Determining the Regularization Parameter: A Hybrid Reconstruction Technique in Fluorescence Molecular Tomography

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.

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.

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 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.

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.

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) 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.

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.

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.

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.

The combined system of micro-CT and fluorescence molecular tomography (FMT) offers a new tool to provide anatomical and functional information of small animals in a single study. To take advantages of the combined system, a data preprocessing method is proposed to extract the valid data for FMT reconstruction algorithms using a priori information provided by CT. The boundary information of the animal and animal holder is extracted from reconstructed CT volume data. A ray tracing method is used to trace the path of the excitation beam, calculate the locations and directions of the optional sources and determine whether the optional sources are valid. To accurately calculate the projections of the detectors on optical images and judge their validity, a combination of perspective projection and inverse ray tracing method are adopted to offer optimal performance. The imaging performance of the combined system with the presented method is validated through experimental rat imaging.

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.

To investigate feasibility of applying deep learning image reconstruction (DLIR) algorithm in a low-kilovolt enhanced scan of the upper abdomen. A total of 64 patients (BMI<28) are selected for the enhanced upper abdomen scan and divided evenly into two groups. The tube voltages in Group A are 100kV in arterial phase and 80kV in venous phase, while tube voltages are 120kV during two phases in Group B. Image reconstruction algorithms used in Group A include the filtered back projection (FBP) algorithm, the adaptive statistical iterative reconstruction-Veo (ASIR-V 40% and 80%) algorithm, and the DLIR algorithm (DL-L, DL-M, DL-H). Image reconstruction algorithm used in Group B is ASIR-V40%. The different reconstruction algorithm images are used to measure the common hepatic artery, liver, renal cortex, erector spinae, and subcutaneous adipose in the arterial phase and the average CT value and standard deviation of the portal vein, liver, spleen, erector spinae, and subcutaneous adipose in the portal phase. The signal-to-noise ratio (SNR) is calculated, and the images are also scored subjectively. In Group A, noise in the aorta, liver, portal vein (the portal phase), spleen (the portal phase), renal cortex, retroperitoneal adipose, and muscle is significantly lower in both the DL-H and ASIR-V80% images, and the SNR is significantly higher than those in the remaining groups (P<0.05). The SNR of each tissue and organ in Group B is not significantly different from that in DL-M, DL-L, and ASIR-V40% in Group A (P>0.05). The subjective image quality scores in the DL-H and B groups are higher than those in the other groups, and the FBP group has significantly lower image quality than the remaining groups (P<0.05). For upper abdominal low-kilovolt enhanced scan data, the DLIR-H gear yields a more satisfactory image quality than the FBP and ASIR-V.

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