Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging

Dictionary Learning Method Based on K-Sparse Approximation and Orthogonal Procrustes Analysis for Reconstruction in Bioluminescence Tomography

Bioluminescence tomography (BLT) is one kind of noninvasive optical molecular imaging technology, widely used to study molecular activities and disease progression inside live animals. By combining the optical propagation model and inversion algorithm, BLT enables three-dimensional imaging and quantitative analysis of light sources within organisms. However, challenges like light scattering and absorption in tissues, and the complexity of biological structures, significantly impact the accuracy of BLT reconstructions. Here, we propose a dictionary learning method based on K-sparse approximation and Orthogonal Procrustes analysis (KSAOPA). KSAOPA uses an iterative alternating optimization strategy, enhancing solution sparsity with k-coefficients Lipschitzian mappings for sparsity(K-LIMAPS) in the sparse coding stage, and reducing errors with Orthogonal Procrustes analysis in the dictionary update stage, leading to stable and precise reconstructions. We assessed the method performance through simulations and in vivo experiments, which showed that KSAOPA excels in localization accuracy, morphological recovery, and in vivo applicability compared to other methods.

Deep orthogonal multi-wavelength fusion for tomogram-free diagnosis in diffuse optical imaging

Novel portable diffuse optical tomography (DOT) devices for breast cancer lesions hold great promise for non-invasive, non-ionizing breast cancer screening. Critical to this capability is not just the identification of lesions but rather the complex problem of discriminating between malignant and benign lesions. To accurately reconstruct the highly heterogeneous tissue of a cancer lesion in healthy breast tissue using DOT, multiple wavelengths can be leveraged to maximize signal penetration while minimizing sensitivity to noise. However, these wavelength responses can overlap, capture common information, and correlate, potentially confounding reconstruction and downstream end tasks. We show that an orthogonal fusion loss regularizes multi-wavelength DOT leading to improved reconstruction and accuracy of end-to-end discrimination of malignant versus benign lesions. We further show that our raw-to-task model significantly reduces computational complexity without sacrificing accuracy, making it ideal for real-time throughput, desired in medical settings where handheld devices have severely restricted power budgets. Furthermore, our results indicate that image reconstruction is not necessary for unbiased classification of lesions with a balanced accuracy of 77% and 66% on the synthetic dataset and clinical dataset, respectively, using the raw-to-task model. Code is available at https://github.com/sfu-mial/FuseNet.

Logarithmic total variation regularization via preconditioned conjugate gradient method for sparse reconstruction of bioluminescence tomography

BACKGROUND AND OBJECTIVE

Bioluminescence Tomography (BLT) is a powerful optical molecular imaging technique that enables the noninvasive investigation of dynamic biological phenomena. It aims to reconstruct the three-dimensional spatial distribution of bioluminescent sources from optical measurements collected on the surface of the imaged object. However, BLT reconstruction is a challenging ill-posed problem due to the scattering effect of light and the limitations in detecting surface photons, which makes it difficult for existing methods to achieve satisfactory reconstruction results. In this study, we propose a novel method for sparse reconstruction of BLT based on a preconditioned conjugate gradient with logarithmic total variation regularization (PCG-logTV).

METHOD

This PCG-logTV method incorporates the sparsity of overlapping groups and enhances the sparse structure of these groups using logarithmic functions, which can preserve edge features and achieve more stable reconstruction results in BLT. To accelerate the convergence of the algorithm solution, we use the preconditioned conjugate gradient iteration method on the objective function and obtain the reconstruction results. We demonstrate the performance of our proposed method through numerical simulations and in vivo experiment.

RESULTS AND CONCLUSIONS

The results show that the PCG-logTV method obtains the most accurate reconstruction results, and the minimum position error (LE) is 0.254mm, which is 26%, 31% and 34% of the FISTA (0.961), IVTCG (0.81) and L1-TV (0.739) methods, and the root mean square error (RMSE) and relative intensity error (RIE) are the smallest, indicating that it is closest to the real light source. In addition, compared with the other three methods, the PCG-logTV method also has the highest DICE similarity coefficient, which is 0.928, which means that this method can effectively reconstruct the three-dimensional spatial distribution of bioluminescent light sources, has higher resolution and robustness, and is beneficial to the preclinical and clinical studies of BLT.

