A fast reconstruction algorithm for fluorescence molecular tomography via multipath subspace pursuit method

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.

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.

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.

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) 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.

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.

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.

Fluorescence molecular tomography (FMT) is an emerging tool for biomedical research. There are two factors that influence FMT reconstruction most effectively. The first one is regularization techniques. Traditional methods such as Tikhonov regularization suffer from low resolution and poor signal to noise ratio. Therefore, sparse regularization techniques have been introduced to improve the reconstruction quality. The second factor is the illumination pattern. A better illumination pattern ensures the quantity and quality of the information content of the data set, thus leading to better reconstructions. In this work, we take advantage of the discrete formulation of the forward problem to give a rigorous definition of an illumination pattern as well as the admissible set of patterns. We add restrictions in the admissible set as different types of regularizers to a discrepancy functional, generating another inverse problem with the illumination pattern as unknown. Both inverse problems of reconstructing the fluorescence distribution and finding the optimal illumination pattern are solved by efficient iterative algorithms. Numerical experiments have shown that with a suitable choice of regularization parameters, the two-step approach converges to an optimal illumination pattern quickly and the reconstruction result is improved significantly regardless of the initial illumination setting.

A fast surface reconstruction method for fluorescence molecular tomography based on cross-beam edge back projection

Through the reconstruction of the fluorescent probe distributions, fluorescence molecular tomography (FMT) can three-dimensionally resolve the molecular processes in small animals in vivo. In this paper, we propose an FMT reconstruction algorithm based on the iterated shrinkage method. By incorporating a surrogate function, the original optimization problem can be decoupled, which enables us to use the general sparsity regularization. Due to the sparsity characteristic of the fluorescent sources, the performance of this method can be greatly enhanced, which leads to a fast reconstruction algorithm. Numerical simulations and physical experiments were conducted. Compared to Newton method with Tikhonov regularization, the iterated shrinkage based algorithm can obtain more accurate results, even with very limited measurement data.

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.

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.

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.

The adaptive finite element method (AFEM) is an effective way to retain enough resolution in selected regions while improving computational efficiency for reconstruction in fluorescent molecular tomography (FMT). In addition, background optical properties acquired by diffuse optical tomography (DOT) will improve the quality of reconstructed images. In this work, a DOT-guided adaptive reconstruction method (DGARM) is proposed, in which DOT is introduced into an adaptive reconstruction framework of FMT. Besides being used as functional a priori information in the forward modeling, the reconstructed local absorption coefficients in DOT are also used to form internal structural a priori information, which is further used to identify regions of interest (ROIs) in the mesh refinement of the adaptive procedure. Because optical properties are recovered before the formulation of FMT, a linear relationship is established between the fluorescent field and boundary measurements. We implemented numerical simulations and physical experiments to evaluate the performance of the algorithm. Compared with the strategies of uniform meshing with DOT and AFEM without DOT, DGAM improves localization accuracy of the reconstruction of fluorescence inclusion.