Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern

Fluorescence molecular tomography (FMT) is a promising imaging technique to noninvasively resolve the three-dimensional spatial distributions of fluorescent targets associated with molecular and cellular functions. The reconstruction quality, including the localization and quantitative accuracy, are greatly improved by the use of normalized Born ratio method. However, the reconstruction quality is still far from reaching their potential of accurately visualizing biological information with a high localization and quantitative accuracy. It is because the inverse problem of FMT is severely ill-posed and is easily affected by the noise in the measurement data. Here we provided a scaling normalization method for FMT to restrain the influence of excitation noise on fluorescence molecular tomography reconstruction. In this method, we use the total intensity of the excitation data detected by CCD camera to normalize the fluorescence measurements. It's feasible to suppress excitation noise when compared with the normalized Born ration method. Furthermore, by applying singular-value decomposition to the forward matrices, we find that the method we proposed has more useful singular values than the normalized Born ratio method which means that it reduces the ill-posedness of FMT inverse problem. To examine its performance, we perform phantom experiments with a hybrid FMT-XCT system. To check the robustness of our method to excitation noise, we add 10% Gaussian white noise to the measured excitation data. The reconstruction results are compared with those of the normalized Born ratio method. The results indicate that our method has a better reconstruction results and a better noise robustness.

Fluorescence Molecular Tomography (FMT) is one of the most important preclinical research techniques, which can obtain three-dimensional reconstruction of tumors in mouse in vivo. However, the ill-posedness of FMT makes its reconstruction a challenging problem. Therefore, more effective, robust, and accurate reconstruction methods are needed to be developed to solve the FMT reconstruction problem. In this paper, a reconstruction method named multipath subspace pursuit (MSP) is applied to solve the FMT problem. At the end of an iteration, the MSP method creates several candidate support set. Through evaluating the normal of final residual vector, the best candidate can be selected as the final support set. Then the support set is used for reconstructing sense matrix to achieve the goal of FMT reconstruction. In order to verity the reconstruction result of the proposed MSP method, the simulated experiment of triple fluorescent sources and quantitative analyses of position error and relative intensity error for the experiment have been conducted. The MSP method obtains satisfactory results, and the source position error is below 1 mm. Moreover, the computation time of the MSP method is about one order of magnitude less than iterated shrinkage with the L1-norm (ISlL1) method. The MSP method not only can obtain the result of robustness but also can reduce the artifacts in the background. The above results revealed the MSP method for the potential FMT application.

In vivo fluorescence molecular tomography (FMT) has been a popular functional imaging modality in research labs in the past two decades. One of the major difficulties of FMT lies in the ill-posed and ill-conditioned nature of the inverse problem in reconstructing the distribution of fluorophores inside objects. The popular regularization methods based on L2, L1 and total variation (TV ) norms have been applied in FMT reconstructions. The non-convex Lq(0 < q < 1) semi-norm and Log function have also been studied recently. In this paper, we adopt a uniform optimization transfer framework for these regularization methods in FMT and compare their individual, as well as the combined effects on both small, localized targets, such as tumors in the early stage, and large targets, such as liver. Numerical simulation studies and phantom experiments have been carried out, and we found that Lq with q near 1/2 performs the best in reconstructing small targets, while joint L2 and Log performs the best for large targets.

Fluorescence molecular tomography (FMT) is an important tool for life science, which can noninvasive real-time three-dimensional (3-D) visualization for fluorescence source location. FMT is widely used in tumor research due to its high-sensitive and low cost. However, the reconstruction of FMT is difficult. Although the reconstruction methods of FMT have developed rapidly in recent years, the morphological reconstruction of FMT is still a challenge problem. Thus, the purpose of this study is to realize the morphological reconstruction performance of FMT in glioma research. In this study, group sparsity was used as a new priori information for FMT. Besides sparsity, group sparsity also takes the group structure of the fluorescent sources, which can maintain the morphological information of the sources. Fused LASSO method (FLM) was proved it can efficiently model the group sparsity prior. Thus, we utilize FLM to reconstruct the morphological information of glioma. Furthermore, to reduce the influence of the high scattering of skull, we modified the FLM for improving the accuracy of morphological reconstruction. Glioma numerical simulation model and in vivo glioma model were established to evaluate the performance of morphological reconstruction of the proposed method. The results demonstrated that the proposed method was efficient to reconstruct the morphological information of glioma. Group sparsity priori can effectively improve the morphological accuracy of FMT reconstruction. Group sparsity can maintain the morphological information of fluorescent sources effectively, which has great application potential in FMT. The group sparsity based methods can realize the morphological reconstruction, which is of great practical significance in tumor research.

