Reweighted L1 regularization for restraining artifacts in FMT reconstruction images with limited measurements

Deep background-mismodeling-learned reconstruction for high-accuracy fluorescence diffuse optical tomography

We present a deep background-mismodeling-learned reconstruction framework for high-accuracy fluorescence diffuse optical tomography (FDOT). A learnable regularizer incorporating background mismodeling is formulated in the form of certain mathematical constraints. The regularizer is then learned to obtain the background mismodeling automatically using a physics-informed deep network implicitly. Here, a deep-unrolled FIST-Net for optimizing L1-FDOT is specially designed to obtain fewer learning parameters. Experiments show that the accuracy of FDOT is significantly improved via implicitly learning the background mismodeling, which proves the validity of the deep background-mismodeling-learned reconstruction. The proposed framework can also be used as a general method to improve a class of image modalities based on linear inverse problems with unknown background modeling errors.

Multi-target reconstruction strategy based on blind source separation of surface measurement signals in FMT

Fluorescence molecular tomography (FMT) is a promising molecular imaging technique for tumor detection in the early stage. High-precision multi-target reconstructions are necessary for quantitative analysis in practical FMT applications. The existing reconstruction methods perform well in retrieving a single fluorescent target but may fail in reconstructing a multi-target, which remains an obstacle to the wider application of FMT. In this paper, a novel multi-target reconstruction strategy based on blind source separation (BSS) of surface measurement signals was proposed, which transformed the multi-target reconstruction problem into multiple single-target reconstruction problems. Firstly, by multiple points excitation, multiple groups of superimposed measurement signals conforming to the conditions of BSS were constructed. Secondly, an efficient nonnegative least-correlated component analysis with iterative volume maximization (nLCA-IVM) algorithm was applied to construct the separation matrix, and the superimposed measurement signals were separated into the measurements of each target. Thirdly, the least squares fitting method was combined with BSS to determine the number of fluorophores indirectly. Lastly, each target was reconstructed based on the extracted surface measurement signals. Numerical simulations and in vivo experiments proved that it has the ability of multi-target resolution for FMT. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.

High-fidelity mesoscopic fluorescence molecular tomography based on SSB-Net

The imaging fidelity of mesoscopic fluorescence molecular tomography (MFMT) in reflective geometry suffers from spatial nonuniformity of measurement sensitivity and ill-posed reconstruction. In this study, we present a spatially adaptive split Bregman network (SSB-Net) to simultaneously overcome the spatial nonuniformity of measurement sensitivity and promote reconstruction sparsity. The SSB-Net is derived by unfolding the split Bregman algorithm. In each layer of the SSB-Net, residual block and 3D convolution neural networks (3D-CNNs) can adaptively learn spatially nonuniform error compensation, the spatially dependent proximal operator, and sparsity transformation. Simulations and experiments show that the proposed SSB-Net enables high-fidelity MFMT reconstruction of multifluorophores at different positions within a depth of a few millimeters. Our method paves the way for a practical reflection-mode diffuse optical imaging technique.

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.

Multi-branch attention prior based parameterized generative adversarial network for fast and accurate limited-projection reconstruction in fluorescence molecular tomography

