A fast gradient projection method for 3D image reconstruction from limited tomographic data

Coli, Vanna Lisa; Piccolomini, Elena Loli; Morotti, Elena; Zanni, Luca

doi:10.1088/1742-6596/904/1/012013

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…where m α is a nonnegative integer and τ k is a positive real number (we refer to the next section for the setting of these parameters). Other steplength updating rules are currently investigated in literature [14,19,16]; in particular, in [12] it has been shown that, for the CT image recontruction application, the step-length selection proposed in [30] seems to well compare with the above alternated BB rule and deeper studies are in progress on this topic.…”

Section: A Scaled Gradient Approach For Ct Image Reconstructionmentioning

confidence: 99%

Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

et al. 2017

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We propose a scaled gradient projection algorithm for the reconstruction of 3D X-ray tomographic images from limited data. The problem arises from the discretization of an ill-posed integral problem and, due to the incompleteness of the data, has infinite possible solutions. Hence, by following a regularization approach, we formulate the reconstruction problem as the nonnegatively constrained minimization of an objective function given by the sum of a fit-to-data term and a smoothed differentiable Total Variation function. The problem is challenging for its very large size and because a good reconstruction is required in a very short time. For these reasons, we propose to use a gradient projection method, accelerated by exploiting a scaling strategy for defining gradient-based descent directions and generalized Barzilaiâ\u80\u93Borwein rules for the choice of the step-lengths. The numerical results on a 3D phantom are very promising since they show the ability of the scaling strategy to accelerate the convergence in the first iterations

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Section: A Scaled Gradient Approach For Ct Image Reconstructionmentioning

confidence: 99%

Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

et al. 2017

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“…The challenge of reconstructing a high-quality image x ∈ R n from its degraded measurement b ∈ R n is commonly formulated as a linear inverse problem. Such a problem has to be addressed in several imaging frameworks, such as in medicine [1][2][3][4], microscopy [5][6][7], and astronomy [8][9][10]. Although these are different and maybe distant topics, they share a common linear model [11] for the image acquisition process: namely, b = Ax + η, (1) where A ∈ R n×n is a known blur operator called the Point Spread Function (PSF) [12], and η ∈ R n represents additive random noise with a standard deviation of σ η .…”

Section: Introductionmentioning

confidence: 99%

Constrained Plug-and-Play Priors for Image Restoration

Benfenati,

Cascarano

2024

J. Imaging

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The Plug-and-Play framework has demonstrated that a denoiser can implicitly serve as the image prior for model-based methods for solving various inverse problems such as image restoration tasks. This characteristic enables the integration of the flexibility of model-based methods with the effectiveness of learning-based denoisers. However, the regularization strength induced by denoisers in the traditional Plug-and-Play framework lacks a physical interpretation, necessitating demanding parameter tuning. This paper addresses this issue by introducing the Constrained Plug-and-Play (CPnP) method, which reformulates the traditional PnP as a constrained optimization problem. In this formulation, the regularization parameter directly corresponds to the amount of noise in the measurements. The solution to the constrained problem is obtained through the design of an efficient method based on the Alternating Direction Method of Multipliers (ADMM). Our experiments demonstrate that CPnP outperforms competing methods in terms of stability and robustness while also achieving competitive performance for image quality.

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A fast gradient projection method for 3D image reconstruction from limited tomographic data

Cited by 2 publications

References 16 publications

Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

Constrained Plug-and-Play Priors for Image Restoration

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