\(L^1\) regularization method in electrical impedance tomography by using the \(L^1\)-curve (Pareto frontier curve)

DOI10.1016/j.apm.2011.07.055zbMath1243.78041OpenAlexW2056132468MaRDI QIDQ437855

André van Schaik, J. Nasehi Tehrani, C. Jin, Alistair McEwan

Publication date: 20 July 2012

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2011.07.055

zbMATH Keywords

regularizationelectrical impedance tomography\(L^1\)-curvePareto frontier curve

Mathematics Subject Classification ID

Biological applications of optics and electromagnetic theory (78A70) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Inverse problems in optimal control (49N45)

Related Items (6)

A hybrid sensitivity function and Lanczos bidiagonalization-Tikhonov method for structural model updating: application to a full-scale bridge structure ⋮ A wavelet frame constrained total generalized variation model for imaging conductivity distribution ⋮ A General Theory of Singular Values with Applications to Signal Denoising ⋮ Modelling of an oesophageal electrode for cardiac function tomography ⋮ Sparse identification of nonlinear dynamical systems via reweighted \(\ell_1\)-regularized least squares ⋮ Electrical impedance tomography with multiplicative regularization

Uses Software

• Regularization tools
• PDCO
• SPGL1
• EIDORS

Cites Work

• The discrete Picard condition for discrete ill-posed problems
• The truncated SVD as a method for regularization
• A bisection method for computing the \(H_{\infty}\) norm of a transfer matrix and related problems
• Least angle regression. (With discussion)
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Atomic Decomposition by Basis Pursuit
• Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-Determined Numerical Rank
• Probing the Pareto Frontier for Basis Pursuit Solutions
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
• On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems

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