Uniqueness of minimizers of weighted least gradient problems arising in conductivity imaging

2014/04/23 by Amir Moradifam, Adrian Nachman, Moradifam, Amir +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Electrical and Bioimpedance Tomography #FOS: Mathematics #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #math.AP

paper · pdf · doi:10.48550/arxiv.1404.5992

arxiv created 2014/04/23 · openalex publication_date 2014/04/23 · arxiv updated 2014/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove uniqueness for minimizers of the weighted least gradient problem inf \lbrace ∫_Ω a|Du|: u∈ BV(Ω), u|_{∂ Ω}=f \rbrace. The weight function a is assumed to be continuous and it is allowed to vanish in certain subsets of Ω. Existence is assumed a priori. Our approach is motivated by the hybrid inverse problem of imaging electric conductivity from interior knowledge (obtainable by MRI) of the magnitude of one current density vector field.

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• Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class

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