Limited-projection fluorescence molecular tomography (FMT) allows rapid reconstruction of the three-dimensional (3D) distribution of fluorescent targets within a shorter data acquisition time. However, the limited-projection FMT is severely ill-posed and ill-conditioned due to insufficient fluorescence measurements and the strong scattering properties of photons in biological tissues. Previously, regularization-based methods, combined with the sparse distribution of fluorescent sources, have been commonly used to alleviate the severe ill-posed nature of the limited-projection FMT. Due to the complex iterative computations, time-consuming solution procedures, and less stable reconstruction results, the limited-projection FMT remains an intractable challenge for achieving fast and accurate reconstructions. In this work, we completely discard the previous iterative solving-based reconstruction themes and propose multi-branch attention prior based parameterized generative adversarial network (MAP-PGAN) to achieve fast and accurate limited-projection FMT reconstruction. Firstly, the multi-branch attention can provide parameterized weighted sparse prior information for fluorescent sources, enabling MAP-PGAN to effectively mitigate the ill-posedness and significantly improve the reconstruction accuracy of limited-projection FMT. Secondly, since the end-to-end direct reconstruction strategy is adopted, the complex iterative computation process in traditional regularization algorithms can be avoided, thus greatly accelerating the 3D visualization process. The numerical simulation results show that the proposed MAP-PGAN method outperforms the state-of-the-art methods in terms of localization accuracy and morphological recovery. Meanwhile, the reconstruction time is only about 0.18s, which is about 100 to 1000 times faster than the conventional iteration-based regularization algorithms. The reconstruction results from the physical phantoms and in vivo experiments further demonstrate the feasibility and practicality of the MAP-PGAN method in achieving fast and accurate limited-projection FMT reconstruction.

Interpretable model-driven projected gradient descent network for high-quality fDOT reconstruction

In fluorescence diffuse optical tomography (fDOT), the quality of reconstruction is severely limited by mismodeling and ill-posedness of inverse problems. Although data-driven deep learning methods improve the quality of image reconstruction, the network architecture lacks interpretability and requires a lot of data for training. We propose an interpretable model-driven projected gradient descent network (MPGD-Net) to improve the quality of fDOT reconstruction using only a few training samples. MPGD-Net unfolds projected gradient descent into a novel deep network architecture that is naturally interpretable. Simulation and in vivo experiments show that MPGD-Net greatly improves the fDOT reconstruction quality with superior generalization ability.

Depth-recognizable time-domain fluorescence molecular tomography in reflective geometry

Conventional fluorescence molecular tomography (FMT) reconstruction requires photons penetrating the whole object, which limits its applications to small animals. However, by utilizing reflective photons, fluorescence distribution near the surface could be reconstructed regardless of the object size, which may extend the applications of FMT to surgical navigation and so on. Therefore, time-domain reflective fluorescence molecular tomography (TD-rFMT) is proposed in this paper. The system excites and detects the emission light from the same angle within a field of view of 5 cm. Because the detected intensities of targets depend strongly on the depth, the reconstruction of targets in deep regions would be evidently affected. Therefore, a fluorescence yield reconstruction method with depth regularization and a weighted separation reconstruction strategy for lifetime are developed to enhance the performance for deep targets. Through simulations and phantom experiments, TD-rFMT is proved capable of reconstructing fluorescence distribution within a 2.5-cm depth with accurate reconstructed yield, lifetime, and target position(s).

Recent methodology advances in fluorescence molecular tomography

Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.

Adaptive threshold method for recovered images of FMT

This paper proposes a post-processing strategy for recovered images of fluorescence molecular tomography. A threshold value is adaptively obtained from the recovered images without external interference, which is objective because it is extracted from the reconstructed result. The recovered images from simulation experiments and physical phantom experiments are processed by this threshold method. And by visualization, the processed images are clearer than those with no post-processing. The full width at half-maximum and contrast-to-noise ratio are then utilized to further verify the effectiveness of the post-processing method, being capable of removing spurious information from the original images, thus bringing convenience to users.

Sparsity-promoting Bayesian approximation error method for compensating for the mismodeling of optical properties in fluorescence molecular tomography

In fluorescence molecular tomography, the quality of image reconstruction of fluorophore distribution is heavily reduced by the mismodeling of inaccurately known tissue optical properties. We propose an efficient sparsity-promoting Bayesian approximation error (spBAE) method to compensate for this mismodeling. The spBAE method incorporates sparsity prior into the BAE method by updating the parameters of the Gaussian prior according to its initial solution. In vivo experiments demonstrate that this new method greatly improves the reconstruction quality.

