A PET reconstruction formulation that enforces non-negativity in projection space for bias reduction in Y-90 imaging

Lim, Hongki; Dewaraja, Yuni K.; Fessler, Jeffrey A.

doi:10.1088/1361-6560/aaa71b

Cited by 23 publications

(28 citation statements)

References 19 publications

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“…For fan beam and cone beam CT, we use the synthetic extended cardiac-torso (XCAT) data [59] and follow the setup of [68]. For PET, we use the data of [41] and follow its setup.…”

Section: Methodsmentioning

confidence: 99%

Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET

Ryu¹,

Ko²,

Won³

2020

SIAM J. Sci. Comput.

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Many imaging problems, such as total variation reconstruction of X-ray computed tomography (CT) and positron-emission tomography (PET), are solved via a convex optimization problem with near-circulant, but not actually circulant, linear systems. The popular methods to solve these problems, alternating directions method of multipliers (ADMM) and primal-dual hybrid gradient (PDHG), do not directly utilize this structure. Consequently, ADMM requires a costly matrix inversion as a subroutine, and PDHG takes too many iterations to converge. In this paper, we present Near-Circulant Splitting (NCS), a novel splitting method that leverages the near-circulant structure. We show that NCS can converge with an iteration count close to that of ADMM, while paying a computational cost per iteration close to that of PDHG. Through experiments on a CUDA GPU, we empirically validate the theory and demonstrate that NCS can effectively utilize the parallel computing capabilities of CUDA.

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“…For fan beam and cone beam CT, we use the synthetic extended cardiac-torso (XCAT) data [59] and follow the setup of [68]. For PET, we use the data of [41] and follow its setup.…”

Section: Methodsmentioning

confidence: 99%

Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET

Ryu¹,

Ko²,

Won³

2020

SIAM J. Sci. Comput.

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“…In practice, the first assumption is most consistent with the physics in that it reflects the physical constraint that emission counts are non-negative. The last two assumptions were proposed to reduce positive bias in the cold region [30], i.e., the region that has zero count. In this work, we shall focus on the last two constraints.…”

Section: Problem Formulationmentioning

confidence: 99%

Expectation propagation for Poisson data

2019

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The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation propagation for approximating the posterior distribution formed from the Poisson likelihood function and a Laplace type prior distribution, e.g., the anisotropic total variation prior. The approach iteratively yields a Gaussian approximation, and at each iteration, it updates the Gaussian approximation to one factor of the posterior distribution by moment matching. We derive explicit update formulas in terms of one-dimensional integrals, and also discuss stable and efficient quadrature rules for evaluating these integrals. The method is showcased on two-dimensional PET images.

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“…In addition, these methods break the statistical model and therefore are vulnerable to noise amplification. More recently, Lim et al [15] have developed a penalized maximum-likelihood (PML) algorithm for PET that performs maximization of the penalized log-likelihood (PLL) with positivity constraint on the projections, by maximizing the PLL over its entire domain of definition. The optimization problem was reformulated as an augmented Lagrangian saddle point problem, which was solved with the help of an alternative direction method of multipliers (ADMM) [16].…”

Section: Introductionmentioning

confidence: 99%

PET Reconstruction With Non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence

Bousse

Emond

Thielemans

et al. 2020

IEEE Trans. Med. Imaging

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Standard positron emission tomography (PET) reconstruction techniques are based on maximum-likelihood (ML) optimization methods, such as the maximum-likelihood expectation-maximization (MLEM) algorithm and its variations. Most of these methodologies rely on a positivity constraint on the activity distribution image. Although this constraint is meaningful from a physical point of view, it can be a source of bias for low-count/high-background PET, which can compromise accurate quantification. Existing methods that allow for negative values in the estimated image usually utilize a modified loglikelihood, and therefore break the data statistics. In this work we propose to incorporate the positivity constraint on the projections only, by approximating the (penalized) log-likelihood function by an adequate sequence of objective functions that are easily maximized without constraint. This sequence is constructed such that there is hypo-convergence (a type of convergence that allows the convergence of the maximizers under some conditions) to the original log-likelihood, hence allowing us to achieve maximization with positivity constraint on the projections using simple settings. A complete proof of convergence under weak assumptions is given. We provide results of experiments on simulated data where we compare our methodology with the alternative direction method of multipliers (ADMM) method, showing that our algorithm converges to a maximizer which stays in the desired feasibility set, with faster convergence than ADMM. We also show that this approach reduces the bias, as compared with MLEM images, in necrotic tumors-which are characterized by cold regions surrounded by hot structures-while reconstructing similar activity values in hot regions.

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A PET reconstruction formulation that enforces non-negativity in projection space for bias reduction in Y-90 imaging

Cited by 23 publications

References 19 publications

Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET

Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET

Expectation propagation for Poisson data

PET Reconstruction With Non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence

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