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Purpose Magnetoacoustic tomography with magnetic induction (MAT-MI) is a technique that utilizes the acoustic signals induced by magnetic stimulation to reconstruct the electrical impedance distribution in biological tissues. Most algorithms ignored the fact that acoustic properties in human tissues are heterogeneous, which lead to distortion and blurring of small reconstructed objects. In this study, a novel algorithm is proposed for exact reconstruction of the sound source distribution in acoustic heterogeneous tissues. Methods Based on the ring transducer array, we develop an algorithm which combines algebraic reconstruction technique (ART) and time reversal method. Different to existing reconstruction methods, the ultrasonic transmission tomography (UTT) and the MAT-MI can be completed in same system, which decreases the system complexity. The sound velocity distribution is reconstructed with the ART so that the propagation time of the magnetoacoustic signals in the heterogeneous tissue is corrected. And then, the sound source image is reconstructed based on the time reversal method from new sound pressure data. Both numerical simulations and phantom experiments are established to validate the proposed method. Results Compared with the results without consideration of the variation on acoustic speed, sound sources reconstructed by our method are more consistent with the model in terms of size and shape. Conclusions The novel algorithm can be used to reconstruct the high-accuracy image of MAT-MI sound source in the sound velocity inhomogeneous media. In addition, this method is applicable to scenarios that the prior knowledge of the imaging targets is unknown. The signal acquisition time of MAT-MI in acoustically heterogeneity media is greatly reduced due to the introduction of ring transducer array into the imaging system. Therefore, our method will promote the application of MAT-MI in noninvasive early diagnosis of tumor for preclinical study.

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.

Fluorescence molecular tomography (FMT), as a promising imaging modality in preclinical research, can obtain the three-dimensional location information of the specific tumor for small animal imaging. A lot of methods based on orthogonal matching pursuit (OMP) have been used for FMT reconstruction. OMP and most of its variants use the mean square error criterion to estimate the sparse vector which depends on the Gaussian assumption of the error distribution. However, this method has poor performance on reconstruction with non-Gaussian noise. In this study, we propose correntropy matching pursuit (CMP) method to alleviate this problem of OMP. Unlike some other matching pursuit methods, CMP method is independent of the error distribution. This method can assign small weights on severely corrupted entries of data and large weights on clean ones adaptively, thus reducing the effect of large noise. The Gaussian assumption of the noise distribution is often used in the matching pursuit (MP) methods so that they can't work well with the non- Gaussian noise. Our method is independent of the noise distribution and has better performance on FMT reconstruction. Compared with StOMP and SASP, CMP method shows better performance on FMT reconstruction with non-Gaussian noise and similar performance on FMT.

Bioluminescence tomography (BLT) is a molecular imaging modality which can three-dimensionally resolve the molecular processes in small animalsin vivo. The ill-posedness nature of BLT problem makes its reconstruction bears nonunique solution and is sensitive to noise. In this paper, we proposed a sparse BLT reconstruction algorithm based on semigreedy method. To reduce the ill-posedness and computational cost, the optimal permissible source region was automatically chosen by using an iterative search tree. The proposed method obtained fast and stable source reconstruction from the whole body and imposed constraint without using a regularization penalty term. Numerical simulations on a mouse atlas, andin vivomouse experiments were conducted to validate the effectiveness and potential of the method.

Molecular imaging, including fluorescence imaging (FMI), bioluminescence imaging (BLI), positron emission tomography (PET), single-photon emission-computed tomography (SPECT), and computed tomography (CT), has a pivotal role in the process of tumor and relevant drug research. CT, especially Micro-CT, can provide the anatomic information for a region of interest (ROI); PET and SPECT can provide functional information for the ROI. BLI and FMI can provide optical information for an ROI. Tumor angiogenesis and relevant drug development is a lengthy, high-risk, and costly process, in which a novel drug needs about 10–15 years of testing to obtain Federal Drug Association (FDA) approval. Molecular imaging can enhance the development process by understanding the tumor mechanisms and drug activity. In this paper, we focus on tumor angiogenesis, and we review the characteristics of molecular imaging modalities and their applications in tumor angiogenesis and relevant drug research.

