Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition

<p>Abstract</p> <p>Background</p> <p>The inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity. In this research, a tree structured Schur complement decomposition strategy is proposed to accelerate the reconstruction process and reduce the computational complexity. Additionally, an adaptive regularization scheme is developed to improve the ill-posedness of the inverse problem.</p> <p>Methods</p> <p>The global system is decomposed level by level with the Schur complement system along two paths in the tree structure. The resultant subsystems are solved in combination with the biconjugate gradient method. The mesh for the inverse problem is generated incorporating the prior information. During the reconstruction, the regularization parameters are adaptive not only to the spatial variations but also to the variations of the objective function to tackle the ill-posed nature of the inverse problem.</p> <p>Results</p> <p>Simulation results demonstrate that the strategy of the tree structured Schur complement decomposition obviously outperforms the previous methods, such as the conventional Conjugate-Gradient (CG) and the Schur CG methods, in both reconstruction accuracy and speed. As compared with the Tikhonov regularization method, the adaptive regularization scheme can significantly improve ill-posedness of the inverse problem.</p> <p>Conclusions</p> <p>The methods proposed in this paper can significantly improve the reconstructed image quality of FMT and accelerate the reconstruction process.</p

Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization

We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse reconstruction-based approach, which performs truncated singular value decomposition-based preconditioning followed by fast iterative shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation for this approach is that sparsity information could be accounted for within the initialization, while MLEM would accurately model Poisson noise in the FMT system. Simulation experiments show the proposed method significantly improves images qualitatively and quantitatively. The method results in over 20 times faster convergence compared to uniformly initialized MLEM and improves robustness to noise compared to pure sparse reconstruction. We also theoretically justify the ability of the proposed approach to reduce noise in the background region compared to pure sparse reconstruction. Overall, these results provide strong evidence to model Poisson noise in FMT reconstruction and for application of the proposed reconstruction framework to FMT imaging

Split operator method for fluorescence diffuse optical tomography using anisotropic diffusion regularisation with prior anatomical information

Fluorescence diffuse optical tomography (fDOT) is an imaging modality that provides images of the fluorochrome distribution within the object of study. The image reconstruction problem is ill-posed and highly underdetermined and, therefore, regularisation techniques need to be used. In this paper we use a nonlinear anisotropic diffusion regularisation term that incorporates anatomical prior information. We introduce a split operator method that reduces the nonlinear inverse problem to two simpler problems, allowing fast and efficient solution of the fDOT problem. We tested our method using simulated, phantom and ex-vivo mouse data, and found that it provides reconstructions with better spatial localisation and size of fluorochrome inclusions than using the standard Tikhonov penalty term

Tomographic Laser Absorption Imaging of Combustion Gases in the Mid-wave Infrared

This dissertation describes advancements in mid-infrared laser absorption tomography for spatio-temporal measurements of thermochemistry in reacting flows relevant to combustion systems. Tunable laser absorption spectroscopy is combined with tomographic reconstruction techniques to resolve small diameter ( &lt; 1 cm) non-uniform flow fields with steep spatial gradients, leveraging emerging mid-wave infrared photonics. Multiple novel measurement methods, hardware configurations, and image processing techniques were investigated. Initially, a mid-infrared laser absorption tomography sensing method was developed for quantitative measurement of CO and CO2 concentrations and temperature distributions in turbulent premixed jet flames using a translation-stage-mounted optical system. This sensing approach was used to examine effects of varying fuel structure on carbon oxidation over a range of Reynolds number regimes. It was found that spatial and temporal resolution is limited in this method due to the finite laser beam size (~ 1 mm) and the slow mechanical translation of the optical system. To address these limitations, a novel laser absorption imaging (LAI) technique, that expands a single laser beam and replaces the detector with a high-speed infrared camera, was introduced to achieve enhanced spatial and temporal resolution for thermo-chemical imaging. As a demonstration of this new technique, distributions of combustion species were imaged in both axisymmetric and non-axisymmetric flow fields using linear tomography algorithms. For non-axisymetric flows, the limited view tomography problem often results in a blurring effect and artifacts in the reconstructed flow-field. In an effort to address these issues, state-of-the-art deep learning neural networks were developed and applied to solve the limited angle inversion. Initial results suggest that deep neural networks have potential to more accurately predict flame structures with fewer projection angles than linear tomography. This work provides a foundation for a new approach to quantitative time-resolved 3D thermo-chemical imaging in high-temperature reacting flows

Guest Editorial to the Special Letters Issue on Emerging Technologies in Multiparameter Biomedical Optical Imaging and Image Analysis

The past two decades have witnessed revolutionary advances in biomedical imaging modalities capable of providing biological and physiological information from the cellular scale to the organ level. Recent advances have also been focused on cost-effective, noninvasive, portable, and molecularimaging technologies for imaging at microscopic, mesoscopic, and macroscopic levels. These technologies have significant potential to advance biomedical research and clinical practice. They can also provide a better understanding and monitoring of physiological and functional disorders, which could lead to mainstream diagnostic technologies of the future

An Efficient Numerical Method for General

Reconstruction algorithms for fluorescence tomography have to address two crucial issues : 1) the ill-posedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3-D samples. Our contribution is the design and implementation of a reconstruction algorithm that incorporates general Lp regularization (p ≥ 1). The originality of this work lies in the application of general Lp constraints to fluorescence tomography, combined with an efficient matrix-free strategy that enables the algorithm to deal with large reconstruction problems at reduced memory and computational costs. In the experimental part, we specialize the application of the algorithm to the case of sparsity promoting constraints (L1). We validate the adequacy of L1 regularization for the investigation of phenomena that are well described by a sparse model, using data acquired during phantom experiments

Improved Modeling and Image Generation for Fluorescence Molecular Tomography (FMT) and Positron Emission Tomography (PET)

In this thesis, we aim to improve quantitative medical imaging with advanced image generation algorithms. We focus on two specific imaging modalities: fluorescence molecular tomography (FMT) and positron emission tomography (PET). For FMT, we present a novel photon propagation model for its forward model, and in addition, we propose and investigate a reconstruction algorithm for its inverse problem. In the first part, we develop a novel Neumann-series-based radiative transfer equation (RTE) that incorporates reflection boundary conditions in the model. In addition, we propose a novel reconstruction technique for diffuse optical imaging that incorporates this Neumann-series-based RTE as forward model. The proposed model is assessed using a simulated 3D diffuse optical imaging setup, and the results demonstrate the importance of considering photon reflection at boundaries when performing photon propagation modeling. In the second part, we propose a statistical reconstruction algorithm for FMT. The algorithm is based on sparsity-initialized maximum-likelihood expectation maximization (MLEM), taking into account the Poisson nature of data in FMT and the sparse nature of images. The proposed method is compared with a pure sparse reconstruction method as well as a uniform-initialized MLEM reconstruction method. Results indicate the proposed method is more robust to noise and shows improved qualitative and quantitative performance. For PET, we present an MRI-guided partial volume correction algorithm for brain imaging, aiming to recover qualitative and quantitative loss due to the limited resolution of PET system, while keeping image noise at a low level. The proposed method is based on an iterative deconvolution model with regularization using parallel level sets. A non-smooth optimization algorithm is developed so that the proposed method can be feasibly applied for 3D images and avoid additional blurring caused by conventional smooth optimization process. We evaluate the proposed method using both simulation data and in vivo human data collected from the Baltimore Longitudinal Study of Aging (BLSA). Our proposed method is shown to generate images with reduced noise and improved structure details, as well as increased number of statistically significant voxels in study of aging. Results demonstrate our method has promise to provide superior performance in clinical imaging scenarios