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

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.

3D-deep optical learning: a multimodal and multitask reconstruction framework for optical molecular tomography

Optical molecular tomography (OMT) is an emerging imaging technique. To date, the poor universality of reconstruction algorithms based on deep learning for various imaged objects and optical probes limits the development and application of OMT. In this study, based on a new mapping representation, a multimodal and multitask reconstruction framework-3D deep optical learning (3DOL), was presented to overcome the limitations of OMT in universality by decomposing it into two tasks, optical field recovery and luminous source reconstruction. Specifically, slices of the original anatomy (provided by computed tomography) and boundary optical measurement of imaged objects serve as inputs of a recurrent convolutional neural network encoded parallel to extract multimodal features, and 2D information from a few axial planes within the samples is explicitly incorporated, which enables 3DOL to recognize different imaged objects. Subsequently, the optical field is recovered under the constraint of the object geometry, and then the luminous source is segmented by a learnable Laplace operator from the recovered optical field, which obtains stable and high-quality reconstruction results with extremely few parameters. This strategy enable 3DOL to better understand the relationship between the boundary optical measurement, optical field, and luminous source to improve 3DOL's ability to work in a wide range of spectra. The results of numerical simulations, physical phantoms, and in vivo experiments demonstrate that 3DOL is a compatible deep-learning approach to tomographic imaging diverse objects. Moreover, the fully trained 3DOL under specific wavelengths can be generalized to other spectra in the 620-900 nm NIR-I window.

Two-stage deep learning method for sparse-view fluorescence molecular tomography reconstruction

Fluorescence molecular tomography (FMT) is a preclinical optical tomographic imaging technique that can trace various physiological and pathological processes at the cellular or even molecular level. Reducing the number of FMT projection views can improve the data acquisition speed, which is significant in applications such as dynamic problems. However, a reduction in the number of projection views will dramatically aggravate the ill-posedness of the FMT inverse problem and lead to significant degradation of the reconstructed images. To deal with this problem, we have proposed a deep-learning-based reconstruction method for sparse-view FMT that only uses four perpendicular projection views and divides the image reconstruction into two stages: image restoration and inverse Radon transform. In the first stage, the projection views of the surface fluorescence are restored to eliminate the blur derived from photon diffusion through a fully convolutional neural network. In the second stage, another convolutional neural network is used to implement the inverse Radon transform between the restored projections from the first stage and the reconstructed transverse slices. Numerical simulation and phantom and mouse experiments are carried out. The results show that the proposed method can effectively deal with the image reconstruction problem of sparse-view FMT.

Adaptive Sparsity Orthogonal Least Square with Neighbor Strategy for Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive optical imaging technique which has been widely applied to disease diagnosis and drug discovery. However, FMT reconstruction is a highly ill-posed problem. In this work, L0-norm regularization is employed to construct the mathematical model of the inverse problem of FMT. And an adaptive sparsity orthogonal least square with a neighbor strategy (ASOLS-NS) is proposed to solve this model. This algorithm can provide an adaptive sparsity and can establish the candidate sets by a novel neighbor expansion strategy for the orthogonal least square (OLS) algorithm. Numerical simulation experiments have shown that the ASOLS-NS improves the reconstruction of images, especially for the double targets reconstruction.Clinical relevance- The purpose of this work is to improve the reconstruction results of FMT. Current experiments are focused on simulation experiments, and the proposed algorithm will be applied to the clinical tumor detection in the future.

Robust transformed l1 metric for fluorescence molecular tomography

BACKGROUND AND OBJECTIVE

Fluorescence molecular tomography (FMT) is a non-invasive molecular imaging modality that can be used to observe the three-dimensional distribution of fluorescent probes in vivo. FMT is a promising imaging technique in clinical and preclinical research that has attracted significant attention. Numerous regularization based reconstruction algorithms have been proposed. However, traditional algorithms that use the squared l₂-norm distance usually exaggerate the influence of noise and measurement and calculation errors, and their robustness cannot be guaranteed.

