Guobao Wang

Generalized Algorithms for Direct Reconstruction of Parametric Images From Dynamic PET Data

Indirect and direct methods have been developed for reconstructing parametric images from dynamic positron emission tomography (PET) data. Indirect methods are simple and easy to implement because reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from dynamic PET sinograms and, in theory, can be statistically more efficient, but the algorithms are often difficult to implement and are very specific to the kinetic model being used. This paper presents a class of generalized algorithms for direct reconstruction of parametric images that are relatively easy to implement and can be adapted to different kinetic models. The proposed algorithms use optimization transfer principle to convert the maximization of a penalized likelihood into a pixel-wise weighted least squares (WLS) kinetic fitting problem at each iteration. Thus, it can employ existing WLS algorithms developed for kinetic models. The proposed algorithms resemble the empirical iterative implementation of the indirect approach, but converge to a solution of the direct formulation. Computer simulations showed that the proposed direct reconstruction algorithms are flexible and achieve a better bias-variance tradeoff than indirect reconstruction methods.

Maximum a posteriori reconstruction of the Patlak parametric image from sinograms in dynamic PET

Parametric imaging using Patlak graphical method has been widely used to analyze dynamic PET data. The conventional way to generate Patlak parametric image is to reconstruct dynamic images first and then perform Patlak graphical analysis on the time activity curves pixel-by-pixel. In this paper we present a Bayesian method for reconstructing Patlak parametric images directly from raw sinogram data by combining the Patlak plot model with image reconstruction. A preconditioned conjugate gradient algorithm is used to find the maximum a posteriori solution. We conduct computer simulations to validate the proposed method. The comparison with conventional indirect approaches shows that the proposed method results in more accurate estimate of the parametric image

Penalized Likelihood PET Image Reconstruction Using Patch-Based Edge-Preserving Regularization

Iterative image reconstruction for positron emission tomography (PET) can improve image quality by using spatial regularization that penalizes image intensity difference between neighboring pixels. The most commonly used quadratic penalty often oversmoothes edges and fine features in reconstructed images. Nonquadratic penalties can preserve edges but often introduce piece-wise constant blocky artifacts and the results are also sensitive to the hyper-parameter that controls the shape of the penalty function. This paper presents a patch-based regularization for iterative image reconstruction that uses neighborhood patches instead of individual pixels in computing the nonquadratic penalty. The new regularization is more robust than the conventional pixel-based regularization in differentiating sharp edges from random fluctuations due to noise. An optimization transfer algorithm is developed for the penalized maximum likelihood estimation. Each iteration of the algorithm can be implemented in three simple steps: an EM-like image update, an image smoothing and a pixel-by-pixel image fusion. Computer simulations show that the proposed patch-based regularization can achieve higher contrast recovery for small objects without increasing background variation compared with the quadratic regularization. The reconstruction is also more robust to the hyper-parameter than conventional pixel-based nonquadratic regularizations. The proposed regularization method has been applied to real 3-D PET data.

Acceleration of the direct reconstruction of linear parametric images using nested algorithms

Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

Direct estimation of kinetic parametric images for dynamic PET.

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed.

An Optimization Transfer Algorithm for Nonlinear Parametric Image Reconstruction From Dynamic PET Data

Direct reconstruction of kinetic parameters from raw projection data is a challenging task in molecular imaging using dynamic positron emission tomography (PET). This paper presents a new optimization transfer algorithm for penalized likelihood direct reconstruction of nonlinear parametric images that is easy to use and has a fast convergence rate. Each iteration of the proposed algorithm can be implemented in three simple steps: a frame-by-frame maximum likelihood expectation-maximization (EM)-like image update, a frame-by-frame image smoothing, and a pixel-by-pixel time activity curve fitting. Computer simulation shows that the direct algorithm can achieve a better bias-variance performance than the indirect reconstruction algorithm. The convergence rate of the new algorithm is substantially faster than our previous algorithm that is based on a separable paraboloidal surrogate function. The proposed algorithm has been applied to real 4-D PET data.

Recursive computation of Tchebichef moment and its inverse transform

Tchebichef moment is a novel set of orthogonal moment applied in the fields of image analysis and pattern recognition. Less work has been made for the computation of Tchebichef moment and its inverse moment transform. In this paper, both a direct recursive algorithm and a compact algorithm are developed for the computation of Tchebichef moment. The effective recursive algorithm for inverse Tchebichef moment transform is also presented. Clenshaws recurrence formula was used in this paper to transform kernels of the forward and inverse Tchebichef moment transform. There is no need for the proposed algorithms to compute the Tchebichef polynomial values. The approaches presented are more efficient compared with the straightforward methods, and particularly suitable for parallel VLSI implementation due to their regular and simple filter structures.

Three-Dimensional Fluorescence Optical Tomography in Small Animal Imaging using Simultaneous Positron Emission Tomography Priors

We propose three-dimensional fluorescence optical tomography imaging for small animals guided by simultaneous priors from positron emission tomography (PET). Using a sparsity regularization, the target prior from PET images was incorporated into the reconstruction algorithm for optical imaging. The method and algorithms are validated with numerical simulations and a phantom experiment performed on a combined optical-PET scanner based on a conical mirror geometry.

PET Image Reconstruction Using Kernel Method

Image reconstruction from low-count PET projection data is challenging because the inverse problem is ill-posed. Inspired by the kernel methods for machine learning, this paper proposes a kernel based method that models PET image intensity in each pixel as a function of a set of features obtained from prior information. The kernel-based image model is incorporated into the forward model of PET projection data and the coefficients can be readily estimated by maximum likelihood or penalized likelihood image reconstruction. Computer simulation shows that the proposed approach can achieve a higher signal-to-noise ratio for dynamic PET image reconstruction than the conventional maximum likelihood method with and without post-reconstruction denoising.

Measurement of sinusoidal vibration from motion blurred images

Previous vision-based methods usually measure vibration from large sequence of unblurred images recorded by high-speed video or stroboscopic photography. In this paper, we propose a novel method for sinusoidal vibration measurement based on motion blurred images. We represent the motion blur information in images by the relationship between the geometric moments of the motion blurred images and the motion, and estimate the vibration parameters from this motion blur cue. We need only one motion blurred image and an unblurred image or two successive frames of blurred images to calculate the parameters of low-frequency vibration as well as the amplitude and direction of high-frequency vibration, while unblurred-image-based techniques rely on much more images to obtain the same results and existing motion-blurred-image-based approaches only estimate the amplitude of high-frequency vibration. Experimental results with both simulated and real vibrations of low and high frequencies are employed to demonstrate the effectiveness of the proposed scheme.