Search arXivSearch

arXiv · 2402.01175

Nonconvex weighted variational metal artifacts removal via convergent primal-dual algorithms

Abstract

Direct reconstruction through filtered back projection engenders metal artifacts in polychromatic computed tomography images, attributed to highly attenuating implants, which further poses great challenges for subsequent image analysis. Inpainting the metal trace directly in the Radon domain for the extant variational method leads to strong edge diffusion and potential inherent artifacts. With normalization based on pre-segmentation, the inpainted outcome can be notably ameliorated. However, its reconstructive fidelity is heavily contingent on the precision of the presegmentation, and highly accurate segmentation of images with metal artifacts is non-trivial in actuality. In this paper, we propose a nonconvex weighted variational approach for metal artifact reduction. Specifically, in lieu of employing a binary function with zeros in the metal trace, an adaptive weight function is designed in the Radon domain, with zeros in the overlapping regions of multiple disjoint metals as well as areas of highly attenuated projections, and the inverse square root of the measured projection in other regions. A nonconvex L1-alpha L2 regularization term is incorporated to further enhance edge contrast, alongside a box-constraint in the image domain. Efficient first-order primal-dual algorithms, proven to be globally convergent and of low computational cost owing to the closed-form solution of all subproblems, are devised to resolve such a constrained nonconvex model. Both simulated and real experiments are conducted with comparisons to other variational algorithms, validating the superiority of the presented method. Especially in comparison to Reweighted JSR, our proposed algorithm can curtail the total computational cost to at most one-third, and for the case of inaccurate pre-segmentation, the recovery outcomes by the proposed algorithms are notably enhanced.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lianfang Wang, Zhangling Chen, Zhifang Liu, Yutong Li, Yunsong Zhao, Hongwei Li, Huibin Chang. 2024-02-02. Nonconvex weighted variational metal artifacts removal via convergent primal-dual algorithms. https://arxiv.org/abs/2402.01175

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Subpath-Based Column Generation for Electric Vehicle Routing Problems

Motivated by widespread electrification targets, this paper studies an Electric Vehicle Routing Problem with Time Windows and Nonlinear Charging (EVRPTWNL) that jointly optimizes routing-scheduling decisions and charging decisions given vehicle capacities, time windows and battery capacities. We develop a column generation scheme with a subpath-based label-setting algorithm that decomposes the pricing problem into two phases: (i) generating subpaths between charging stations, and (ii) combining subpaths into paths while optimizing charging decisions in between. We formalize a domination framework to establish the convergence and exactness of the algorithm, and prove that the methodology can solve a range of EVRP variants (e.g., with vehicle capacities, time windows, and nonlinear charging) and relaxation-tightening strategies (e.g., ng-relaxations and subset-row cuts). Computational results show improvements over path-based benchmarks in both computational time and solution quality, especially when time windows become wider, when vehicles can perform multiple tasks on a single charge and when vehicles still need to recharge several times across the planning horizon. Ultimately, the methodology can scale to otherwise intractable instances with up to 100 customers, thereby enhancing fleet management capabilities across electrified logistics areas.

math.OC

Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs

Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they do not address \emph{complexity}: for broad operator classes described only through regularity (e.g.\ uniform continuity or $C^r$-regularity), information-theoretic lower bounds imply that minimax-optimal NO approximation rates scale \emph{exponentially} in the reciprocal accuracy $1/\varepsilon$. This has shifted the focus of NO theory toward identifying additional problem-specific structure, beyond regularity, under which suitably tailored NO architectures can leverage to unlock polynomial scaling in $1/\varepsilon$. We exhibit the first polynomial-scaling regime for NO approximations of solution operators in stochastic analysis; by identifying structured families of \emph{non-Markovian} BSDEs with randomized terminal condition parameterized by the Sobolev-regular terminal condition and by Sobolev-regular additive nonlinear perturbations of the generator. We prove that their solution operator can be approximated (uniformly over the family) by a tailored NO whose number of trainable parameters grows \emph{polynomially} in $1/\varepsilon$. We unlock this polynomial scaling regime by \emph{informing the NO's inductive bias} by factoring out the singular part of the associated semilinear elliptic PDE Green's function and by incorporating the Doléans--Dade exponential of the BSDE's common non-Markovian factor into the NO's decoding layers. As a byproduct, we extend polynomial-scaling guarantees from families of linear elliptic PDEs on regular domains to the semilinear setting.

math.OC

The Competive Spectral Radius of Families of Nonexpansive Mappings

We consider a new class of repeated zero-sum games in which the payoff is the escape rate of a switched dynamical system, where at every stage, the transition is given by a nonexpansive operator depending on the actions of both players. This generalizes to the two-player (and non-linear) case the notion of joint spectral radius of a family of matrices. We show that the value of this game does exist, and we characterize it in terms of an infinite dimensional non-linear eigenproblem. This provides a two-player analogue of Mañe's lemma from ergodic control. This also extends to the two-player case results of Kohlberg and Neyman (1981), Karlsson (2001), and Vigeral and the second author (2012), concerning the asymptotic behavior of nonexpansive mappings. We discuss two special cases of this game: order preserving and positively homogeneous self-maps of a cone equipped with Funk's and Thompson's metrics, and translations of a finite dimensional normed space.

math.OC