METHODS

In this study, we propose a novel robust transformed l₁ (TL1) metric that interpolates l₀ and l₁ norms through a nonnegative parameter α∈(0,+∞). The TL1 metric looks like the l_p-norm with p∈(0,1). These are markedly different because TL1 metric has two properties, boundedness and Lipschitz-continuity, which make the TL1 criterion suitable distance metric, particularly for robustness, owing to its stronger noise suppression. Subsequently, we apply the proposed metric to FMT and build a robust model to reduce the influence of noise. The nonconvexity of the proposed model made direct optimization difficult, and a continuous optimization method was developed to solve the model. The problem was converted into a difference in convex programming problem for the TL1 metric (DCATL1), and the corresponding algorithm converged linearly.

RESULTS

Various numerical simulations and in vivo bead-implanted mouse experiments were conducted to verify the performance of the proposed method. The experimental results show that the DCATL1 algorithm is more robust than the state-of-the-art approaches and achieves better source localization and morphology recovery.

CONCLUSIONS

The in vivo experiments showed that DCATL1 can be used to visualize the distribution of fluorescent probes inside biological tissues and promote preclinical application in small animals, demonstrating the feasibility and effectiveness of the proposed method.

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 novel weighted auxiliary set matching pursuit method for glioma in Cerenkov luminescence tomography reconstruction

Cerenkov luminescence tomography (CLT) is a promising three-dimensional imaging technology that has been actively investigated in preclinical studies. However, because of the ill-posedness in the inverse problem of CLT reconstruction, the reconstruction performance is still not satisfactory for broad biomedical applications. In this study, a novel weighted auxiliary set matching pursuit (WASMP) method was explored to enhance the accuracy of CLT reconstruction. The numerical simulations and in vivo imaging studies using tumor-bearing mice models were conducted to evaluate the performance of the WASMP method. The results of the above experiments proved that the WASMP method achieved superior reconstruction performance than other approaches in terms of positional accuracy and shape recovery. It further demonstrates that the atom selection strategy proposed in this study has a positive effect on improving the accuracy of atoms. The proposed WASMP improves the accuracy for CLT reconstruction for biomedical applications.

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.

A Fast and Automated FMT/XCT Reconstruction Strategy Based on Standardized Imaging Space

The traditional finite element method-based fluorescence molecular tomography (FMT)/ X-ray computed tomography (XCT) imaging reconstruction suffers from complicated mesh generation and dual-modality image data fusion, which limits the application of in vivo imaging. To solve this problem, a novel standardized imaging space reconstruction (SISR) method for the quantitative determination of fluorescent probe distributions inside small animals was developed. In conjunction with a standardized dual-modality image data fusion technology, and novel reconstruction strategy based on Laplace regularization and L1-fused Lasso method, the in vivo distribution can be calculated rapidly and accurately, which enables standardized and algorithm-driven data process. We demonstrated the method's feasibility through numerical simulations and quantitatively monitored in vivo programmed death ligand 1 (PD-L1) expression in mouse tumor xenografts, and the results demonstrate that our proposed SISR can increase data throughput and reproducibility, which helps to realize the dynamically and accurately in vivo imaging.

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.

Attention mechanism-based locally connected network for accurate and stable reconstruction in Cerenkov luminescence tomography

Cerenkov luminescence tomography (CLT) is a novel and highly sensitive imaging technique, which could obtain the three-dimensional distribution of radioactive probes to achieve accurate tumor detection. However, the simplified radiative transfer equation and ill-conditioned inverse problem cause a reconstruction error. In this study, a novel attention mechanism based locally connected (AMLC) network was proposed to reduce barycenter error and improve morphological restorability. The proposed AMLC network consisted of two main parts: a fully connected sub-network for providing a coarse reconstruction result, and a locally connected sub-network based on an attention matrix for refinement. Both numerical simulations and in vivo experiments were conducted to show the superiority of the AMLC network in accuracy and stability over existing methods (MFCNN, KNN-LC network). This method improved CLT reconstruction performance and promoted the application of machine learning in optical imaging research.

