Augmented Lagrangian methods for penalized likelihood reconstruction in emission tomography

Lingenfelter, Daniel J.; Fessier, Jeffrey A.

doi:10.1109/nssmic.2010.5874413

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…To evaluate the performance of the proposed algorithm, we introduce five representative algorithms in comparison (the maximum likelihood-expectation maximization (ML–EM) algorithm [5], the penalized weighted least square (PWLS) method [8], the total variation optimized by augmented Lagrangian (TV-AL) method [48], the penalized likelihood incremental optimization method regularized by hyperbolic potential function [45,49] (denoted as PLH-IO), and the spatial-temporal total variation (ST-TV) method [50]) proposed for dynamic PET reconstruction.…”

Section: Experiments and Resultsmentioning

confidence: 99%

3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction

Xie

Chen

Liu

2019

Sensors

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Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably degraded by the limitations of photon emissions and the trade-off between temporal and spatial resolution. In this paper, we develop a novel tensor based nonlocal low-rank framework for dynamic PET reconstruction. Spatial structures are effectively enhanced not only by nonlocal and sparse features, but momentarily by tensor-formed low-rank approximations in the temporal realm. Moreover, the total variation is well regularized as a complementation for denoising. These regularizations are efficiently combined into a Poisson PET model and jointly solved by distributed optimization. The experiments demonstrated in this paper validate the excellent performance of the proposed method in dynamic PET.

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Section: Experiments and Resultsmentioning

confidence: 99%

3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction

Xie

Chen

Liu

2019

Sensors

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“…It is difficult to solve (5) directly. The variable splitting method, such as the augmented Lagrangian method [13–15], can be efficiently used. Using this approach (5) can be subdivided into different parts to get the desired solution as:

\begin{matrix} right leftthickmathspace.5em \\ bold-italicL (bold-italicI, bold-italicp, bold-italicq, bold-italicm, bold-italicn) \\ = γ {bold-italicp}_{1} + {bold-italicq}_{1} - {bold-italicn}^{T} (bold-italicp - bold-italicH bold-italicI + bold-italicy) + \frac{ρ_{n}}{2} p - H I + y^{2} - m^{T} ()(, q - \nabla I) + \frac{ρ_{m}}{2} bold-italicq - \nabla {bold-italicI}^{2}, \end{matrix}

where ρ n and ρ m are the penalty parameters related to the penalty term p − HI + y 2 and

q - \nabla I^{2},

respectively; and n and m are Lagrange multipliers associated with the terms ( p − HI + y ) and

()(, q - \nabla I),

respectively.…”

Section: Algorithmsmentioning

confidence: 99%

Combination of hybrid median filter and total variation minimisation for medical X‐ray image restoration

D.M.Bappy

Jeon

2016

IET Image Processing

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“…The alternating direction method of multipliers (ADMM) has been developed for Poisson image deconvolution under different names (PIDAL [22] and PIDSplit [23]) and has been applied to PET and SPECT image reconstruction [24], [25]. ADMM-type algorithms can be very fast, but are not guaranteed to converge monotonically.…”

Section: Introductionmentioning

confidence: 99%

Edge-Preserving PET Image Reconstruction Using Trust Optimization Transfer

Wang

2015

IEEE Trans. Med. Imaging

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Iterative image reconstruction for positron emission tomography (PET) can improve image quality by using spatial regularization. The most commonly used quadratic penalty often over-smoothes sharp edges and fine features in reconstructed images, while non-quadratic penalties can preserve edges and achieve higher contrast recovery. Existing optimization algorithms such as the expectation maximization (EM) and preconditioned conjugate gradient (PCG) algorithms work well for the quadratic penalty, but are less efficient for high-curvature or non-smooth edge-preserving regularizations. This paper proposes a new algorithm to accelerate edge-preserving image reconstruction by using two strategies: trust surrogate and optimization transfer descent. Trust surrogate approximates the original penalty by a smoother function at each iteration, but guarantees the algorithm to descend monotonically; Optimization transfer descent accelerates a conventional optimization transfer algorithm by using conjugate gradient and line search. Results of computer simulations and real 3D data show that the proposed algorithm converges much faster than the conventional EM and PCG for smooth edge-preserving regularization and can also be more efficient than the current state-of-art algorithms for the non-smooth ℓ1 regularization.

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Augmented Lagrangian methods for penalized likelihood reconstruction in emission tomography

Cited by 4 publications

References 10 publications

3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction

3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction

Combination of hybrid median filter and total variation minimisation for medical X‐ray image restoration

Edge-Preserving PET Image Reconstruction Using Trust Optimization Transfer

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