Fluorescence molecular tomography based on an online maximum a posteriori estimation algorithm

Fluorescence molecular tomography (FMT) is a non-invasive, radiation-free, and highly sensitive optical molecular imaging technique for early tumor detection. However, inadequate measurement information along with significant scattering of near-infrared light within the tissue leads to high ill-posedness in the inverse problem of FMT. To improve the quality and efficiency of FMT reconstruction, we build a reconstruction model based on log-sum regularization and introduce an online maximum a posteriori estimation (OPE) algorithm to solve the non-convex optimization problem. The OPE algorithm approximates a stationary point by evaluating the gradient of the objective function at each iteration, and its notable strength lies in the remarkable speed of convergence. The results of simulations and experiments demonstrate that the OPE algorithm ensures good reconstruction quality and exhibits outstanding performance in terms of reconstruction efficiency.

Regularized reconstruction based on joint smoothly clipped absolute deviation regularization and graph manifold learning for fluorescence molecular tomography

Objective.Fluorescence molecular tomography (FMT) is an optical imaging modality that provides high sensitivity and low cost, which can offer the three-dimensional distribution of biomarkers by detecting the fluorescently labeled probe noninvasively. In the field of preclinical cancer diagnosis and treatment, FMT has gained significant traction. Nonetheless, the current FMT reconstruction results suffer from unsatisfactory morphology and location accuracy of the fluorescence distribution, primarily due to the light scattering effect and the ill-posed nature of the inverse problem.Approach.To address these challenges, a regularized reconstruction method based on joint smoothly clipped absolute deviation regularization and graph manifold learning (SCAD-GML) for FMT is presented in this paper. The SCAD-GML approach combines the sparsity of the fluorescent sources with the latent manifold structure of fluorescent source distribution to achieve more accurate and sparse reconstruction results. To obtain the reconstruction results efficiently, the non-convex gradient descent iterative method is employed to solve the established objective function. To assess the performance of the proposed SCAD-GML method, a comprehensive evaluation is conducted through numerical simulation experiments as well asin vivoexperiments.Main results.The results demonstrate that the SCAD-GML method outperforms other methods in terms of both location and shape recovery of fluorescence biomarkers distribution.Siginificance.These findings indicate that the SCAD-GML method has the potential to advance the application of FMT inin vivobiological research.

Excitation-based fully connected network for precise NIR-II fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is a novel imaging modality to obtain fluorescence biomarkers' three-dimensional (3D) distribution. However, the simplified mathematical model and complicated inverse problem limit it to achieving precise results. In this study, the second near-infrared (NIR-II) fluorescence imaging was adopted to mitigate tissue scattering and reduce noise interference. An excitation-based fully connected network was proposed to model the inverse process of NIR-II photon propagation and directly obtain the 3D distribution of the light source. An excitation block was embedded in the network allowing it to autonomously pay more attention to neurons related to the light source. The barycenter error was added to the loss function to improve the localization accuracy of the light source. Both numerical simulation and in vivo experiments showed the superiority of the novel NIR-II FMT reconstruction strategy over the baseline methods. This strategy was expected to facilitate the application of machine learning in biomedical research.

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.

L1-L2 norm regularization via forward-backward splitting for fluorescence molecular tomography

Fluorescent molecular tomography (FMT) is a highly sensitive and noninvasive imaging approach for providing three-dimensional distribution of fluorescent marker probes. However, owing to its light scattering effect and the ill-posedness of inverse problems, it is challenging to develop an efficient reconstruction algorithm that can achieve the exact location and morphology of the fluorescence source. In this study, therefore, in order to satisfy the need for early tumor detection and improve the sparsity of solution, we proposed a novel L ₁-L ₂ norm regularization via the forward-backward splitting method for enhancing the FMT reconstruction accuracy and the robustness. By fully considering the highly coherent nature of the system matrix of FMT, it operates by splitting the objective to be minimized into simpler functions, which are dealt with individually to obtain a sparser solution. An analytic solution of L ₁-L ₂ norm proximal operators and a forward-backward splitting algorithm were employed to efficiently solve the nonconvex L ₁-L ₂ norm minimization problem. Numerical simulations and an in-vivo glioma mouse model experiment were conducted to evaluate the performance of our algorithm. The comparative results of these experiments demonstrated that the proposed algorithm obtained superior reconstruction performance in terms of spatial location, dual-source resolution, and in-vivo practicability. It was believed that this study would promote the preclinical and clinical applications of FMT in early tumor detection.