In mathematics, optical molecular imaging including bioluminescence tomography (BLT), fluorescence tomography (FMT) and Cerenkov luminescence tomography (CLT) are concerned with a similar inverse source problem. They all involve the reconstruction of the 3D location of a single/multiple internal luminescent/fluorescent sources based on 3D surface flux distribution. To achieve that, an accurate fusion between 2D luminescent/fluorescent images and 3D structural images that may be acquired form micro-CT, MRI or beam scanning is extremely critical. However, the absence of a universal method that can effectively convert 2D optical information into 3D makes the accurate fusion challengeable. In this study, to improve the fusion accuracy, a new fusion method for dual-modality tomography (luminescence/fluorescence and micro-CT) based on natural light surface reconstruction (NLSR) and iterated closest point (ICP) was presented. It consisted of Octree structure, exact visual hull from marching cubes and ICP. Different from conventional limited projection methods, it is 360° free-space registration, and utilizes more luminescence/fluorescence distribution information from unlimited multi-orientation 2D optical images. A mouse mimicking phantom (one XPM-2 Phantom Light Source, XENOGEN Corporation) and an in-vivo BALB/C mouse with implanted one luminescent light source were used to evaluate the performance of the new fusion method. Compared with conventional fusion methods, the average error of preset markers was improved by 0.3 and 0.2 pixels from the new method, respectively. After running the same 3D internal light source reconstruction algorithm of the BALB/C mouse, the distance error between the actual and reconstructed internal source was decreased by 0.19 mm.

As a high-sensitivity imaging modality, bioluminescence tomography can reconstruct the three-dimensional (3-D) location of an internal luminescent source based on the 3-D surface light distribution. However, we can only get the multi-orientation two-dimensional (2-D) bioluminescence distribution in the experiments. Therefore, developing an accurate universal registration method is essential for following bioluminescent source reconstruction. We can then map the multi-orientation 2-D bioluminescence distribution to the 3-D surface derived from anatomical information with it. We propose a 2-D -to-3-D registration method based on iterated optimal projection and applied it in a registration and reconstruction study of three transgenic mice. Compared with traditional registration methods based on the fixed points, our method was independent of the markers and the registration accuracy of the three experiments was improved by 0.3, 0.5, and 0.4 pixels, respectively. In addition, based on the above two registration results using the two registration methods, we reconstructed the 3-D location of the inner bioluminescent source in the three transgenic mice. The reconstruction results showed that the average error distance between the center of the reconstructed element and the center of the real element were reduced by 0.32, 0.48, and 0.39 mm, respectively.

Optical molecular imaging has been rapidly developed to noninvasively visualize in vivo physiological and pathological processes involved in normal and suffering organisms at the cellular and molecular levels, in which advanced optical imaging technology and modern molecular biology are being combined to provide a state-of-the-art tool for preclinical biomedical research. Among optical molecular imaging modalities, bioluminescence tomography (BLT) has experienced considerable growth and attracted much attention in recent years for its excellent performance, unique advantages, and high cost-effectiveness. This article focuses on the genesis and development of BLT, especially for its computational methodology, imaging system, and biomedical application. An overview of the advantages and challenges of the conventional planar bioluminescence imaging technique is first described in comparison with currently available molecular imaging modalities. The imaging algorithms for inverse source reconstruction are classified and summarized according to different a priori knowledge, followed by a simple depiction of the uniqueness theorems of BLT solution. Diverse imaging systems for obtaining three-dimensional quantitative information of internal bioluminescent sources are then reviewed. The latest application examples of BLT in tumor study and drug discovery are introduced and compared with other mature imaging technologies. Finally, the paper is concluded and an attractive prospect for BLT ispredicted.