Fluorescence imaging is a cornerstone of preclinical research, yet its utility is hindered by semi‐quantitative limitations due to light scattering. Fluorescence molecular tomography (FMT) aims to overcome these constraints by generating 3D fluorophore maps through model‐based reconstruction. However, background fluorescence, resulting from non‐specific probe binding and autofluorescence, significantly compromises FMT image quality with severe artifacts. Solution decomposition FMT (SD‐FMT) is introduced, an innovative reconstruction method that employs an advanced prior model to decompose the solution into multiple stochastic components. The reformulated inverse problem is resolved using a hybrid projection method (HPM), ensuring robustness and efficiency. Validated through exhaustive phantom and in vivo proof‐of‐concept studies, SD‐FMT represents a paradigm shift in FMT reconstruction, with significant implications for expanding applications in preclinical research and advancing fluorescence‐guided surgical navigation.

As an optical molecular imaging modality, fluorescence molecular tomography (FMT) can monitor the activities of organisms in vivo at the molecular and cellular levels. However, the recovered image quality is affected by mesh voxel when the finite element method is utilized to recover the fluorescence probe. The target localization is likely to deviate from the actual target under the coarse mesh, but using the fine mesh will increase the number of unknowns, which makes the computational burden heavier and further aggravate the ill-posedness. To solve the problem, a reconstruction strategy using a non-uniform mesh for FMT is developed in this paper. The numerical experiment and physical experiment validated that the strategy is capable and effective for FMT.

BackgroundImplicit shape-based reconstruction method in fluorescence molecular tomography (FMT) is capable of achieving higher image clarity than image-based reconstruction method. However, the implicit shape method suffers from a low convergence speed and performs unstably due to the utilization of gradient-based optimization methods. Moreover, the implicit shape method requires priori information about the number of targets.MethodsA shape-based reconstruction scheme of FMT with a cosinoidal level set method is proposed in this paper. The Heaviside function in the classical implicit shape method is replaced with a cosine function, and then the reconstruction can be accomplished with the Levenberg–Marquardt method rather than gradient-based methods. As a result, the priori information about the number of targets is not required anymore and the choice of step length is avoided.ResultsNumerical simulations and phantom experiments were carried out to validate the proposed method. Results of the proposed method show higher contrast to noise ratios and Pearson correlations than the implicit shape method and image-based reconstruction method. Moreover, the number of iterations required in the proposed method is much less than the implicit shape method.ConclusionsThe proposed method performs more stably, provides a faster convergence speed than the implicit shape method, and achieves higher image clarity than the image-based reconstruction method.

Fluorescence molecular tomography (FMT) plays an important role in in vivo small animal imaging. However, due to the diffusive nature of photon propagation in biological tissues, FMT suffers from a low spatial resolution, which limits its capability of resolving the distribution of fluorescent biomarkers. In this paper, we investigate the effect of functional and structural a priori information on the accuracy of FMT reconstruction by a hybrid FMT and X-ray computed tomography imaging system. The results from numerical simulation and phantom experiments suggest that the fluorescence targets embedded in heterogeneous medium can be localized when structural a priori information is utilized to constrain the reconstruction process. In addition, both the functional and structural a priori information are essential for the recovery of fluorophore concentration.

Herein a two-step Tikhonov regularization-based reconstruction algorithm in fluorescence molecular tomography (FMT) was proposed. The suboptimal and optimal parameter was obtained in two steps alternately. Experimental results suggested that such technique outperform the traditional L-curve criterion that estimating the optimal parameter when applying into the FMT reconstruction.

Non-invasive in vivo imaging of diffuse and wide-spread colonization within the lungs, rather than distinct solid primary tumors, is still a challenging work. In this work, a lung colonization mouse model bearing A549 human lung tumor was simultaneously scanned by a dual-modality fluorescence molecular tomography (FMT) and X-ray computed tomography (CT) system in vivo. A two steps method which incorporates CT structural information into the FMT reconstruction procedure is employed to provide concurrent anatomical and functional information. By using the target-specific fluorescence agent, the fluorescence tomographic results show elevated fluorescence intensity deep within the lungs which is colonized with diffuse and wide-spread tumors. The results were confirmed with ex vivo fluorescence reflectance imaging and histological examination of the lung tissues. With FMT reconstruction combined with the CT information, the dual-modality FMT/micro-CT system is expected to offer sensitive and noninvasive imaging of diffuse tumor colonization within the lungs in vivo.

