Bayesian algorithms for PET image reconstruction with mean curvature and Gauss curvature diffusion regularizations

Zhu, Hongqing; Hu, Shu; Zhou, Jian; Bao, Xudong; Luo, Limin

doi:10.1016/j.compbiomed.2006.08.015

Cited by 21 publications

(16 citation statements)

References 25 publications

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“…Construction of a Bayesian network facilitated visualization of the strongest links between the sleep phenotypes and QTL and identification of sub-networks and patterns defined by those links that otherwise might not be seen [13], [14]. While some links are obvious (e.g.…”

Section: Resultsmentioning

confidence: 99%

Uncovering the Genetic Landscape for Multiple Sleep-Wake Traits

et al. 2009

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Despite decades of research in defining sleep-wake properties in mammals, little is known about the nature or identity of genes that regulate sleep, a fundamental behaviour that in humans occupies about one-third of the entire lifespan. While genome-wide association studies in humans and quantitative trait loci (QTL) analyses in mice have identified candidate genes for an increasing number of complex traits and genetic diseases, the resources and time-consuming process necessary for obtaining detailed quantitative data have made sleep seemingly intractable to similar large-scale genomic approaches. Here we describe analysis of 20 sleep-wake traits from 269 mice from a genetically segregating population that reveals 52 significant QTL representing a minimum of 20 genomic loci. While many (28) QTL affected a particular sleep-wake trait (e.g., amount of wake) across the full 24-hr day, other loci only affected a trait in the light or dark period while some loci had opposite effects on the trait during the light vs. dark. Analysis of a dataset for multiple sleep-wake traits led to previously undetected interactions (including the differential genetic control of number and duration of REM bouts), as well as possible shared genetic regulatory mechanisms for seemingly different unrelated sleep-wake traits (e.g., number of arousals and REM latency). Construction of a Bayesian network for sleep-wake traits and loci led to the identification of sub-networks of linkage not detectable in smaller data sets or limited single-trait analyses. For example, the network analyses revealed a novel chain of causal relationships between the chromosome 17@29cM QTL, total amount of wake, and duration of wake bouts in both light and dark periods that implies a mechanism whereby overall sleep need, mediated by this locus, in turn determines the length of each wake bout. Taken together, the present results reveal a complex genetic landscape underlying multiple sleep-wake traits and emphasize the need for a systems biology approach for elucidating the full extent of the genetic regulatory mechanisms of this complex and universal behavior.

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Section: Resultsmentioning

confidence: 99%

Uncovering the Genetic Landscape for Multiple Sleep-Wake Traits

et al. 2009

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“…If R H (U )=0, the corresponding U is then a piecewise minimal surface (i.e., ∀ x, H(U )=0). Compared to TV regularization, R H leads to better results for image denoising in practice [31], [32], which has been explained theoretically from a geometry point of view in [14], [11], [15] and a function analysis point of view in [12], [13].…”

Section: B Mean Curvature In Image Processingmentioning

confidence: 99%

Weighted mean curvature

Gong

Göksel

2019

Signal Processing

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In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature.

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“…The mean curvature and the Gauss curvature diffusion algorithms for filtering the PET images during reconstruction were investigated in [12]. An anatomically driven anisotropic diffusion filter (ADADF) as a penalized maximum likelihood expectation maximization optimization framework was proposed in [2].…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

“…The main drawback of the above filter, with respect to sinogram images is that the diffusion produces important oscillations in the gradient. This leads to a poorly smoothed image [11,12]. Moreover, the adopted diffusivity functions do not consider the special properties of the sinogram, which are high level of Poisson noise and curved-shape features.…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

“…It has to be noted that the diffusivity function (12) fits in the cluster of backward-forward diffusivities, and it has no free parameters to be set. Moreover, for the considered PET sinograms, the noise standard deviation, , in (16) is estimated as 2 = Var( Ln ), where the image noise, Ln , is reconstructed via wavelet decomposition of , from the two finest resolution levels coefficients, using Daubechies (4) wavelet.…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

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A Novel Adaptive Probabilistic Nonlinear Denoising Approach for Enhancing PET Data Sinogram

Alrefaya

Sahli

2013

Journal of Applied Mathematics

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We propose filtering the PET sinograms with a constraint curvature motion diffusion. The edge-stopping function is computed in terms of edge probability under the assumption of contamination by Poisson noise. We show that the Chi-square is the appropriate prior for finding the edge probability in the sinogram noise-free gradient. Since the sinogram noise is uncorrelated and follows a Poisson distribution, we then propose an adaptive probabilistic diffusivity function where the edge probability is computed at each pixel. The filter is applied on the 2D sinogram prereconstruction. The PET images are reconstructed using the Ordered Subset Expectation Maximization (OSEM). We demonstrate through simulations with images contaminated by Poisson noise that the performance of the proposed method substantially surpasses that of recently published methods, both visually and in terms of statistical measures.

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Bayesian algorithms for PET image reconstruction with mean curvature and Gauss curvature diffusion regularizations

Cited by 21 publications

References 25 publications

Uncovering the Genetic Landscape for Multiple Sleep-Wake Traits

Uncovering the Genetic Landscape for Multiple Sleep-Wake Traits

Weighted mean curvature

A Novel Adaptive Probabilistic Nonlinear Denoising Approach for Enhancing PET Data Sinogram

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