Reconstructing high-dimensional sparse signals from low-dimensional low-count photon observations is a challenging nonlinear optimization problem. In this paper, we build upon previous work on minimizing the Poisson log-likelihood and incorporate recent work on the generalized nonconvex Shannon entropy function for promoting sparsity in solutions. We explore the effectiveness of the proposed approach using numerical experiments.
Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.
Image reconstruction in diffuse optical tomography (DOT) is challenging because its inverse problem is nonlinear, ill-posed and ill-conditioned. Anatomical guidance from high spatial resolution imaging modalities can substantially improve the quality of reconstructed DOT images. In this paper, inspired by the kernel methods in machine learning, we propose the kernel method to introduce anatomical information into the DOT image reconstruction algorithm. In this kernel method, optical absorption coefficient at each finite element node is represented as a function of a set of features obtained from anatomical images such as computed tomography (CT). The kernel based image model is directly incorporated into the forward model of DOT, which exploits the sparseness of the image in the feature space. Compared with Laplacian approaches to include structural priors, the proposed method does not require the image segmentation of distinct regions. The proposed kernel method is validated with numerical simulations of 3D DOT reconstruction using synthetic CT data. We added 15% Gaussian noise onto both the numerical DOT measurements and the simulated CT image. We have also validated the proposed method by agar phantom experiment with anatomical guidance from a CT scan. We have studied the effects of voxel size and number of nearest neighborhood size in kernel method on the reconstructed DOT images. Our results indicate that the spatial resolution and the accuracy of the reconstructed DOT images have been improved substantially after applying the anatomical guidance with the proposed kernel method.
Reconstruction of fluorescence molecular tomography (FMT) is an ill-posed inverse problem. Anatomical guidance in the FMT reconstruction can improve FMT reconstruction efficiently. We have developed a kernel method to introduce the anatomical guidance into FMT robustly and easily. The kernel method is from machine learning for pattern analysis and is an efficient way to represent anatomical features. For the finite element method based FMT reconstruction, we calculate a kernel function for each finite element node from an anatomical image, such as a micro-CT image. Then the fluorophore concentration at each node is represented by a kernel coefficient vector and the corresponding kernel function. In the FMT forward model, we have a new system matrix by multiplying the sensitivity matrix with the kernel matrix. Thus, the kernel coefficient vector is the unknown to be reconstructed following a standard iterative reconstruction process. We convert the FMT reconstruction problem into the kernel coefficient reconstruction problem. The desired fluorophore concentration at each node can be calculated accordingly. Numerical simulation studies have demonstrated that the proposed kernel-based algorithm can improve the spatial resolution of the reconstructed FMT images. In the proposed kernel method, the anatomical guidance can be obtained directly from the anatomical image and is included in the forward modeling. One of the advantages is that we do not need to segment the anatomical image for the targets and background.
Diffuse optical tomography (DOT) has attracted attentions in the last two decades due to its intrinsic sensitivity in imaging chromophores of tissues such as blood, water, and lipid. However, DOT has not been clinically accepted yet due to its low spatial resolution caused by strong optical scattering in tissues. Structural guidance provided by an anatomical imaging modality enhances the DOT imaging substantially. Here, we propose a computed tomography (CT) guided multispectral DOT imaging system for breast cancer detection. To validate its feasibility, we have built a prototype DOT imaging system which consists of a laser at wavelengths of 650 and an electron multiplying charge coupled device (EMCCD) camera. We have validated the CT guided DOT reconstruction algorithms with numerical simulations and phantom experiments, in which different imaging setup parameters, such as projection number of measurements, the width of measurement patch, have been investigated. Our results indicate that an EMCCD camera with air cooling is good enough for the transmission mode DOT imaging. We have also found that measurements at six projections are sufficient for DOT to reconstruct the optical targets with 4 times absorption contrast when the CT guidance is applied. Finally, we report our effort and progress on the integration of the multispectral DOT imaging system into a breast CT scanner.
We have developed a new fluorescence molecular tomography (FMT) imaging system, in which we utilized a phase shifting method to extract the mouse surface geometry optically and a rotary laser scanning approach to excite fluorescence molecules and acquire fluorescent measurements on the whole mouse body. Nine fringe patterns with a phase shifting of 2π/9 are projected onto the mouse surface by a projector. The fringe patterns are captured using a webcam to calculate a phase map that is converted to the geometry of the mouse surface with our algorithms. We used a DigiWarp approach to warp a finite element mesh of a standard digital mouse to the measured mouse surface thus the tedious and time-consuming procedure from a point cloud to mesh is avoided. Experimental results indicated that the proposed method is accurate with errors less than 0.5 mm. In the FMT imaging system, the mouse is placed inside a conical mirror and scanned with a line pattern laser that is mounted on a rotation stage. After being reflected by the conical mirror, the emitted fluorescence photons travel through central hole of the rotation stage and the band pass filters in a motorized filter wheel, and are collected by a CCD camera. Phantom experimental results of the proposed new FMT imaging system can reconstruct the target accurately.