Unconventional computing devices operating on nonlinear chemical media offer an interesting alternative to standard, semiconductor-based computers. In this work we study in-silico a chemical medium composed of communicating droplets that functions as a database classifier. The droplet network can be "programmed" by an externally provided illumination pattern. The complex relationship between the illumination pattern and the droplet behavior makes manual programming hard. We introduce an evolutionary algorithm that automatically finds the optimal illumination pattern for a given classification problem. Notably, our approach does not require us to prespecify the signals that represent the output classes of the classification problem, which is achieved by using a fitness function that measures the mutual information between chemical oscillation patterns and desired output classes. We illustrate the feasibility of our approach in computer simulations by evolving droplet classifiers for three machine learning datasets. We demonstrate that the same medium composed of 25 droplets located on a square lattice can be successfully used for different classification tasks by applying different illumination patterns as its externally supplied program.

We examine approaches to the incorporation of anatomic structural information into the inverse problem of fluorescence molecular tomography (FMT). Using an appropriate relationship between anatomic and reconstruction image resolution, we build an inverse problem parameterized along the anatomical segmentation. These values serve as the basis for two new regularization techniques. The first regularizes individual voxels in proportion to the importance of the underlying segments in reducing the residual error. The second is based on a well known statistical interpretation of Tikhonov-type regularization in which the statistical prior is defined implicitly as the solution to a PDE whose structure is based on the anatomical segmentation. Results are shown using both techniques for a simulated experiment within the chest cavity of a mouse.

Fluorescence molecular tomography (FMT) could exploit the distribution of fluorescent biomarkers that target tumors accurately and effectively, which enables noninvasive real-time 3-D visualization as well as quantitative analysis of small tumors in small animal studies in vivo. Due to the difficulties of reconstruction, continuous efforts are being made to find more practical and efficient approaches to accurately obtain the characteristics of fluorescent regions inside biological tissues. In this paper, we propose a region reconstruction method for FMT, which is defined as an L1-norm regularization piecewise constant level set approach. The proposed approach adopts a priori information including the sparsity of the fluorescent sources and the fluorescent contrast between the target and background. When the contrast of different fluorescent sources is low to a certain degree, our approach can simultaneously solve the detection and characterization problems for the reconstruction of FMT. To evaluate the performance of the region reconstruction method, numerical phantom experiments and in vivo bead-implanted mouse experiments were performed. The results suggested that the proposed region reconstruction method was able to reconstruct the features of the fluorescent regions accurately and effectively, and the proposed method was able to be feasibly adopted in in vivo application.

Learning-based methods have been proved to perform well in a variety of areas in the biomedical field, such as biomedical image segmentation, and histopathological image analysis. Deep learning, as the most recently presented approach of learning-based methods, has attracted more and more attention. For instance, massive researches of deep learning methods for image reconstructions of computed tomography (CT) and magnetic resonance imaging (MRI) have been reported, indicating the great potential of deep learning for inverse problems. Optical technology-related medical imaging modalities including diffuse optical tomography (DOT), fluorescence molecular tomography (FMT), bioluminescence tomography (BLT), and photoacoustic tomography (PAT) are also dramatically innovated by introducing learning-based methods, in particular deep learning methods, to obtain better reconstruction results. This review depicts the latest researches on learning-based optical tomography of DOT, FMT, BLT, and PAT. According to the most recent studies, learning-based methods applied in the field of optical tomography are categorized as kernel-based methods and deep learning methods. In this review, the former are regarded as a sort of conventional learning-based methods and the latter are subdivided into model-based methods, post-processing methods, and end-to-end methods. Algorithm as well as data acquisition strategy are discussed in this review. The evaluations of these methods are summarized to illustrate the performance of deep learning-based reconstruction.

BackgroundThe inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity. In this research, a tree structured Schur complement decomposition strategy is proposed to accelerate the reconstruction process and reduce the computational complexity. Additionally, an adaptive regularization scheme is developed to improve the ill-posedness of the inverse problem.MethodsThe global system is decomposed level by level with the Schur complement system along two paths in the tree structure. The resultant subsystems are solved in combination with the biconjugate gradient method. The mesh for the inverse problem is generated incorporating the prior information. During the reconstruction, the regularization parameters are adaptive not only to the spatial variations but also to the variations of the objective function to tackle the ill-posed nature of the inverse problem.ResultsSimulation results demonstrate that the strategy of the tree structured Schur complement decomposition obviously outperforms the previous methods, such as the conventional Conjugate-Gradient (CG) and the Schur CG methods, in both reconstruction accuracy and speed. As compared with the Tikhonov regularization method, the adaptive regularization scheme can significantly improve ill-posedness of the inverse problem.ConclusionsThe methods proposed in this paper can significantly improve the reconstructed image quality of FMT and accelerate the reconstruction process.