Correntropy-induced metric with Laplacian kernel for robust fluorescence molecular tomography

Fluorescence molecular tomography (FMT), which is used to visualize the three-dimensional distribution of fluorescence probe in small animals via the reconstruction method, has become a promising imaging technique in preclinical research. However, the classical reconstruction criterion is formulated based on the squared l ₂-norm distance metric, leaving it prone to being influenced by the presence of outliers. In this study, we propose a robust distance based on the correntropy-induced metric with a Laplacian kernel (CIML). The proposed metric satisfies the conditions of distance metric function and contains first and higher order moments of samples. Moreover, we demonstrate important properties of the proposed metric such as nonnegativity, nonconvexity, and boundedness, and analyze its robustness from the perspective of M-estimation. The proposed metric includes and extends the traditional metrics such as l ₀-norm and l ₁-norm metrics by setting an appropriate parameter. We show that, in reconstruction, the metric is a sparsity-promoting penalty. To reduce the negative effects of noise and outliers, a novel robust reconstruction framework is presented with the proposed correntropy-based metric. The proposed CIML model retains the advantages of the traditional model and promotes robustness. However, the nonconvexity of the proposed metric renders the CIML model difficult to optimize. Furthermore, an effective iterative algorithm for the CIML model is designed, and we present a theoretical analysis of its ability to converge. Numerical simulation and in vivo mouse experiments were conducted to evaluate the CIML method's performance. The experimental results show that the proposed method achieved more accurate fluorescent target reconstruction than the state-of-the-art methods in most cases, which illustrates the feasibility and robustness of the CIML method.

A robust elastic net-ℓ1ℓ2reconstruction method for x-ray luminescence computed tomography

Objective. X-ray luminescence computed tomography (XLCT) has played a crucial role in pre-clinical research and effective diagnosis of disease. However, due to the ill-posed of the XLCT inverse problem, the generalization of reconstruction methods and the selection of appropriate regularization parameters are still challenging in practical applications. In this research, an robust Elastic net-ℓ₁ℓ₂reconstruction method is proposed aiming to the challenge.Approach. Firstly, our approach consists of ℓ₁and ℓ₂regularization to enhance the sparsity and suppress the smoothness. Secondly, through optimal approximation of the optimization problem, double modification of Landweber algorithm is adopted to solve the Elastic net-ℓ₁ℓ₂regulazation. Thirdly, drawing on the ideal of supervised learning, multi-parameter K-fold cross validation strategy is proposed to determin the optimal parameters adaptively.Main results. To evaluate the performance of the Elastic net-ℓ₁ℓ₂method, numerical simulations, phantom and in vivo experiments were conducted. In these experiments, the Elastic net-ℓ₁ℓ₂method achieved the minimum reconstruction error (with smallest location error, fluorescent yield relative error, normalized root-mean-square error) and the best image reconstruction quality (with largest contrast-to-noise ratio and Dice similarity) among all methods. The results demonstrated that Elastic net-ℓ₁ℓ₂can obtain superior reconstruction performance in terms of location accuracy, dual source resolution, robustness and in vivo practicability.Significance. It is believed that this study will further benefit preclinical applications with a view to provide a more reliable reference for the later researches on XLCT.

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 shrinking reconstruction framework for cone-beam X-ray luminescence computed tomography

Cone-beam X-ray luminescence computed tomography (CB-XLCT) emerged as a novel hybrid technique for early detection of small tumors in vivo. However, severe ill-posedness is still a challenge for CB-XLCT imaging. In this study, an adaptive shrinking reconstruction framework without a prior information is proposed for CB-XLCT. In reconstruction processing, the mesh nodes are automatically selected with higher probability to contribute to the distribution of target for imaging. Specially, an adaptive shrinking function is designed to automatically control the permissible source region at a multi-scale rate. Both 3D digital mouse and in vivo experiments were carried out to test the performance of our method. The results indicate that the proposed framework can dramatically improve the imaging quality of CB-XLCT.

NIR-II/NIR-I Fluorescence Molecular Tomography of Heterogeneous Mice Based on Gaussian Weighted Neighborhood Fused Lasso Method

