Yu An

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

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

A Novel Region Reconstruction Method for Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) could exploit the distribution of fluorescent biomarkers that target tumors accurately and effectively, which enables noninvasive real-time 3-D visualization as well as quantitative analysis of small tumors in small animal studies in vivo. Due to the difficulties of reconstruction, continuous efforts are being made to find more practical and efficient approaches to accurately obtain the characteristics of fluorescent regions inside biological tissues. In this paper, we propose a region reconstruction method for FMT, which is defined as an L1-norm regularization piecewise constant level set approach. The proposed approach adopts a priori information including the sparsity of the fluorescent sources and the fluorescent contrast between the target and background. When the contrast of different fluorescent sources is low to a certain degree, our approach can simultaneously solve the detection and characterization problems for the reconstruction of FMT. To evaluate the performance of the region reconstruction method, numerical phantom experiments and in vivo bead-implanted mouse experiments were performed. The results suggested that the proposed region reconstruction method was able to reconstruct the features of the fluorescent regions accurately and effectively, and the proposed method was able to be feasibly adopted in in vivo application.

Reconstruction of fluorescence molecular tomography via a nonmonotone spectral projected gradient pursuit method

Abstract. Fluorescence molecular tomography (FMT) is a promising imaging technique in preclinical research, enabling three-dimensional location of the specific tumor position for small animal imaging. However, FMT presents a challenging inverse problem that is quite ill-posed and ill-conditioned. Thus, the reconstruction of FMT faces various challenges in its robustness and efficiency. We present an FMT reconstruction method based on nonmonotone spectral projected gradient pursuit (NSPGP) with l1-norm optimization. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. A nonmonotone line search strategy is utilized to get the appropriate updating direction, which guarantees global convergence. Additionally, the Barzilai–Borwein step length is applied to build the optimal step length, further improving the convergence speed of the proposed method. Several numerical simulation studies, including multisource cases as well as comparative analyses, have been performed to evaluate the performance of the proposed method. The results indicate that the proposed NSPGP method is able to ensure the accuracy, robustness, and efficiency of FMT reconstruction. Furthermore, an in vivo experiment based on a heterogeneous mouse model was conducted, and the results demonstrated that the proposed method held the potential for practical applications of FMT.

L p Regularization for Bioluminescence Tomography Based on the Split Bregman Method.

PurposeBioluminescence tomography (BLT) is a promising in vivo optical imaging technique in preclinical research at cellular and molecular levels. The problem of BLT reconstruction is quite ill-posed and ill-conditioned. In order to achieve high accuracy and efficiency for its inverse reconstruction, we proposed a novel approach based on Lp regularization with the Split Bregman method.ProceduresThe diffusion equation was used as the forward model. Then, we defined the objective function of Lp regularization and developed a Split Bregman iteration algorithm to optimize this function. After that, we conducted numerical simulations and in vivo experiments to evaluate the accuracy and efficiency of the proposed method.ResultsThe results of the simulations indicated that compared with the conjugate gradient and iterative shrinkage methods, the proposed method is more accurate and faster for multisource reconstructions. Furthermore, in vivo imaging suggested that it could clearly distinguish the viable and apoptotic tumor regions.ConclusionsThe Split Bregman iteration method is able to minimize the Lp regularization problem and achieve fast and accurate reconstruction in BLT.

Novel l 2,1-norm optimization method for fluorescence molecular tomography reconstruction.

Fluorescence molecular tomography (FMT) is a promising tomographic method in preclinical research, which enables noninvasive real-time three-dimensional (3-D) visualization for in vivo studies. The ill-posedness of the FMT reconstruction problem is one of the many challenges in the studies of FMT. In this paper, we propose a l 2,1-norm optimization method using a priori information, mainly the structured sparsity of the fluorescent regions for FMT reconstruction. Compared to standard sparsity methods, the structured sparsity methods are often superior in reconstruction accuracy since the structured sparsity utilizes correlations or structures of the reconstructed image. To solve the problem effectively, the Nesterovs method was used to accelerate the computation. To evaluate the performance of the proposed l 2,1-norm method, numerical phantom experiments and in vivo mouse experiments are conducted. The results show that the proposed method not only achieves accurate and desirable fluorescent source reconstruction, but also demonstrates enhanced robustness to noise.

Meshless reconstruction method for fluorescence molecular tomography based on compactly supported radial basis function.

Abstract. Fluorescence molecular tomography (FMT) is a promising tool in the study of cancer, drug discovery, and disease diagnosis, enabling noninvasive and quantitative imaging of the biodistribution of fluorophores in deep tissues via image reconstruction techniques. Conventional reconstruction methods based on the finite-element method (FEM) have achieved acceptable stability and efficiency. However, some inherent shortcomings in FEM meshes, such as time consumption in mesh generation and a large discretization error, limit further biomedical application. In this paper, we propose a meshless method for reconstruction of FMT (MM-FMT) using compactly supported radial basis functions (CSRBFs). With CSRBFs, the image domain can be accurately expressed by continuous CSRBFs, avoiding the discretization error to a certain degree. After direct collocation with CSRBFs, the conventional optimization techniques, including Tikhonov, L1-norm iteration shrinkage (L1-IS), and sparsity adaptive matching pursuit, were adopted to solve the meshless reconstruction. To evaluate the performance of the proposed MM-FMT, we performed numerical heterogeneous mouse experiments and in vivo bead-implanted mouse experiments. The results suggest that the proposed MM-FMT method can reduce the position error of the reconstruction result to smaller than 0.4 mm for the double-source case, which is a significant improvement for FMT.

