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Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors.

ABSTRACT: The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We use the framework of the alternating direction method of multipliers to design an efficient minimization algorithm for the proposed model. Since the objective function is the sum of the non-quadratic log-likelihood and nonconvex nondifferentiable regularizer, we propose to solve the intractable subproblems by the majorization-minimization (MM) method and the iteratively reweighted least squares (IRLS) algorithm, respectively. Numerical experiments show the efficiency of the proposed method for Poissonian image restoration including denoising and deblurring.

SUBMITTER: Jon K

PROVIDER: S-EPMC8057597 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors.

Jon Kyongson K Liu Jun J Lv Xiaoguang X Zhu Wensheng W

PloS one 20210420 4

The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We ...[more]

PMID: 33878121

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Project description:The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements.

Project description:Objective.Complete time of flight (TOF) sinograms of state-of-the-art TOF PET scanners have a large memory footprint. Currently, they contain ∼4 · 109data bins which amount to ∼17 GB in 32 bit floating point precision. Moreover, their size will continue to increase with advances in the achievable detector TOF resolution and increases in the axial field of view. Using iterative algorithms to reconstruct such enormous TOF sinograms becomes increasingly challenging due to the memory requirements and the computation time needed to evaluate the forward model for every data bin. This is especially true for more advanced optimization algorithms such as the stochastic primal-dual hybrid gradient (SPDHG) algorithm which allows for the use of non-smooth priors for regularization using subsets with guaranteed convergence. SPDHG requires the storage of additional sinograms in memory, which severely limits its application to data sets from state-of-the-art TOF PET systems using conventional computing hardware.Approach.Motivated by the generally sparse nature of the TOF sinograms, we propose and analyze a new listmode (LM) extension of the SPDHG algorithm for image reconstruction of sparse data following a Poisson distribution. The new algorithm is evaluated based on realistic 2D and 3D simulationsn, and a real data set acquired on a state-of-the-art TOF PET/CT system. The performance of the newly proposed LM SPDHG algorithm is compared against the conventional sinogram SPDHG and the listmode EM-TV algorithm.Main results.We show that the speed of convergence of the proposed LM-SPDHG is equivalent the original SPDHG operating on binned data (TOF sinograms). However, we find that for a TOF PET system with 400 ps TOF resolution and 25 cm axial FOV, the proposed LM-SPDHG reduces the required memory from approximately 56 to 0.7 GB for a short dynamic frame with 107prompt coincidences and to 12.4 GB for a long static acquisition with 5·108prompt coincidences.Significance.In contrast to SPDHG, the reduced memory requirements of LM-SPDHG enables a pure GPU implementation on state-of-the-art GPUs-avoiding memory transfers between host and GPU-which will substantially accelerate reconstruction times. This in turn will allow the application of LM-SPDHG in routine clinical practice where short reconstruction times are crucial.

Dataset Information

Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors.

Publications

Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors.

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