Fluorescence molecular tomography (FMT), which can visualize the distribution of fluorescence biomarkers, has become a novel three-dimensional noninvasive imaging technique for in vivo studies such as tumor detection and lymph node location. However, it remains a challenging problem to achieve satisfactory reconstruction performance of conventional FMT in the first near-infrared window (NIR-I, 700-900nm) because of the severe scattering of NIR-I light. In this study, a promising FMT method for heterogeneous mice was proposed to improve the reconstruction accuracy using the second near-infrared window (NIR-II, 1000-1700nm), where the light scattering significantly reduced compared with NIR-I. The optical properties of NIR-II were analyzed to construct the forward model for NIR-II FMT. Furthermore, to raise the accuracy of solution of the inverse problem, we proposed a novel Gaussian weighted neighborhood fused Lasso (GWNFL) method. Numerical simulation was performed to demonstrate the outperformance of GWNFL compared with other algorithms. Besides, a novel NIR-II/NIR-I dual-modality FMT system was developed to contrast the in vivo reconstruction performance between NIR-II FMT and NIR-I FMT. To compare the reconstruction performance of NIR-II FMT with traditional NIR-I FMT, numerical simulations and in vivo experiments were conducted. Both the simulation and in vivo results showed that NIR-II FMT outperformed NIR-I FMT in terms of location accuracy and spatial overlap index. It is believed that this study could promote the development and biomedical application of NIR-II FMT in the future.

An Artificial Intelligent Signal Amplification System for in vivo Detection of miRNA

MicroRNAs (miRNA) have been identified as oncogenic drivers and tumor suppressors in every major cancer type. In this work, we design an artificial intelligent signal amplification (AISA) system including double-stranded SQ (S, signal strand; Q, quencher strand) and FP (F, fuel strand; P, protect strand) according to thermodynamics principle for sensitive detection of miRNA in vitro and in vivo. In this AISA system for miRNA detection, strand S carries a quenched imaging marker inside the SQ. Target miRNA is constantly replaced by a reaction intermediate and circulatively participates in the reaction, similar to enzyme. Therefore, abundant fluorescent substances from S and SP are dissociated from excessive SQ for in vitro and in vivo visualization. The versatility and feasibility for disease diagnosis using this system were demonstrated by constructing two types of AISA system to detect Hsa-miR-484 and Hsa-miR-100, respectively. The minimum target concentration detected by the system in vitro (10 min after mixing) was 1/10th that of the control group. The precancerous lesions of liver cancer were diagnosed, and the detection accuracy were larger than 94% both in terms of location and concentration. The ability to establish this design framework for AISA system with high specificity provides a new way to monitor tumor progression and to assess therapeutic responses.

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.

Adaptive block forward and backward stagewise orthogonal matching pursuit algorithm applied to rolling bearing fault signal reconstruction

In the process of block compressed sensing (CS) applied to the rolling bearing fault signal, the reconstruction accuracy of the signal is low due to the large difference in sparsity between blocks and the unreasonable components of reconstruction support set, which affects the overall reconstruction effect of the signal. To improve the signal reconstruction results, forward and backward stagewise orthogonal matching pursuit (FBStOMP) based on the adaptive block method is proposed. First, to equalize the sparsity of each block signal, the fault signal is divided into blocks according to the adaptive block length, which is obtained by the short-time autocorrelation algorithm. Then, the K-singular value decomposition algorithm is used to train the sparse dictionary to obtain a better sparse effect. Finally, the FBStOMP algorithm is proposed. The atom backtracking and screening process is added in the reconstruction process to improve the possibility that all the effective atoms can be selected into the support set. The experimental analysis of the simulation signal and bearing fault signal show that, compared with the traditional CS reconstruction algorithm, the adaptive block-FBStOMP algorithm proposed in the paper can effectively improve the reconstruction accuracy of the bearing fault signal.

Smart Toolkit for Fluorescence Tomography: Simulation, Reconstruction, and Validation

OBJECTIVE

Fluorescence molecular tomography (FMT) can provide valuable molecular information by mapping the bio-distribution of fluorescent reporter molecules in the intact organism. Various prototype FMT systems have been introduced during the past decade. However, none of them has evolved as a standard tool for routine biomedical research. The goal of this paper is to develop a software package that can automate the complete FMT reconstruction procedure.

METHODS

We present smart toolkit for fluorescence tomography (STIFT), a comprehensive platform comprising three major protocols: 1) virtual FMT, i.e., forward modeling and reconstruction of simulated data; 2) control of actual FMT data acquisition; and 3) reconstruction of experimental FMT data.

RESULTS

Both simulation and phantom experiments have shown robust reconstruction results for homogeneous and heterogeneous tissue-mimicking phantoms containing fluorescent inclusions.

CONCLUSION

STIFT can be used for optimization of FMT experiments, in particular for optimizing illumination patterns.

SIGNIFICANCE

This paper facilitates FMT experiments by bridging the gaps between simulation, actual experiments, and data reconstruction.