Two Dimensional Magnetic Current Imaging Via L1-Curl Regularized Divergence Free Wavelet Reconstruction

• DOI: 10.48550/arxiv.2408.16550
• Publication Date: 2024-08-29
• Authors: Christopher Miller; Adrian Mariano; Sean M. Oliver; J. Lenz; Dmitro Martynowych
• Keywords: Curl (programming language); Divergence (linguistics)

The reconstruction of current distributions from samples their induced magnetic field is a challenging problem due to multiple factors. First, the reconstructing general three dimensional ill-posed. Second, current-to-field operator performs low-pass filter that dampens high-spatial frequency information, so even in situations where inversion formally possible, attempting employ formal inverse will result solutions with unacceptable noise. Most contemporary methods for two dimensions are based on Fourier techniques and apply low pass $B$-field data, which prevents excessive noise amplification during at cost admitting blurring reconstructed solution. In this report, we present method recovery penalizing $L1$ norm curl distribution. utility observation microelectronics settings, conductivity piecewise constant. We also reconstruct fields using divergence-free wavelet basis. This has advantage automatically enforcing continuity halving number unknowns must be solved for. Additionally, can computed exactly analytically expansion, simplifies application $L1-\textrm{curl}$ regularizer. demonstrate improved quality relative Fourier-based both simulated laboratory-acquired data.