A projection-domain iterative algorithm for metal artifact reduction by minimizing the total-variation norm and the negative-pixel energy

Metal objects in X-ray computed tomography can cause severe artifacts. The state-of-the-art metal artifact reduction methods are in the sinogram inpainting category and are iterative methods. This paper proposes a projection-domain algorithm to reduce the metal artifacts. In this algorithm, the unknowns are the metal-affected projections, while the objective function is set up in the image domain. The data fidelity term is not utilized in the objective function. The objective function of the proposed algorithm consists of two terms: the total variation of the metal-removed image and the energy of the negative-valued pixels in the image. After the metal-affected projections are modified, the final image is reconstructed via the filtered backprojection algorithm. The feasibility of the proposed algorithm has been verified by real experimental data.

Exponential ergodicity for regime-switching diffusion processes in total variation norm

<p style='text-indent:20px;'>We investigate the long time behavior for a class of regime-switching diffusion processes. Based on direct evaluation of moments and exponential functionals of hitting time of the underlying process, we adopt coupling method to obtain existence and uniqueness of the invariant probability measure and establish explicit exponential bounds for the rate of convergence to the invariant probability measure in total variation norm. In addition, we provide some concrete examples to illustrate our main results which reveal impact of random switching on stochastic stability and convergence rate of the system.</p>

Non-Blind Image Deblurring Method Using Shear High Order Total Variation Norm

In this paper, we propose a shear high-order gradient (SHOG) operator by combining the shear operator and high-order gradient (HOG) operator. Compared with the HOG operator, the proposed SHOG operator can incorporate more directionality and detect more abundant edge information. Based on the SHOG operator, we extend the total variation (TV) norm to shear high-order total variation (SHOTV), and then propose a SHOTV deblurring model. We also study some properties of the SHOG operator, and show that the SHOG matrices are Block Circulant with Circulant Blocks (BCCB) when the shear angle is [see formula in PDF]. The proposed model is solved efficiently by the alternating direction method of multipliers (ADMM). Experimental results demonstrate that the proposed method outperforms some state-of-the-art non-blind deblurring methods in both objective and perceptual quality.

Bayesian inference of a non-local proliferation model

From a systems biology perspective, the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental data. Having this in mind, in this paper, we aim at contributing to the improvement of many cancer models which contain a proliferation term. To this end, we propose a new non-local model of cell proliferation. We select data that are suitable to perform Bayesian inference for unknown parameters and we provide a discussion on the range of applicability of the model. Furthermore, we provide proof of the stability of posterior distributions in total variation norm which exploits the theory of spaces of measures equipped with the weighted flat norm. In a companion paper, we provide detailed proof of the well-posedness of the problem and we investigate the convergence of the escalator boxcar train (EBT) algorithm applied to solve the equation.

Inverse potential problems in divergence form for measures in the plane

We study inverse potential problems with source term the divergence of some unknown (R 3 -valued) measure supported in a plane; e.g., inverse magnetization problems for thin plates. We investigate methods for recovering a magnetization μ by penalizing the measure-theoretic total variation norm kμk T V , and appealing to the decomposition of divergence-free measures in the plane as superpositions of unit tangent vector fields on rectifiable Jordan curves. In particular, we prove for magnetizations supported in a plane that T V -regularization schemes always have a unique minimizer, even in the presence of noise. It is further shown that T V -norm minimization (among magnetizations generating the same field) uniquely recovers planar magnetizations in the following two cases: (i) when the magnetization is carried by a collection of sufficiently separated line segments and a set that is purely 1-unrectifiable; (ii) when a superset of the support is tree- like. We note that such magnetizations can be recovered via T V -regularization schemes in the zero noise limit by taking the regularization parameter to zero. This suggests definitions of sparsity in the present infinite dimensional context, that generate results akin to compressed sensing.

Imaging Noise Suppression: Fourth-Order Partial Differential Equations and Travelling Wave Solutions

In this paper, we discuss travelling wave solutions for image smoothing based on a fourth-order partial differential equation. One of the recurring issues of digital imaging is the amount of noise. One solution to this is to minimise the total variation norm of the image, thus giving rise to non-linear equations. We investigate the variational properties of the Lagrange functionals associated with these minimisation problems.

Extension of emission expectation maximization lookalike algorithms to Bayesian algorithms

We recently developed a family of image reconstruction algorithms that look like the emission maximum-likelihood expectation-maximization (ML-EM) algorithm. In this study, we extend these algorithms to Bayesian algorithms. The family of emission-EM-lookalike algorithms utilizes a multiplicative update scheme. The extension of these algorithms to Bayesian algorithms is achieved by introducing a new simple factor, which contains the Bayesian information. One of the extended algorithms can be applied to emission tomography and another to transmission tomography. Computer simulations are performed and compared with the corresponding un-extended algorithms. The total-variation norm is employed as the Bayesian constraint in the computer simulations. The newly developed algorithms demonstrate a stable performance. A simple Bayesian algorithm can be derived for any noise variance function. The proposed algorithms have properties such as multiplicative updating, non-negativity, faster convergence rates for bright objects, and ease of implementation. Our algorithms are inspired by Green’s one-step-late algorithm. If written in additive-update form, Green’s algorithm has a step size determined by the future image value, which is an undesirable feature that our algorithms do not have.

Digital superresolution in seismic AVO inversion

The sparseness promoted by the total variation norm is utilized to achieve superresolution amplitude-variation-with-offset (AVO) inversion. The total variation norm promotes solutions that have constant values within unspecified regions and thus are well suited for an earth model consisting of layers bounded by faults and erosion surfaces. Algorithmic developments from digital image and video restoration are utilized to solve the geophysical problem. A spatial point spread function is used to model the resulting effect of wave propagation, migration, and processing. The methodology is compared to current alternatives and discussed in the context of AVO inversion. Good results are obtained in a Barents Sea test case.

Asymptotic analysis of the Ginzburg–Landau functional on point clouds

The Ginzburg–Landau functional is a phase transition model which is suitable for classification type problems. We study the asymptotics of a sequence of Ginzburg–Landau functionals with anisotropic interaction potentials on point clouds Ψnwherendenotes the number data points. In particular, we show the limiting problem, in the sense of Γ-convergence, is related to the total variation norm restricted to functions taking binary values, which can be understood as a surface energy. We generalize the result known for isotropic interaction potentials to the anisotropic case and add a result concerning the rate of convergence.