Reconstruction for Fluorescence Molecular Tomography via Adaptive Group Orthogonal Matching Pursuit

Multi-target reconstruction based on subspace decision optimization for bioluminescence tomography

BACKGROUND AND OBJECTIVE

Bioluminescence tomography (BLT) is a noninvasive optical imaging technique that provides qualitative and quantitative information on the spatial distribution of tumors in living animals. Researchers have proposed a list of algorithms and strategies for BLT reconstruction to improve its reconstruction quality. However, multi-target BLT reconstruction remains challenging in practical clinical applications due to the mutual interference of optical signals and difficulty in source separation.

METHODS

To solve this problem, this study proposes the subspace decision optimization (SDO) approach based on the traditional iterative permissible region strategy. The SDO approach transforms a single permissible region into multiple subspaces by clustering analysis. These subspaces are shrunk based on subspace shrinking optimization to achieve spatial continuity of the permissible regions. In addition, these subspaces are merged to construct a new permissible region and then the next iteration of reconstruction is carried out to ensure the stability of the results. Finally, all the iterative results are optimized based on the normal distribution model and the distribution properties of the targets to ensure the sparsity of each target and the non-biasing of the overall results.

RESULTS

Experimental results show that the SDO approach can automatically identify and separate different targets, ensuring the accuracy and quality of multi-target BLT reconstruction results. Meanwhile, SDO can combine various types of reconstruction algorithms and provide stable and high-quality reconstruction results independent of the algorithm parameters.

CONCLUSIONS

The SDO approach provides an integrated solution to the multi-target BLT reconstruction problem, realizing the whole process including target recognition, separation, reconstruction, and result enhancement, which can extend the application domain of BLT.

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.

Generalized conditional gradient method with adaptive regularization parameters for fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an optical imaging technology with the ability of visualizing the three-dimensional distribution of fluorescently labelled probes in vivo. However, due to the light scattering effect and ill-posed inverse problems, obtaining satisfactory FMT reconstruction is still a challenging problem. In this work, to improve the performance of FMT reconstruction, we proposed a generalized conditional gradient method with adaptive regularization parameters (GCGM-ARP). In order to make a tradeoff between the sparsity and shape preservation of the reconstruction source, and to maintain its robustness, elastic-net (EN) regularization is introduced. EN regularization combines the advantages of L₁-norm and L₂-norm, and overcomes the shortcomings of traditional L_p-norm regularization, such as over-sparsity, over-smoothness, and non-robustness. Thus, the equivalent optimization formulation of the original problem can be obtained. To further improve the performance of the reconstruction, the L-curve is adopted to adaptively adjust the regularization parameters. Then, the generalized conditional gradient method (GCGM) is used to split the minimization problem based on EN regularization into two simpler sub-problems, which are determining the direction of the gradient and the step size. These sub-problems are addressed efficiently to obtain more sparse solutions. To assess the performance of our proposed method, a series of numerical simulation experiments and in vivo experiments were implemented. The experimental results show that, compared with other mathematical reconstruction methods, GCGM-ARP method has the minimum location error (LE) and relative intensity error (RIE), and the maximum dice coefficient (Dice) in the case of different sources number or shape, or Gaussian noise of 5%-25%. This indicates that GCGM-ARP has superior reconstruction performance in source localization, dual-source resolution, morphology recovery, and robustness. In conclusion, the proposed GCGM-ARP is an effective and robust strategy for FMT reconstruction in biomedical application.

Reconstruction based on adaptive group least angle regression for fluorescence molecular tomography

Fluorescence molecular tomography can combine two-dimensional fluorescence imaging with anatomical information to reconstruct three-dimensional images of tumors. Reconstruction based on traditional regularization with tumor sparsity priors does not take into account that tumor cells form clusters, so it performs poorly when multiple light sources are used. Here we describe reconstruction based on an "adaptive group least angle regression elastic net" (AGLEN) method, in which local spatial structure correlation and group sparsity are integrated with elastic net regularization, followed by least angle regression. The AGLEN method works iteratively using the residual vector and a median smoothing strategy in order to adaptively obtain a robust local optimum. The method was verified using numerical simulations as well as imaging of mice bearing liver or melanoma tumors. AGLEN reconstruction performed better than state-of-the-art methods with different sizes of light sources at different distances from the sample and in the presence of Gaussian noise at 5-25%. In addition, AGLEN-based reconstruction accurately imaged tumor expression of cell death ligand-1, which can guide immunotherapy.

D2-RecST: Dual-domain joint reconstruction strategy for fluorescence molecular tomography based on image domain and perception domain

BACKGROUND AND OBJECTIVE

Fluorescence molecular tomography (FMT) is a promising molecular imaging modality for quantifying the three-dimensional (3D) distribution of fluorescent probes in small animals. Over the past few years, learning-based FMT reconstruction methods have achieved promising results. However, these methods typically attempt to minimize the mean-squared error (MSE) between the reconstructed image and the ground truth. Although signal-to-noise ratios (SNRs) are improved, they are susceptible to non-uniform artifacts and loss of structural detail, making it extremely challenging to obtain accurate and robust FMT reconstructions under noisy measurements.

METHODS

We propose a novel dual-domain joint strategy based on the image domain and perception domain for accurate and robust FMT reconstruction. First, we formulate an explicit adversarial learning strategy in the image domain, which greatly facilitates training and optimization through two enhanced networks to improve anti-noise ability. Besides, we introduce a novel transfer learning strategy in the perceptual domain to optimize edge details by providing perceptual priors for fluorescent targets. Collectively, the proposed dual-domain joint reconstruction strategy can significantly eliminate the non-uniform artifacts and effectively preserve the structural edge details.

RESULTS

Both numerical simulations and in vivo mouse experiments demonstrate that the proposed method markedly outperforms traditional and cutting-edge methods in terms of positioning accuracy, image contrast, robustness, and target morphological recovery.

CONCLUSIONS

The proposed method achieves the best reconstruction performance and has great potential to facilitate precise localization and 3D visualization of tumors in in vivo animal experiments.

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.

Accurate and fast reconstruction for bioluminescence tomography based on adaptive Newton hard thresholding pursuit algorithm

As a promising noninvasive medical imaging technique, bioluminescence tomography (BLT) dynamically offers three-dimensional visualization of tumor distribution in living animals. However, due to the high ill-posedness caused by the strong scattering property of biological tissues and the limited boundary measurements with noise, BLT reconstruction still cannot meet actual preliminary clinical application requirements. In our research, to recover 3D tumor distribution quickly and precisely, an adaptive Newton hard thresholding pursuit (ANHTP) algorithm is proposed to improve the performance of BLT. The ANHTP algorithm fully combines the advantages of sparsity constrained optimization and convex optimization to guarantee global convergence. More precisely, an adaptive sparsity adjustment strategy was developed to obtain the support set of the inverse system matrix. Based on the strong Wolfe line search criterion, a modified damped Newton algorithm was constructed to obtain optimal source distribution information. A series of numerical simulations and phantom and in vivo experiments show that ANHTP has high reconstruction accuracy, fast reconstruction speed, and good robustness. Our proposed algorithm can further increase the practicality of BLT in biomedical applications.

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.

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.