Reconstruction for Limited-Projection Fluorescence Molecular Tomography Based on a Double-Mesh Strategy

Limited-projection fluorescence molecular tomography (FMT) has short data acquisition time that allows fast resolving of the three-dimensional visualization of fluorophore within small animal in vivo. However, limited-projection FMT reconstruction suffers from severe ill-posedness because only limited projections are used for reconstruction. To alleviate the ill-posedness, a feasible region extraction strategy based on a double mesh is presented for limited-projection FMT. First, an initial result is rapidly recovered using a coarse discretization mesh. Then, the reconstructed fluorophore area in the initial result is selected as a feasible region to guide the reconstruction using a fine discretization mesh. Simulation experiments on a digital mouse and small animal experiment in vivo are performed to validate the proposed strategy. It demonstrates that the presented strategy provides a good distribution of fluorophore with limited projections of fluorescence measurements. Hence, it is suitable for reconstruction of limited-projection FMT.

High-dynamic-range fluorescence molecular tomography for imaging of fluorescent targets with large concentration differences

When CCD-based free-space fluorescence molecular tomography (FMT) is used for imaging of fluorescent targets with a large concentration difference, the limited dynamic range of the CCD diminishes the localization and quantitative accuracy of FMT. To overcome this, we present a high-dynamic-range FMT (HDR-FMT) method. Under the multiple-exposure scheme, HDR fluorescence projection images are constructed using the recovered CCD response curve. Image reconstruction is implemented using iterative reweighted L1 regularization which can reduce artifacts by using fewer HDR fluorescence projection images. Phantom and in vivo animal studies indicate that localization of fluorescent targets with a large concentration difference is effectively improved with HDR-FMT and with good quantitative accuracy.

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.

Noncontact full-angle fluorescence molecular tomography system based on rotary mirrors

We propose a novel noncontact fluorescence molecular tomography system that achieves full-angle capacity with the use of a new rotary-mirrors-based imaging head. In the imaging head, four plane mirrors are mounted on a rotating gantry to enable illumination and detection over 360°. In comparison with existing full-angle systems, our system does not require rotation of the specimen animal, a large and heavy light source (with scanning head), or a bulky camera (with filters and lens). The system design and implementation are described in detail. Both physical phantom and in vivo experiments are performed to verify the performance of the proposed system.

Accurate quantification of fluorescent targets within turbid media based on a decoupled fluorescence Monte Carlo model

We propose a method based on a decoupled fluorescence Monte Carlo model for constructing fluorescence Jacobians to enable accurate quantification of fluorescence targets within turbid media. The effectiveness of the proposed method is validated using two cylindrical phantoms enclosing fluorescent targets within homogeneous and heterogeneous background media. The results demonstrate that our method can recover relative concentrations of the fluorescent targets with higher accuracy than the perturbation fluorescence Monte Carlo method. This suggests that our method is suitable for quantitative fluorescence diffuse optical tomography, especially for in vivo imaging of fluorophore targets for diagnosis of different diseases and abnormalities.

Fluorescence molecular tomography reconstruction via discrete cosine transform-based regularization

Fluorescence molecular tomography (FMT) as a noninvasive imaging modality has been widely used for biomedical preclinical applications. However, FMT reconstruction suffers from severe ill-posedness, especially when a limited number of projections are used. In order to improve the quality of FMT reconstruction results, a discrete cosine transform (DCT) based reweighted L1-norm regularization algorithm is proposed. In each iteration of the reconstruction process, different reweighted regularization parameters are adaptively assigned according to the values of DCT coefficients to suppress the reconstruction noise. In addition, the permission region of the reconstructed fluorophores is adaptively constructed to increase the convergence speed. In order to evaluate the performance of the proposed algorithm, physical phantom and in vivo mouse experiments with a limited number of projections are carried out. For comparison, different L1-norm regularization strategies are employed. By quantifying the signal-to-noise ratio (SNR) of the reconstruction results in the phantom and in vivo mouse experiments with four projections, the proposed DCT-based reweighted L1-norm regularization shows higher SNR than other L1-norm regularizations employed in this work.