Compactly supported radial basis function-based meshless method for photon propagation model of fluorescence molecular tomography

Fluorescence Molecular Tomography (FMT) is a powerful imaging modality for the research of cancer diagnosis, disease treatment and drug discovery. Via three-dimensional (3-D) imaging reconstruction, it can quantitatively and noninvasively obtain the distribution of fluorescent probes in biological tissues. Currently, photon propagation of FMT is conventionally described by the Finite Element Method (FEM), and it can obtain acceptable image quality. However, there are still some inherent inadequacies in FEM, such as time consuming, discretization error and inflexibility in mesh generation, which partly limit its imaging accuracy. To further improve the solving accuracy of photon propagation model (PPM), we propose a novel compactly supported radial basis functions (CSRBFs)-based meshless method (MM) to implement the PPM of FMT. We introduced a series of independent nodes and continuous CSRBFs to interpolate the PPM, which can avoid complicated mesh generation. To analyze the performance of the proposed MM, we carried out numerical heterogeneous mouse simulation to validate the simulated surface fluorescent measurement. Then we performed an in vivo experiment to observe the tomographic reconstruction. The experimental results confirmed that our proposed MM could obtain more similar surface fluorescence measurement with the golden standard (Monte-Carlo method), and more accurate reconstruction result was achieved via MM in in vivo application.

Reconstruction Method for Optical Tomography Based on the Linearized Bregman Iteration with Sparse Regularization

Optical molecular imaging is a promising technique and has been widely used in physiology, and pathology at cellular and molecular levels, which includes different modalities such as bioluminescence tomography, fluorescence molecular tomography and Cerenkov luminescence tomography. The inverse problem is ill-posed for the above modalities, which cause a nonunique solution. In this paper, we propose an effective reconstruction method based on the linearized Bregman iterative algorithm with sparse regularization (LBSR) for reconstruction. Considering the sparsity characteristics of the reconstructed sources, the sparsity can be regarded as a kind of a priori information and sparse regularization is incorporated, which can accurately locate the position of the source. The linearized Bregman iteration method is exploited to minimize the sparse regularization problem so as to further achieve fast and accurate reconstruction results. Experimental results in a numerical simulation and in vivo mouse demonstrate the effectiveness and potential of the proposed method.

A fast and effective reconstruction method for fluorescence molecular tomography based on sparsity adaptive subspacepursuit

Fluorescence molecular tomography (FMT), which is a promising tomographic method for in vivo small animal imaging, has many successful applications. However, FMT reconstruction is usually an ill-posed problem because only the photon distribution over the body surface is measurable. The Lp-norm regularization is generally adopted to stabilize the solution, which can be regarded as a type of a priori information of the fluorescent probe bio-distribution. When FMT is used for the early detection of tumors, an important feature is the sparsity of the fluorescent sources because tumors are usually very small and sparse at early stage. Considering this, we propose a fast and effective method with L1-norm based on sparsity adaptive subspace pursuit to solve the FMT problem in this paper. Our proposed method treats FMT problem with sparsity-promoting L1-norm as the basis pursuit problem. At each iteration, a sparsity factor that indicates the number of unknowns is estimated and updated adaptively. Then our method seeks a small index set which indicates atoms exhibiting highest correlation with the current residual, and updates the current supporting set by merging the newly selected index set. It can be regarded as a kind of sparse approximation reconstruction strategy. To evaluate our proposed method, we compare it to the iterated-shrinkage-based method with L1-norm regularization in numerical experiments. The results demonstrate that the proposed algorithm is able to obtain satisfactory reconstruction results. In addition, the proposed method is about two orders of magnitude faster compared to the iterated-shrinkage-based method. Our method is a practical and effective FMT reconstruction method.

Sparse Reconstruction of Fluorescence Molecular Tomography Using Variable Splitting and Alternating Direction Scheme

PurposeFluorescence molecular tomography (FMT) is a novel imaging modality for three-dimensional preclinical research and has many potential applications for drug therapy evaluation and tumor diagnosis. However, FMT presents an ill-conditioned and ill-posed inverse problem, which is a challenge for its tomography reconstruction. Due to the importance of FMT reconstruction, it is valuable and necessary to develop further practical reconstruction methods for FMT.ProceduresIn this study, an efficient method using variable splitting strategy as well as alternating direction strategy (VSAD) was proposed for FMT reconstruction. In this method, the variable splitting strategy and the augmented Lagrangian function were first introduced to obtain an equivalent optimization formulation of the original problem. Then, the alternating direction scheme was used to solve the optimization problem and to accelerate its convergence. To examine the property of the VSAD method, three numerical simulation experiments (accuracy assessment experiment, robustness assessment experiment, and reconstruction speed assessment experiment) were performed and analyzed.ResultsThe results indicated that the reconstruction accuracy, the reconstruction robustness, and the reconstruction speed of FMT were satisfactory by using the proposed VSAD method. Two in vivo studies, which were conducted by using two nude mouse models, further confirmed the advantages of the proposed method.ConclusionsThe results indicated that the proposed VSAD algorithm is effective for FMT reconstruction. It was accurate, robust, and efficient for FMT imaging and was feasibly applied for in vivo FMT applications.