We review several recent results concerning two-dimensional systems which exhibit a transport induced by a one-dimensional perturbation of a homogeneous magnetic field. The first concerns the local Iwatsuka model, where a charged particle interacts with a field which is homogeneous outside a finite strip and translationally invariant along it: we present two new sufficient conditions for absolute continuity of the spectrum and show that in most cases the number of open spectral gaps is finite. In the second model the perturbation is a periodic array of point obstacles. In this case the Landau levels remain to be infinitely degenerate eigenvalues, and between them the system has bands of absolutely continuous spectrum.

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Non-line-of-sight imaging aims at recovering obscured objects from multiple scattered lights. It has recently received widespread attention due to its potential applications, such as autonomous driving, rescue operations, and remote sensing. However, in cases with high measurement noise, obtaining high-quality reconstructions remains a challenging task. In this work, we establish a unified regularization framework, which can be tailored for different scenarios, including indoor and outdoor scenes with substantial background noise under both confocal and non-confocal settings. The proposed regularization framework incorporates sparseness and non-local self-similarity of the hidden objects as well as the smoothness of the signals. We show that the estimated signals, albedo, and surface normal of the hidden objects can be reconstructed robustly even with high measurement noise under the proposed framework. Reconstruction results on synthetic and experimental data show that our approach recovers the hidden objects faithfully and outperforms state-of-the-art reconstruction algorithms in terms of both quantitative criteria and visual quality.

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No abstract uploaded!