Tikhonov regularization-based extended Kalman filter technique for robust and accurate reconstruction in diffuse optical tomography

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).

Joint direct estimation of hemodynamic response function and activation level in brain functional high density diffuse optical tomography

High density diffuse optical tomography has become increasingly important to detect underlying neuronal activities. Conventional methods first estimate the time courses of the changes in the absorption coefficients for all the voxels, and then estimate the hemodynamic response function (HRF). Activation-level maps are extracted at last based on this HRF. However, the error propagation among the successive processes degrades and even misleads the final results. Besides, the computation burden is heavy. To address the above problems, a direct method is proposed in this paper to simultaneously estimate the HRF and the activation-level maps from the boundary fluxes. It is assumed that all the voxels in the same activated brain region share the same HRF but differ in the activation levels, and no prior information is imposed on the specific shape of the HRF. The dynamic simulation and phantom experiments demonstrate that the proposed method outperforms the conventional one in terms of the estimation accuracy and computation speed.

Improved Block Sparse Bayesian Learning Method Using K-Nearest Neighbor Strategy for Accurate Tumor Morphology Reconstruction in Bioluminescence Tomography

OBJECTIVE

Bioluminescence tomography (BLT) is a non-invasive technique designed to enable three-dimensional (3D) visualization and quantification of viable tumor cells in living organisms. However, despite the excellent sensitivity and specificity of bioluminescence imaging (BLI), BLT is limited by the photon scattering effect and ill-posed inverse problem. If the complete structural information of a light source is considered when solving the inverse problem, reconstruction accuracy will be improved.

METHODS

This article proposed a block sparse Bayesian learning method based on K-nearest neighbor strategy (KNN-BSBL), which incorporated several types of a priori information including sparsity, spatial correlations among neighboring points, and anatomical information to balance over-sparsity and morphology preservation in BLT. Furthermore, we considered the Gaussian weighted distance prior in a light source and proposed a KNN-GBSBL method to further improve the performance of KNN-BSBL.

RESULTS

The results of numerical simulations and in vivo glioma-bearing mouse experiments demonstrated that KNN-BSBL and KNN-GBSBL achieved superior accuracy for tumor spatial positioning and morphology reconstruction.

CONCLUSION

The proposed method KNN-BSBL incorporated several types of a priori information is an efficient and robust reconstruction method for BLT.

Group-Sparsity-Based Super-Resolution Dipole Orientation Mapping

The dipole orientation of fluorophores could be resolved by fluorescence polarization microscopy (FPM), which in turn reveals structural specificity for the labeled organelles. Conventional FPM can detect only the averaged fluorescence anisotropy collected from dipoles within the diffraction-limited volume. Super-resolution dipole orientation mapping (SDOM) method, which applies sparse deconvolution and least square estimation to fluorescence polarization modulation data, achieves the dipole orientation measurement within a sub-diffraction focal area. However, during SDOM analysis, some pixels with fluorescence signal are not resolved with orientation for relatively small adjusted R². Here we report group-sparsity-based SDOM (GS-SDOM), which utilizes the relevance of modulation sequences to effectively improve the SDOM reconstruction model. More credible resolved dipole orientations with higher adjusted R² can be mapped and false positive estimation for local dipole orientation is vitally corrected. In addition to achieving the same spatial super-resolution as SDOM does, GS-SDOM accesses more morphological information with more credible orientations and more accurate local dipole distribution estimation. During the GS-SDOM analysis of actin filaments in mammalian kidney cells, the dipole orientation of fluorescence is detected always parallel to the direction of the actin filaments. Also with dipole orientation information extracted by GS-SDOM, the reconstructed visual circle from intensity dimension is discerned as jointed by double close filaments and 3-dimensional co-localization is accomplished in the intersection of actin filaments.

