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• A computational binary characterization method for convex object(s). • A unified model for convex object(s) segmentation and convex hull computation. • Linearization technique employed to reduce the difficulty of the model solving. • A convergent proximal alternating direction method of multipliers for the linearization problem. • An interactive procedure to improve the segmentation accurac y in terms of shape distance and D ice coefficient. Convexity prior is one of the main cues for human vision and shape completion with important applications in image processing and computer vision. This paper provides a computable characterization method for shape convexity, and illustrates its applications in image segmentation and convex hull computation. We prove that the convexity of a region is equivalent to a series of quadratic inequality constraints on its indicator function. By incorporating this result, models are proposed for image segmentation with convexity prior and convex hull computation of clean and noisy data sets, respectively. Then, these models are summarized into a unified optimization problem on binary function(s) with the quadratic inequality constraints. Numerical method is proposed by linearizing the quadratic constraints. The linearization problem is solved by a proximal alternating direction method of multipliers, the convergence of which is guaranteed under some proper conditions. Numerical experiments demonstrate the efficiency and effectiveness of the proposed methods for image segmentation and convex hull computation. [ABSTRACT FROM AUTHOR]

We present a novel and computable characterization method for convex shapes. We prove that the shape convexity is equivalent to a quadratic constraint on the associated indicator function. Such a simple characterization method allows us to design efficient algorithms for various applications with convex shape prior. In order to show the effectiveness of the proposed approach, this method is incorporated with a probability-based model to extract an object with convexity prior. The Lagrange multiplier method is used to solve the proposed model. Numerical results on various images show the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved iteration superiorization method for X-ray computed tomography image reconstruction. We simplify the classic superiorized iteration by removing two constraints imposed on the perturbation. A novel method is proposed to determine the perturbation amount and direction for the superiorized iteration simultaneously. Some theoretical properties (convergence for instance) of the superiorized iteration sequence with the proposed perturbation are analysed. We present a general proof for the convergence of ART-like iterations with summable perturbations. In addition, we prove the convergence of simultaneous iterations without the summable perturbation assumption. Experiments on simulated and real data not only verify the theoretical result but also show that the proposed algorithm is superior to the classic superiorized iteration and can reconstruct desirable images. [ABSTRACT FROM AUTHOR]

Synchrotron radiation (SR) X-ray tomography is a main technique in realizing imaging of an object section by section. We apply this technique in recovering shale microstructures which becomes a hot topic recently in non-conventional oil and gas exploration. We first set the experimental setup using SR sources at BL13W1 beamline at Shanghai Synchrotron Radiation Facility to obtain the measured data of the shale sample, and then we establish the -norm constrained regularization model to reconstruct the microstructure of the shale. A fast convergent gradient descent method is developed to realize this purpose. It indicates from our test results that the new method possesses higher resolution of imaging than the conventional results given by the commercial software. [ABSTRACT FROM AUTHOR]

• This paper propose a new image denoising model by coupling the rotation matrix and the weighted matrix into the TVp quasinorm regularization. • Since the proposed model is nonconvex and non-Lipschitz, we employe the ADMM to solve it with the help of the half-quadratic scheme. • The convergence of the proposed numerical methods is also discussed. • Numerical comparisons show that the proposed model leaded to considerable performance gains when testing on several denoising tasks. Image denoising problem still remains an active research field in the image processing. To improve the denoising quality, it is very important to describe the local structure of the image in the proposed model. This fact motivates us to introduce an adaptive weighted TVp regularization-based denoising model, where the rotation matrix and the weighted matrix depend on the local structure of the image. Specially, these two matrices can enhance the diffusion of the responding Euler-Lagrangian equation along with the tangential direction of the edge. This procedure offers more control over the regularization and then allows more denoising in smooth regions and less denoising when processing edge regions. In addition, since the proposed model is nonsmooth and non-Lipschitz, we employ the alternating direction method of multipliers (ADMM) to solve it with the help of using the half-quadratic scheme to solve the related ℓ 2 − ℓ p subproblem. In particular, we also provide the convergence analysis of the used numerical methods. Some numerical comparisons show that the proposed model leads to considerable performance gains when tested on several denoising tasks. [ABSTRACT FROM AUTHOR]