Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing.

Fluorescence diffuse optical tomography (FDOT) is an emerging molecular imaging modality that uses near infrared light to excite the fluorophore injected into tissue; and to reconstruct the fluorophore concentration from boundary measurements. The FDOT image reconstruction is a highly ill-posed inverse problem due to a large number of unknowns and limited number of measurements. However, the fluorophore distribution is often very sparse in the imaging domain since fluorophores are typically designed to accumulate in relatively small regions. In this paper, we use compressive sensing (CS) framework to design light illumination and detection patterns to improve the reconstruction of sparse fluorophore concentration. Unlike the conventional FDOT imaging where spatially distributed light sources illuminate the imaging domain one at a time and the corresponding boundary measurements are used for image reconstruction, we assume that the light sources illuminate the imaging domain simultaneously several times and the corresponding boundary measurements are linearly filtered prior to image reconstruction. We design a set of optical intensities (illumination patterns) and a linear filter (detection pattern) applied to the boundary measurements to improve the reconstruction of sparse fluorophore concentration maps. We show that the FDOT sensing matrix can be expressed as a columnwise Kronecker product of two matrices determined by the excitation and emission light fields. We derive relationships between the incoherence of the FDOT forward matrix and these two matrices, and use these results to reduce the incoherence of the FDOT forward matrix. We present extensive numerical simulation and the results of a real phantom experiment to demonstrate the improvements in image reconstruction due to the CS-based light illumination and detection patterns in conjunction with relaxation and greedy-type reconstruction algorithms

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