A Kalman-based tomographic scheme for directly reconstructing activation levels of brain function

In functional near-infrared spectroscopy (fNIRS), the conventional indirect approaches first separately recover the spatial distribution of the changes in the optical properties at every time point, and then extract the activation levels by a time-course analysis process at every site. In the tomographic implementation of fNIRS, i.e., diffuse optical tomography (DOT), these approaches not only suffer from the ill-posedness of the optical inversions and error propagation between the two successive steps, but also fail to achieve satisfactory temporal resolution due to the requirement for a complete data set. To cope with the above adversities of the indirect approaches, we propose herein a direct approach to tomographically reconstructing the activation levels by incorporating a Kalman scheme. Dynamic simulative and phantom experiments were conducted for the performance validation of the proposed approach, demonstrating its potentials to improve the calculated images and to relax the speed limitation of the instruments.

Back-propagation neural network-based reconstruction algorithm for diffuse optical tomography

Diffuse optical tomography (DOT) is a promising noninvasive imaging modality and is capable of providing functional characteristics of biological tissue by quantifying optical parameters. The DOT image reconstruction is ill-posed and ill-conditioned, due to the highly diffusive nature of light propagation in biological tissues and limited boundary measurements. The widely used regularization technique for DOT image reconstruction is Tikhonov regularization, which tends to yield oversmoothed and low-quality images containing severe artifacts. It is necessary to accurately choose a regularization parameter for Tikhonov regularization. To overcome these limitations, we develop a noniterative reconstruction method, whereby optical properties are recovered based on a back-propagation neural network (BPNN). We train the parameters of BPNN before DOT image reconstruction based on a set of training data. DOT image reconstruction is achieved by implementing a single evaluation of the trained network. To demonstrate the performance of the proposed algorithm, we compare with the conventional Tikhonov regularization-based reconstruction method. The experimental results demonstrate that image quality and quantitative accuracy of reconstructed optical properties are significantly improved with the proposed algorithm.

Reconstruction of Fluorescence Molecular Tomography via a Fused LASSO Method Based on Group Sparsity Prior

OBJECTIVE

The aim of this paper is to improve the reconstruction accuracy in both position and source region of fluorescence molecular tomography (FMT).

METHODS

The reconstruction of the FMT is challenging due to its serious ill-posedness and ill-condition. Currently, to obtain the fluorescent sources accurately, more a priori information of the fluorescent sources is utilized and more efficient and practical methods are proposed. In this paper, we took the group sparsity of the fluorescent sources as a new type of priori information in the FMT, and proposed the fused LASSO method (FLM) for FMT. The FLM based on group sparsity prior not only takes advantage of the sparsity of the fluorescent sources, but also utilizes the structure of the sources, thus making the reconstruction results more accuracy and morphologically similar to the sources. To further improve the reconstruction efficiency, we adopt Nesterov's method to solve the FLM.

RESULTS

Both heterogeneous numerical simulation experiments and in vivo mouse experiments were carried out to verify the property of the FLM. The results have verified the superiority of the FLM over conventional methods in tumor detection and tumor morphological reconstruction. Furthermore, the in vivo experiments had demonstrated that the FLM has great potential in preclinical application of the FMT.

SIGNIFICANCE

The reconstruction method based on group sparsity prior has a great potential in the FMT study, it can further improve the reconstruction quality, which has practical significance in preclinical research.

Reconstruction method for fluorescence molecular tomography based on L1-norm primal accelerated proximal gradient

Fluorescence molecular tomography (FMT) has been widely used in preclinical tumor imaging, which enables three-dimensional imaging of the distribution of fluorescent probes in small animal bodies via image reconstruction method. However, the reconstruction results are usually unsatisfactory in the term of robustness and efficiency because of the ill-posed and ill-conditioned of FMT problem. In this study, an FMT reconstruction method based on primal accelerated proximal gradient (PAPG) descent and L1-norm regularized projection (L1RP) is proposed. The proposed method utilizes the current and previous iterations to obtain a search point at each iteration. To achieve fast convergence, the PAPG method is applied to efficiently solve the search point, and then L1RP is performed to obtain the robust and accurate reconstruction. To verify the performance of the proposed method, simulation experiments are conducted. The comparative results revealed that it held advantages of robustness, accuracy, and efficiency in FMT reconstructions. Furthermore, a phantom experiment and an in vivo mouse experiment were also performed, which proved the potential and feasibility of the proposed method for practical applications.

