PET Image Reconstruction With Kernel and Kernel Space Composite Regularizer.

Led by the kernelized expectation maximization (KEM) method, the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration numbers, and the difficulty in preserving image details and suppressing image variance simultaneously. To solve these problems, this paper derives, using the ideas of data manifold and graph regularization, a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction.

Dynamic PET images denoising using spectral graph wavelet transform.

Positron emission tomography (PET) is a non-invasive molecular imaging method for quantitative observation of physiological and biochemical changes in living organisms. The quality of the reconstructed PET image is limited by many different physical degradation factors. Various denoising methods including Gaussian filtering (GF) and non-local mean (NLM) filtering have been proposed to improve the image quality.

Kernel graph filtering-A new method for dynamic sinogram denoising.

Low count PET (positron emission tomography) imaging is often desirable in clinical diagnosis and biomedical research, but its images are generally very noisy, due to the very weak signals in the sinograms used in image reconstruction. To address this issue, this paper presents a novel kernel graph filtering method for dynamic PET sinogram denoising. This method is derived from treating the dynamic sinograms as the signals on a graph, and learning the graph adaptively from the kernel principal components of the sinograms to construct a lowpass kernel graph spectrum filter.

Optimal design of multichannel equalizers for the structural similarity index.

The optimization of multichannel equalizers is studied for the structural similarity (SSIM) criteria. The closed-form formula is provided for the optimal equalizer when the mean of the source is zero. The formula shows that the equalizer with maximal SSIM index is equal to the one with minimal mean square error (MSE) multiplied by a positive real number, which is shown to be equal to the inverse of the achieved SSIM index.