Solution with adjustable sparsity to tomographic imaging of Cerenkov photons is presented in this work. The sparsity of radionuclides' distribution in tissues is an objective but unknown fact, and the inverse model of qualitative data is an ill-posed problem. Based on the optimization technique, the uniqueness of numerical solution to the ill-conditioned compact operator can be guaranteed by use of sparse regularization with the approximate message-passing (AMP) method. After absorbing formulations with the AMP, we analyzed the behavior of the hard thresholding operator. Iteratively numerical solutions were used to approximate the real light source by assuming the number of non-zero solution in manual mode. This modified AMP algorithm was performed in numerical simulation and physical experiments with 2-[18F]fluoro-2-deoxy-D-glucose. Experimental results indicated that the proposed method was a kind of low-complexity iterative thresholding algorithms for reconstructing 3D sparse distribution from a small set of optical measurements.

As a novel molecular imaging technology, bioluminescence tomography (BLT) has become an important tool for biomedical research in recent years, which can perform a quantitative reconstruction of an internal light source distribution with the scattered and transmitted bioluminescent signals measured on the external surface of a small animal. However, BLT is severely ill-posed because of complex photon propagation in the biological tissue and limited boundary measured data with noise. Therefore, sufficient a priori knowledge should be fused for the uniqueness and stability of BLT solution. Permissible source region strategy and spectrally resolved measurements are two kinds of a priori knowledge commonly used in BLT reconstruction. This paper compares their performance with simulation and in vivo heterogeneous mouse experiments. In order to improve the efficiency of large-scale source restoration, this paper introduces an efficient iterative shrinkage thresholding method that not only has faster convergence rate but also has better reconstruction accuracy than the modified Newton-type optimization approach. Finally, a discussion of these two kinds of a priori knowledge is given based on the comparison results.

Fluorescence molecular tomography (FMT) has become a promising imaging modality for in vivo small animal molecular imaging, and has many successful applications. This is partly due to the wealth of the fluorescent probes. By labeling the regions of interest with fluorescent probes, FMT can achieve non-invasive investigation of the biological process by localizing the targeted probes based on certain inverse mathematical models. However, FMT is usually an illposed problem, and some form of regularization should be included to stabilize the problem, which can be considered as the a priori information of the fluorescent probe bio-distribution. When FMT is used for the early detection of tumors, an important characteristic is the sparsity of the fluorescent sources. This is because tumors are usually very small and sparse at this stage. Considering this, general sparsity-promoting Lp-norm regularization is utilized in this paper. The iterated shrinkage based reconstruction method is adopted to solve the general Lp regularization problem. However, the original iterated shrinkage method is proved to have a linear convergence rate, and a large number of iterations are needed to obtain satisfactory results. In this paper, an improved iterated shrinkage based FMT reconstruction algorithm is proposed. By using the solutions from two previous iterations to determine the current solution, the convergence rate can be greatly increased. Heterogeneous simulation experiment shows that the proposed method can obtain comparable results with greatly reduced number of iterations compared with the original iterated shrinkage based method, which makes it a practical reconstruction algorithm.

Among many optical molecular imaging modalities, bioluminescence imaging (BLI) has more and more wide application in tumor detection and evaluation of pharmacodynamics, toxicity, pharmacokinetics because of its noninvasive molecular and cellular level detection ability, high sensitivity and low cost in comparison with other imaging technologies. However, BLI can not present the accurate location and intensity of the inner bioluminescence sources such as in the bone, liver or lung etc. Bioluminescent tomography (BLT) shows its advantage in determining the bioluminescence source distribution inside a small animal or phantom. Considering the deficiency of two-dimensional imaging modality, we developed three-dimensional tomography to reconstruct the information of the bioluminescence source distribution in transgenic mOC-Luc mice bone with the boundary measured data. In this paper, to study the osteocalcin (OC) accumulation in transgenic mOC-Luc mice bone, a BLT reconstruction method based on multilevel adaptive finite element (FEM) algorithm was used for localizing and quantifying multi bioluminescence sources. Optical and anatomical information of the tissues are incorporated as a priori knowledge in this method, which can reduce the ill-posedness of BLT. The data was acquired by the dual modality BLT and Micro CT prototype system that was developed by us. Through temperature control and absolute intensity calibration, a relative accurate intensity can be calculated. The location of the OC accumulation was reconstructed, which was coherent with the principle of bone differentiation. This result also was testified by ex vivo experiment in the black 96-plate well using the BLI system and the chemiluminescence apparatus.