An Lp (0 ≤ p ≤ 1)-norm regularized image reconstruction scheme for breast DOT with non-negative-constraint

Background

In diffuse optical tomography (DOT), the image reconstruction is often an ill-posed inverse problem, which is even more severe for breast DOT since there are considerably increasing unknowns to reconstruct with regard to the achievable number of measurements. One common way to address this ill-posedness is to introduce various regularization methods. There has been extensive research regarding constructing and optimizing objective functions. However, although these algorithms dramatically improved reconstruction images, few of them have designed an essentially differentiable objective function whose full gradient is easy to obtain to accelerate the optimization process.

Methods

This paper introduces a new kind of non-negative prior information, designing differentiable objective functions for cases of L₁-norm, L_p (0 < p < 1)-norm and L₀-norm. Incorporating this non-negative prior information, it is easy to obtain the gradient of these differentiable objective functions, which is useful to guide the optimization process.

Results

Performance analyses are conducted using both numerical and phantom experiments. In terms of spatial resolution, quantitativeness, gray resolution and execution time, the proposed methods perform better than the conventional regularization methods without this non-negative prior information.

Conclusions

The proposed methods improves the reconstruction images using the introduced non-negative prior information. Furthermore, the non-negative constraint facilitates the gradient computation, accelerating the minimization of the objective functions.

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 Nesterov's 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.

Dimensionality Reduction Based Optimization Algorithm for Sparse 3-D Image Reconstruction in Diffuse Optical Tomography

Diffuse optical tomography (DOT) is a relatively low cost and portable imaging modality for reconstruction of optical properties in a highly scattering medium, such as human tissue. The inverse problem in DOT is highly ill-posed, making reconstruction of high-quality image a critical challenge. Because of the nature of sparsity in DOT, sparsity regularization has been utilized to achieve high-quality DOT reconstruction. However, conventional approaches using sparse optimization are computationally expensive and have no selection criteria to optimize the regularization parameter. In this paper, a novel algorithm, Dimensionality Reduction based Optimization for DOT (DRO-DOT), is proposed. It reduces the dimensionality of the inverse DOT problem by reducing the number of unknowns in two steps and thereby makes the overall process fast. First, it constructs a low resolution voxel basis based on the sensing-matrix properties to find an image support. Second, it reconstructs the sparse image inside this support. To compensate for the reduced sensitivity with increasing depth, depth compensation is incorporated in DRO-DOT. An efficient method to optimally select the regularization parameter is proposed for obtaining a high-quality DOT image. DRO-DOT is also able to reconstruct high-resolution images even with a limited number of optodes in a spatially limited imaging set-up.

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

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.

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 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

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 /₁-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.

Nonuniform update for sparse target recovery in fluorescence molecular tomography accelerated by ordered subsets

Fluorescence molecular tomography (FMT) is a promising imaging modality and has been actively studied in the past two decades since it can locate the specific tumor position three-dimensionally in small animals. However, it remains a challenging task to obtain fast, robust and accurate reconstruction of fluorescent probe distribution in small animals due to the large computational burden, the noisy measurement and the ill-posed nature of the inverse problem. In this paper we propose a nonuniform preconditioning method in combination with L (1) regularization and ordered subsets technique (NUMOS) to take care of the different updating needs at different pixels, to enhance sparsity and suppress noise, and to further boost convergence of approximate solutions for fluorescence molecular tomography. Using both simulated data and phantom experiment, we found that the proposed nonuniform updating method outperforms its popular uniform counterpart by obtaining a more localized, less noisy, more accurate image. The computational cost was greatly reduced as well. The ordered subset (OS) technique provided additional 5 times and 3 times speed enhancements for simulation and phantom experiments, respectively, without degrading image qualities. When compared with the popular L (1) algorithms such as iterative soft-thresholding algorithm (ISTA) and Fast iterative soft-thresholding algorithm (FISTA) algorithms, NUMOS also outperforms them by obtaining a better image in much shorter period of time.