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The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
We identify a broad class of phonon modes with persistent vortex fluxes at arbitrarily slow propagating velocities in periodic nano-waveguides. Such phonon vortices are associated with the split band-edges in dispersion dependencies, which…
The reconstruction of current distributions from samples of their induced magnetic field is a challenging problem due to multiple factors. First, the problem of reconstructing general three dimensional current distributions is ill-posed.…
The development of compact indirect microwave holographic set-up by the implementation of low cost, specifically designed directive antennae as transmitter and receiver is proposed. Microwave holograms are recorded by 2D scanning over a…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
Currently, most deep learning methods cannot solve the problem of scarcity of industrial product defect samples and significant differences in characteristics. This paper proposes an unsupervised defect detection algorithm based on a…
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…
This is a continuation of two recent publications of the authors about reconstruction procedures for 3-d phaseless inverse scattering problems. The main novelty of this paper is that the Born approximation for the case of the wave-like…
This article focuses on techniques for acoustic noise reduction, signal filters and source reconstruction. For noise reduction, bandpass filters and cross correlations are found to be efficient and fast ways to improve the signal to noise…
Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
This paper deals with the problem of building fast and reliable 3D reconstruction methods for blood flows for which partial information is given by Doppler ultrasound measurements. This task is of interest in medicine since it could enrich…
Most of the seismic inversion techniques currently proposed focus on robustness with respect to the background model choice or inaccurate physical modeling assumptions, but are not apt to large-scale 3D applications. On the other hand,…
Large-scale Fourier modes of the cosmic density field are of great value for learning about cosmology because of their well-understood relationship to fluctuations in the early universe. However, cosmic variance generally limits the…
Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
We present an analysis of wave propagation and reflection in an acoustic waveguide with random sound soft boundary and a turning point. The waveguide has slowly bending axis and variable cross section. The variation consists of a slow and…
This paper aims to reconstruct the internal structure of a two-dimensional test object via numerically simulated full-wave time domain radar tomography with the presence of wavelength-induced (WI) uncertainties, following from a complex…