Total variation regularization in measurement and image space for PET reconstruction

Burger, Martin; Müller, Jahn; Papoutsellis, Evangelos; Schönlieb, Carola-Bibiane

doi:10.1088/0266-5611/30/10/105003

Cited by 53 publications

(43 citation statements)

References 35 publications

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“…For example, several methods in [10][11][12] set η(·) as the total variation. The Expectation Maximization (EM) algorithm and the Ordered Subset EM (OSEM) algorithms are commonly employed for the minimization.…”

Section: Pet Image Reconstructionmentioning

confidence: 99%

“…The works in [7][8][9] introduced nonnegativity. The works in [10][11][12] introduced the Total Variation (TV) norm of resultant images, or both resultant images and sinograms. These methods reconstruct a PET image from a sinogram measured each time one by one.…”

Section: Introductionmentioning

confidence: 99%

“…A smooth regularizer such as the TV norm of reconstructed PET images is also widely introduced as a regularizer. It is reported that TV-norm regularization improves the SNR of reconstructed PET images [10][11][12]. Lower values of the TV norm can be obtained when the images are partially constant.…”

Section: Introductionmentioning

confidence: 99%

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Parametric PET Image Reconstruction via Regional Spatial Bases and Pharmacokinetic Time Activity Model

Kawamura

Yokota

Hontani

et al. 2017

Entropy

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Abstract:It is known that the process of reconstruction of a Positron Emission Tomography (PET) image from sinogram data is very sensitive to measurement noises; it is still an important research topic to reconstruct PET images with high signal-to-noise ratios. In this paper, we propose a new reconstruction method for a temporal series of PET images from a temporal series of sinogram data. In the proposed method, PET images are reconstructed by minimizing the Kullback-Leibler divergence between the observed sinogram data and sinogram data derived from a parametric model of PET images. The contributions of the proposition include the following: (1) regions of targets in images are explicitly expressed using a set of spatial bases in order to ignore the noises in the background; (2) a parametric time activity model of PET images is explicitly introduced as a constraint; and (3) an algorithm for solving the optimization problem is clearly described. To demonstrate the advantages of the proposed method, quantitative evaluations are performed using both synthetic and clinical data of human brains.

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Section: Pet Image Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parametric PET Image Reconstruction via Regional Spatial Bases and Pharmacokinetic Time Activity Model

Kawamura

Yokota

Hontani

et al. 2017

Entropy

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“…The edge information usually represents the sharp variation in images, such as the object boundaries, which is very important and useful for clinical diagnosis, e.g., of tumors [14]. Given the nature of PET images, researchers have proposed total variation (TV) based methods for both the image space and the projection space in PET image reconstruction [15]. TV was incorporated to provide edge-preserving guidance for the reconstruction [15], and it is well known that it suppresses noise effectively while preserving sharp edges [16–18].…”

Section: Introductionmentioning

confidence: 99%

Low Dose PET Image Reconstruction with Total Variation Using Alternating Direction Method

Wang

et al. 2016

PLoS ONE

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In this paper, a total variation (TV) minimization strategy is proposed to overcome the problem of sparse spatial resolution and large amounts of noise in low dose positron emission tomography (PET) imaging reconstruction. Two types of objective function were established based on two statistical models of measured PET data, least-square (LS) TV for the Gaussian distribution and Poisson-TV for the Poisson distribution. To efficiently obtain high quality reconstructed images, the alternating direction method (ADM) is used to solve these objective functions. As compared with the iterative shrinkage/thresholding (IST) based algorithms, the proposed ADM can make full use of the TV constraint and its convergence rate is faster. The performance of the proposed approach is validated through comparisons with the expectation-maximization (EM) method using synthetic and experimental biological data. In the comparisons, the results of both LS-TV and Poisson-TV are taken into consideration to find which models are more suitable for PET imaging, in particular low-dose PET. To evaluate the results quantitatively, we computed bias, variance, and the contrast recovery coefficient (CRC) and drew profiles of the reconstructed images produced by the different methods. The results show that both Poisson-TV and LS-TV can provide a high visual quality at a low dose level. The bias and variance of the proposed LS-TV and Poisson-TV methods are 20% to 74% less at all counting levels than those of the EM method. Poisson-TV gives the best performance in terms of high-accuracy reconstruction with the lowest bias and variance as compared to the ground truth (14.3% less bias and 21.9% less variance). In contrast, LS-TV gives the best performance in terms of the high contrast of the reconstruction with the highest CRC.

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“…It assumes that the refractive index distribution of the analyzed object is a step function -patches with constant values are present. In the reconstruction process this constraint is applied by iteratively minimizing the total variation function of the calculated reconstruction, or in other words by minimizing the first norm of the reconstruction gradient 14,15 . Despite the fact, that this method gives highquality results in the case of limited-angle tomography, its applicability is limited to a small group of optically piecewise constant samples: mainly technological ones.…”

Section: Introductionmentioning

confidence: 99%

Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures

2015

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Standard tomographic algorithms applied to optical limited-angle tomography result in the reconstructions that have highly anisotropic resolution and thus special algorithms are developed. State of the art approaches utilize the Total Variation (TV) minimization technique. These methods give very good results but are applicable to piecewise constant structures only. In this paper, we propose a novel algorithm for 3D limited-angle tomography -Total Variation Iterative Constraint method (TVIC) which enhances the applicability of the TV regularization to non-piecewise constant samples, like biological cells. This approach consists of two parts. First, the TV minimization is used as a strong regularizer to create a sharp-edged image converted to a 3D binary mask which is then iteratively applied in the tomographic reconstruction as a constraint in the object domain. In the present work we test the method on a synthetic object designed to mimic basic structures of a living cell. For simplicity, the test reconstructions were performed within the straight-line propagation model (SIRT3D solver from the ASTRA Tomography Toolbox), but the strategy is general enough to supplement any algorithm for tomographic reconstruction that supports arbitrary geometries of plane-wave projection acquisition. This includes optical diffraction tomography solvers. The obtained reconstructions present resolution uniformity and general shape accuracy expected from the TV regularization based solvers, but keeping the smooth internal structures of the object at the same time. Comparison between three different patterns of object illumination arrangement show very small impact of the projection acquisition geometry on the image quality.

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Total variation regularization in measurement and image space for PET reconstruction

Cited by 53 publications

References 35 publications

Parametric PET Image Reconstruction via Regional Spatial Bases and Pharmacokinetic Time Activity Model

Parametric PET Image Reconstruction via Regional Spatial Bases and Pharmacokinetic Time Activity Model

Low Dose PET Image Reconstruction with Total Variation Using Alternating Direction Method

Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures

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