under a few seconds. The recovery of single objects and multiple (2 and 3) small objects is simulated, and the recovery of images of a mouse phantom and an experimental animal with an existing luminescent source in the abdomen is demonstrated. Matlab code is available at https://github.com/jinchaofeng/code/tree/master.

Synchronization-based clustering algorithm for reconstruction of multiple reconstructed targets in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an important in vivo molecular imaging technique and has been widely studied in preclinical research. Many methods perform well in the reconstruction of a single fluorescent target but may fail in reconstructing multiple targets because of the severe ill-posedness of the FMT inverse problem. In this paper the original synchronization-inspired clustering algorithm (OSC) is introduced into FMT for resolving multiple targets from the reconstruction result. Based on OSC, a synchronization-based clustering algorithm for FMT (SC-FMT) is developed to further improve location accuracy. Both algorithms utilize the minimum spanning tree to automatically identify the number of the reconstructed targets without prior information and human intervention. A serial of numerical simulation results demonstrates that SC-FMT and OSC can resolve multiple targets robustly and automatically, which also shows the potential of the proposed postprocessing algorithms in FMT reconstruction.

Laplacian manifold regularization method for fluorescence molecular tomography

Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ? 1 -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 ? 1 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 ? 1 minimization method in both spatial aggregation and location accuracy.

Mixed Total Variation and L1 Regularization Method for Optical Tomography Based on Radiative Transfer Equation

Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE). It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV) regularization and the L¹ regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L¹ norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L¹ regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L¹ regularizations, the simulation results show the validity and efficiency of the proposed method.

L p Regularization for Bioluminescence Tomography Based on the Split Bregman Method

PURPOSE

Bioluminescence tomography (BLT) is a promising in vivo optical imaging technique in preclinical research at cellular and molecular levels. The problem of BLT reconstruction is quite ill-posed and ill-conditioned. In order to achieve high accuracy and efficiency for its inverse reconstruction, we proposed a novel approach based on L _p regularization with the Split Bregman method.

PROCEDURES

The diffusion equation was used as the forward model. Then, we defined the objective function of L _p regularization and developed a Split Bregman iteration algorithm to optimize this function. After that, we conducted numerical simulations and in vivo experiments to evaluate the accuracy and efficiency of the proposed method.

RESULTS

The results of the simulations indicated that compared with the conjugate gradient and iterative shrinkage methods, the proposed method is more accurate and faster for multisource reconstructions. Furthermore, in vivo imaging suggested that it could clearly distinguish the viable and apoptotic tumor regions.

CONCLUSIONS

The Split Bregman iteration method is able to minimize the L _p regularization problem and achieve fast and accurate reconstruction in BLT.

Reconstruction Method for Optical Tomography Based on the Linearized Bregman Iteration with Sparse Regularization

Optical molecular imaging is a promising technique and has been widely used in physiology, and pathology at cellular and molecular levels, which includes different modalities such as bioluminescence tomography, fluorescence molecular tomography and Cerenkov luminescence tomography. The inverse problem is ill-posed for the above modalities, which cause a nonunique solution. In this paper, we propose an effective reconstruction method based on the linearized Bregman iterative algorithm with sparse regularization (LBSR) for reconstruction. Considering the sparsity characteristics of the reconstructed sources, the sparsity can be regarded as a kind of a priori information and sparse regularization is incorporated, which can accurately locate the position of the source. The linearized Bregman iteration method is exploited to minimize the sparse regularization problem so as to further achieve fast and accurate reconstruction results. Experimental results in a numerical simulation and in vivo mouse demonstrate the effectiveness and potential of the proposed method.

X-ray luminescence computed tomography imaging based on X-ray distribution model and adaptively split Bregman method

X-ray luminescence computed tomography (XLCT) has become a promising imaging technology for biological application based on phosphor nanoparticles. There are mainly three kinds of XLCT imaging systems: pencil beam XLCT, narrow beam XLCT and cone beam XLCT. Narrow beam XLCT can be regarded as a balance between the pencil beam mode and the cone-beam mode in terms of imaging efficiency and image quality. The collimated X-ray beams are assumed to be parallel ones in the traditional narrow beam XLCT. However, we observe that the cone beam X-rays are collimated into X-ray beams with fan-shaped broadening instead of parallel ones in our prototype narrow beam XLCT. Hence we incorporate the distribution of the X-ray beams in the physical model and collected the optical data from only two perpendicular directions to further speed up the scanning time. Meanwhile we propose a depth related adaptive regularized split Bregman (DARSB) method in reconstruction. The simulation experiments show that the proposed physical model and method can achieve better results in the location error, dice coefficient, mean square error and the intensity error than the traditional split Bregman method and validate the feasibility of method. The phantom experiment can obtain the location error less than 1.1 mm and validate that the incorporation of fan-shaped X-ray beams in our model can achieve better results than the parallel X-rays.

A Multi-Camera System for Bioluminescence Tomography in Preclinical Oncology Research

Bioluminescent imaging (BLI) of cells expressing luciferase is a valuable noninvasive technique for investigating molecular events and tumor dynamics in the living animal. Current usage is often limited to planar imaging, but tomographic imaging can enhance the usefulness of this technique in quantitative biomedical studies by allowing accurate determination of tumor size and attribution of the emitted light to a specific organ or tissue. Bioluminescence tomography based on a single camera with source rotation or mirrors to provide additional views has previously been reported. We report here in vivo studies using a novel approach with multiple rotating cameras that, when combined with image reconstruction software, provides the desired representation of point source metastases and other small lesions. Comparison with MRI validated the ability to detect lung tumor colonization in mouse lung.

Improved reconstruction quality of bioluminescent images by combining SP(3) equations and Bregman iteration method

Bioluminescence tomography (BLT) has a great potential to provide a powerful tool for tumor detection, monitoring tumor therapy progress, and drug development; developing new reconstruction algorithms will advance the technique to practical applications. In the paper, we propose a BLT reconstruction algorithm by combining SP₃ equations and Bregman iteration method to improve the quality of reconstructed sources. The numerical results for homogeneous and heterogeneous phantoms are very encouraging and give significant improvement over the algorithms without the use of SP₃ equations and Bregman iteration method.