Bioluminescence tomography (BLT) is a novel optical molecular imaging (MI) modality. It can reconstruct the inner bioluminescent light source distribution, according to the surface light distribution. The trust region method (TRM) can overcome the ill-posedness of BLT for its regularization property. As there exists a "TRUST" function that can solve the trust region subproblem in Matlab and Matlab's powerful matrix operation ability suited for TRM, the TRM is implemented in Matlab. Then the Matlab code of TRM is transformed into a dynamic linked library (DDL) and mixed together with the C++ code of the adaptive finite element (AFE) framework, using the mixed-language programming technology (MLPT). There are two main advantages of the MLPT. The first is taking advantages of all the participated programming languages. The second is time efficient. The usual way of transferring data between programmes written in different programming languages is to write the data first into files that are stored in the hard discs in one programme, and then read the files from another programme. Besides wasting time on writing and reading, it is difficult to keep the precision of the data. The DLL based MLPT can eliminate the need of installing code compilers in the platform running the software. Furthermore, in DLL, the code is implemented in C/C++ with high time efficiency, while the code in Matlab remains relatively low time efficiency. Finally, a numerical experiment is carried out to show MLPT's usage in the source reconstruction procedure of BLT, using the MLPT based on DLL.

Bioluminescence tomography (BLT) is an effective molecular imaging (MI) modality. Because of the ill-posedness, the inverse problem of BLT is still open. We present a trust region method (TRM) for BLT source reconstruction. The TRM is applied in the source reconstruction procedure of BLT for the first time. The results of both numerical simulations and the experiments of cube phantom and nude mouse draw us to the conclusion that based on the adaptive finite element (AFE) framework, the TRM works in the source reconstruction procedure of BLT. To make our conclusion more reliable, we also compare the performance of the TRM and that of the famous Tikhonov regularization method after only one step of mesh refinement of the AFE framework. The conclusion is that the TRM can get faster and better results after only one mesh refinement step of AFE framework than the Tikhonov regularization method when handling large scale data. In the TRM, all the parameters are fixed, while in the Tikhonov method the regularization parameter needs to be well selected.

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.

Bioluminescence tomography (BLT) can three-dimensionally and quantitatively resolve the molecular processes in small animals in vivo. In this paper, we propose a BLT reconstruction algorithm based on duality and variable splitting. By using duality and variable splitting to obtain a new equivalent constrained optimization problem and updating the primal variable as the Lagrangian multiplier in the dual augmented Lagrangian problem, the proposed method can obtain fast and stable source reconstruction even without the permissible source region and multispectral measurements. Numerical simulations on a mouse atlas and in vivo mouse experiments were conducted to validate the effectiveness and potential of the method.

As a new modality of molecular imaging, bioluminescence imaging has been widely used in tumor detection and drug evaluation. However, BLI cannot present the depth of information for internal diseases such as a liver tumor in situ or a lung tumor in situ. In this paper, we describe a bioluminescence tomography (BLT) method based on the bioluminescent intensity attenuation calibration and applied it to the early detection of liver cancer in situ. In comparison with BLT without calibration, this method could improve the reconstruction accuracy by more than 10%. In comparison with micro-computed tomography and other traditional imaging modalities, this method can detect a liver tumor at a very early stage and provide reliable location information.

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.

Tomographic bioluminescence imaging suffers from poor imaging robustness, since it is severely affected by selection of regularization parameter (RP) and initialization for source distribution. In this paper, a global-inexact-Newton based reconstruction methodology, which is regularized by a dynamic sparse term, is demonstrated for in vivo tomographic imaging. The novel method can enhance higher imaging reliability and efficiency. Mouse experimental reconstructions were performed to validate the proposed method. These results demonstrate that the source distribution can be accurately located over a wide range of values of RP and iteration initializations. Moreover, the reconstruction efficiency was also studied.