K-Nearest Neighbor Based Locally Connected Network for Fast Morphological Reconstruction in Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive imaging modality for three-dimensional visualization of fluorescence probe distribution in small animals. However, the simplified photon propagation model and ill-posed inverse problem limit the improvement of FMT reconstruction. In this work, we proposed a novel K-nearest neighbor based locally connected (KNN-LC) network to improve the performance of morphological reconstruction in FMT. It directly builds the inverse process of photon transmission by learning the mapping relation between the surface photon intensity and the distribution of fluorescent source. KNN-LC network cascades a fully connected (FC) sub-network with a locally connected (LC) sub-network, where the FC part provides a coarse reconstruction result and LC part fine-tunes the morphological quality of reconstructed result. To assess the performance of our proposed network, we implemented both numerical simulation and in vivo studies. Furthermore, split Bregman-resolved total variation (SBRTV) regularization method and inverse problem simulation (IPS) method were utilized as baselines in all comparisons. The results demonstrated that KNN-LC network achieved accurate reconstruction in both source localization and morphology recovery in a short time. This promoted the in vivo application of FMT for visualizing the distribution of biomarkers inside biological tissue.

Adaptive Gaussian Weighted Laplace Prior Regularization Enables Accurate Morphological Reconstruction in Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT), as a powerful imaging technique in preclinical research, can offer the three-dimensional distribution of biomarkers by detecting the fluorescently labelled probe noninvasively. However, because of the light scattering effect and the ill-pose of inverse problem, it is challenging to develop an efficient reconstruction method, which can provide accurate location and morphology of the fluorescence distribution. In this research, we proposed a novel adaptive Gaussian weighted Laplace prior (AGWLP) regularization method, which assumed the variance of fluorescence intensity between any two voxels had a non-linear correlation with their Gaussian distance. It utilized an adaptive Gaussian kernel parameter strategy to achieve accurate morphological reconstructions in FMT. To evaluate the performance of the AGWLP method, we conducted numerical simulation and in vivo experiments. The results were compared with fast iterative shrinkage (FIS) thresholding method, split Bregman-resolved TV (SBRTV) regularization method, and Gaussian weighted Laplace prior (GWLP) regularization method. We validated in vivo imaging results against planar fluorescence images of frozen sections. The results demonstrated that the AGWLP method achieved superior performance in both location and shape recovery of fluorescence distribution. This enabled FMT more suitable and practical for in vivo visualization of biomarkers.

Robust Reconstruction of Fluorescence Molecular Tomography Based on Sparsity Adaptive Correntropy Matching Pursuit Method for Stem Cell Distribution

Fluorescence molecular tomography (FMT), as a promising imaging modality in preclinical research, can obtain the three-dimensional (3-D) position information of the stem cell in mice. However, because of the ill-posed nature and sensitivity to noise of the inverse problem, it is a challenge to develop a robust reconstruction method, which can accurately locate the stem cells and define the distribution. In this paper, we proposed a sparsity adaptive correntropy matching pursuit (SACMP) method. SACMP method is independent on the noise distribution of measurements and it assigns small weights on severely corrupted entries of data and large weights on clean ones adaptively. These properties make it more suitable for in vivo experiment. To analyze the performance in terms of robustness and practicability of SACMP, we conducted numerical simulation and in vivo mice experiments. The results demonstrated that the SACMP method obtained the highest robustness and accuracy in locating stem cells and depicting stem cell distribution compared with stagewise orthogonal matching pursuit and sparsity adaptive subspace pursuit reconstruction methods. To the best of our knowledge, this is the first study that acquired such accurate and robust FMT distribution reconstruction for stem cell tracking in mice brain. This promotes the application of FMT in locating stem cell and distribution reconstruction in practical mice brain injury models.

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.

Near-Infrared Fluorescence-Enhanced Optical Tomography

Fluorescence-enhanced optical imaging using near-infrared (NIR) light developed for in vivo molecular targeting and reporting of cancer provides promising opportunities for diagnostic imaging. The current state of the art of NIR fluorescence-enhanced optical tomography is reviewed in the context of the principle of fluorescence, the different measurement schemes employed, and the mathematical tools established to tomographically reconstruct the fluorescence optical properties in various tissue domains. Finally, we discuss the recent advances in forward modeling and distributed memory parallel computation to provide robust, accurate, and fast fluorescence-enhanced optical tomography.

Reconstruction algorithm for fluorescence molecular tomography using sorted L-one penalized estimation

Fluorescence molecular tomography (FMT) has been a promising imaging tool that provides convenience for accurate localization and quantitative analysis of the fluorescent probe. In this study, we present a reconstruction method combining sorted L-one penalized estimation with an iterative-shrinking permissible region strategy to reconstruct fluorescence targets. Both numerical simulation experiments on a three-dimensional digital mouse model and physical experiments on a cubic phantom were carried out to validate the accuracy, effectiveness, and robustness of the proposed method. The results indicate that the proposed method can produce better location and satisfactory fluorescent yield with computational efficiency, which makes it a practical and promising reconstruction method for FMT.

