PET image reconstruction using kernel method

Abstract

Image reconstruction from low-count PET projection data is challenging because the inverse problem is ill-posed. Prior information can be used to improve image quality. Inspired by the kernel methods in 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 the maximum likelihood (ML) or penalized likelihood image reconstruction. A kernelized expectation-maximization (EM) algorithm is presented to obtain the ML estimate. Computer simulations show that the proposed approach can achieve better bias versus variance trade-off and higher contrast recovery for dynamic PET image reconstruction than the conventional maximum likelihood method with and without post-reconstruction denoising. Compared with other regularization-based methods, the kernel method is easier to implement and provides better image quality for low-count data. Application of the proposed kernel method to a 4D dynamic PET patient dataset showed promising results.

A Novel Kernel-Based Regularization Technique for PET Image Reconstruction

“…Inspired by the kernel-based image representation for PET images [25], we propose a new kernel-based image regularization technique to improve the PET image reconstruction. We define x j as a feature map for pixel j that is the output of the kernel, which is a mixture of two sets of information.…”

“…Therefore, to improve the quality of the image, we propose a novel kernel-based image regularization technique. Of the various possible options of the kernel function, an exponentially-modified Gaussian kernel was used [24][25][26]; this is comparable to conventional MLEM reconstruction in terms of simplicity. Noise is modeled in the projection domain, where independent Poisson random variables effectively model the PET data.…”

Detail-Preserving PET Reconstruction with Sparse Image Representation and Anatomical Priors

“…PET reconstruction was performed with pre-reconstruction correction for attenuation, and the estimated scatter and randoms were incorporated in the forward model. The maximum likelihood-expectation maximisation method with no prior [8] (MLEM ), the bowsher method [4] (Bowsher ), the kernelised EM method [11] (KEM ) and the proposed reconstruction algorithm using sparse image representation (SIR) were performed for reconstruction. All the methods used the same resampling operator R in Eq.…”

“…Recent reviews on using anatomical prior information for PET image reconstruction can be found in [5,6,10], and the Bowsher method [4] which encourages PET image smoothness over the neighbour voxels selected from the anatomical image, was found to achieve better performance while being relatively efficient computationally compared to other methods [5]. Apart from the penalised likelihood PET reconstruction frameworks, very recently an alternative perspective of using the image-derived prior was proposed in [11], by incorporating the prior information into the image representation via kernel functions, and the regularisation was applied to the PET forward model. This leads to a very elegant kernelised EM solution and achieves better performance.…”

“…This approach can be considered as a segmentation-based reconstruction method which is potentially able to eliminate the partial volume effect and it is more flexible than the method proposed in [3]. The prior information is integrated in the image representation as in [11], and therefore the regularisation operates in the forward model instead of in the additive penalty term, so the reconstruction is directly solved by the EM algorithm. Experiments using simulated and clinical data show promising results.…”