Journal Article10.1080/00207160802410095
An iterative algorithm based on level set method for the shape recovery problem
Qing Liu,Xiaoliang Cheng +1 more
TL;DR: An iterative algorithm based on the level set method for the shape recovery problem using a suitable preconditioner for the artificial time-dependent system and proving the convergence of the algorithm under some hypothesis.
read more
Abstract: In this paper, we propose an iterative algorithm based on the level set method for the shape recovery problem. We use a suitable preconditioner for the artificial time-dependent system for the level set formulation and propose an iterative algorithm of the level set function. We prove the convergence of our algorithm under some hypothesis. Numerical experiments show the efficiency of the algorithm.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
References
•Book
Computational Methods for Inverse Problems
Curtis R. Vogel
- 01 Jan 1987
TL;DR: Inverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting as mentioned in this paper, and a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
2.7K
Electrical Impedance Tomography
TL;DR: A survey of the work in electrical impedance tomography can be found in this article, where the authors survey some of the most important works in the field. Butt.t.
1.8K
Electrical impedance tomography
Mi Wang,Wuliang Yin +1 more
- 28 Dec 2001
TL;DR: This article focuses on the type of EIT called adaptive current tomography (ACT) in which currents are applied simultaneously to all the electrodes, where a number of current patterns are applied, where each pattern defines the current for each electrode, and the subsequent electrode voltages are measured to generate the data required for image reconstruction.
1.3K
Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum
Stanley Osher,Fadil Santosa +1 more
TL;DR: This paper uses the level set method, the variational level set calculus, and the projected gradient method to construct a simple numerical approach for problems of this type involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry.
581
Iterative methods for the reconstruction of an inverse potential problem
Frank Hettlich,William Rundell +1 more
TL;DR: In this article, an inverse potential problem is considered, which seeks to recover the shape of an obstacle separating two different densities by measurements of the potential, and a representation for the domain derivative of the corresponding operator is established, allowing the investigation of several iterative methods for the solution of this ill-posed problem.
123