Temporal Unmixing of Dynamic Fluorescent Images by Blind Source Separation Method with a Convex Framework

By recording a time series of tomographic images, dynamic fluorescence molecular tomography (FMT) allows exploring perfusion, biodistribution, and pharmacokinetics of labeled substances in vivo. Usually, dynamic tomographic images are first reconstructed frame by frame, and then unmixing based on principle component analysis (PCA) or independent component analysis (ICA) is performed to detect and visualize functional structures with different kinetic patterns. PCA and ICA assume sources are statistically uncorrelated or independent and don't perform well when correlated sources are present. In this paper, we deduce the relationship between the measured imaging data and the kinetic patterns and present a temporal unmixing approach, which is based on nonnegative blind source separation (BSS) method with a convex analysis framework to separate the measured data. The presented method requires no assumption on source independence or zero correlations. Several numerical simulations and phantom experiments are conducted to investigate the performance of the proposed temporal unmixing method. The results indicate that it is feasible to unmix the measured data before the tomographic reconstruction and the BSS based method provides better unmixing quality compared with PCA and ICA.

Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization

Fluorescence molecular tomography (FMT) is a promising imaging technique that allows in vivo visualization of molecular-level events associated with disease progression and treatment response. Accurate and efficient 3D reconstruction algorithms will facilitate the wide-use of FMT in preclinical research. Here, we utilize L1/2-norm regularization for improving FMT reconstruction. To efficiently solve the nonconvex L1/2-norm penalized problem, we transform it into a weighted L1-norm minimization problem and employ a homotopy-based iterative reweighting algorithm to recover small fluorescent targets. Both simulations on heterogeneous mouse model and in vivo experiments demonstrated that the proposed L1/2-norm method outperformed the comparative L1-norm reconstruction methods in terms of location accuracy, spatial resolution and quantitation of fluorescent yield. Furthermore, simulation analysis showed the robustness of the proposed method, under different levels of measurement noise and number of excitation sources.

Fast and robust reconstruction for fluorescence molecular tomography via a sparsity adaptive subspace pursuit method

Fluorescence molecular tomography (FMT), as a promising imaging modality, can three-dimensionally locate the specific tumor position in small animals. However, it remains challenging for effective and robust reconstruction of fluorescent probe distribution in animals. In this paper, we present a novel method based on sparsity adaptive subspace pursuit (SASP) for FMT reconstruction. Some innovative strategies including subspace projection, the bottom-up sparsity adaptive approach, and backtracking technique are associated with the SASP method, which guarantees the accuracy, efficiency, and robustness for FMT reconstruction. Three numerical experiments based on a mouse-mimicking heterogeneous phantom have been performed to validate the feasibility of the SASP method. The results show that the proposed SASP method can achieve satisfactory source localization with a bias less than 1mm; the efficiency of the method is much faster than mainstream reconstruction methods; and this approach is robust even under quite ill-posed condition. Furthermore, we have applied this method to an in vivo mouse model, and the results demonstrate the feasibility of the practical FMT application with the SASP method.

Adaptive regularized method based on homotopy for sparse fluorescence tomography

Determining an appropriate regularization parameter is often challenging work because it has a narrow range and varies with problems, which is likely to lead to large reconstruction errors. In this contribution, an adaptive regularized method based on homotopy is presented for sparse fluorescence tomography reconstruction. Due to the adaptive regularization strategy, the proposed method is always able to reconstruct sources accurately independent of the estimation of the regularization parameter. Moreover, the proposed method is about two orders of magnitude faster than the two contrasting methods. Numerical and in vivo mouse experiments have been employed to validate the robustness and efficiency of the proposed method.

Weighted depth compensation algorithm for fluorescence molecular tomography reconstruction

In fluorescence molecular tomography (FMT), diffuse-light measurements are obtained from a series of source-detector pairs placed on the boundary of the medium. The sensitivity of measurements deteriorates quickly with increased distance from the sources and detectors and therefore yields poor depth quantitative recovery. A depth compensation algorithm is presented in this paper to reconstruct fluorescent inclusions in deep tissues. Two weight matrixes are employed to level off sensitivity differences and enhance prominent elements of the solution. Results of numerical and phantom experiments demonstrate that both relative quantitation and spatial resolution of FMT are improved for inclusions at different depths.

Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography

In this paper, a multilevel, hybrid regularization method is presented for fluorescent molecular tomography (FMT) based on the hp-finite element method (hp-FEM) with a continuous wave. The hybrid regularization method combines sparsity regularization and Landweber iterative regularization to improve the stability of the solution of the ill-posed inverse problem. In the first coarse mesh level, considering the fact that the fluorescent probes are sparsely distributed in the entire reconstruction region in most FMT applications, the sparse regularization method is employed to take full advantage of this sparsity. In the subsequent refined mesh levels, since the reconstruction region is reduced and the initial value of the unknown parameters is provided from the previous mesh, these mesh levels seem to be different from the first level. As a result, the Landweber iterative regularization method is applied for reconstruction. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are conducted to evaluate the performance of our method. The reconstructed results show the potential and feasibility of the proposed approach.

Normalized Born Approximation-Based Two-Stage Reconstruction Algorithm for Quantitative Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is a promising technique forin vivosmall animal imaging. In this paper, a two-stage reconstruction method based on normalized Born approximation is developed for FMT, which includes two steps for quantitative reconstruction. First, the localization of fluorescent fluorophore is determined byl1-norm regularization method. Then, in the location region of fluorophore, which is provided by the first stage, algebraic reconstruction technique (ART) is utilized for the fluorophore concentration reconstruction. The validity of the two-stage quantitative reconstruction algorithm is testified by simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom. The results suggest that we are able to recover the fluorophore location and concentration.

Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis

Dynamic fluorescence diffuse optical tomography (D-FDOT) is important for drug delivery research. However, the low spatial resolution of FDOT and the complex kinetics of drug limit the ability of D-FDOT in resolving metabolic processes of drug throughout whole body of small animals. In this paper, we propose an independent component analysis (ICA)-based method to perform D-FDOT studies. When applied to D-FDOT images, ICA not only generates a set of independent components (ICs) which can illustrate functional structures with different kinetic behaviors, but also provides a set of associated time courses (TCs) which can represent normalized time courses of drug in corresponding functional structures. Further, the drug concentration in specific functional structure at different time points can be recovered by an inverse ICA transformation. To evaluate the performance of the proposed algorithm in the study of drug kinetics at whole-body level, simulation study and phantom experiment are both performed on a full-angle FDOT imaging system with line-shaped excitation pattern. In simulation study, the nanoparticle delivery of indocynaine green (ICG) throughout whole body of a digital mouse is simulated and imaged. In phantom experiment, four tubes containing different ICG concentrations are imaged and used to imitate the uptake and excretion of ICG in organs. The results suggest that we can not only illustrate ICG distributions in different functional structures, but also recover ICG concentrations in specific functional structure at different time points, when ICA is applied to D-FDOT images.

Efficient reconstruction method for L1 regularization in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is a promising technique for in vivo small animal imaging. In this paper, the sparsity of the fluorescent sources is considered as the a priori information and is promoted by incorporating L1 regularization. Then a reconstruction algorithm based on stagewise orthogonal matching pursuit is proposed, which treats the FMT problem as the basis pursuit problem. To evaluate this method, we compare it to the iterated-shrinkage-based algorithm with L1 regularization. Numerical simulations and physical experiments show that the proposed method can obtain comparable or even slightly better results. More importantly, the proposed method was at least 2 orders of magnitude faster in these experiments, which makes it a practical reconstruction algorithm.

Principal component analysis of dynamic fluorescence diffuse optical tomography images

Challenges remain in resolving drug distributions within small animals utilizing fluorescence diffuse optical tomography (FDOT). In this paper, we present a new method for detecting and visualizing organs with different kinetics utilizing principal component analysis (PCA). Indocynaine green (ICG) metabolic processes are simulated and imaged using FDOT. When applied to the time series of generated FDOT images, PCA provides a set of the principal components (PCs) which can represent spatial patterns associated with different kinetic behavior. Simulation and experiment studies are both performed to validate the performance of the proposed algorithm. The results suggest that we are able to extract and illustrate changes in ICG kinetic behavior between the heart and the lungs.

Analysis of fast full angle fluorescence diffuse optical tomography with beam-forming illumination

Challenges remain in imaging fast biological activities through whole body using fluorescence diffuse optical tomography (FDOT). We propose and analyze three full angle FDOT systems with different beam-forming illuminations (BF-FDOT), including line illumination (L-FDOT), area illumination (A-FDOT), and multiple-points illumination (MP-FDOT). Singular value analysis and experimental validation are used to optimize the experimental parameters in terms of hardware design, data collection and utilization. Comparisons are made on the system performance between L-FDOT and the conventional point illumination based full angle FDOT system (P-FDOT) with both numerical simulation and phantom experiment. We demonstrate that at least three cycles of projections are needed for P-FDOT to achieve comparable whole body image quality with L-FDOT. We also compare these three BF-FDOT systems and further discuss how these optimized parameters can be employed to improve spatial and temporal performances within current computational capacities, and guide the design of the BF-FDOT systems.