Related papers: Reconstruction of missing low-angle scattering in …
The problem of low-rank matrix reconstruction arises in various applications in communications and signal processing. The state of the art research largely focuses on the recovery techniques that utilize affine maps satisfying the…
The convergent beam electron diffraction (CBED) patterns of twisted bilayer samples exhibit interference patterns in their CBED spots. Such interference patterns can be treated as off-axis holograms and the phase of the scattered waves,…
The integration of sensing and communication (ISAC) is an essential function of future wireless systems. Due to its large available bandwidth, millimeter-wave (mmWave) ISAC systems are able to achieve high sensing accuracy. In this paper,…
While scattered light conveys most of the information we perceive, scattering may also distort that information before it reaches our detectors. The problem is acute in many applications, such as in high-resolution microscopy of biological…
A crucial step in seismic data processing consists in reconstructing the wavefields at spatial locations where faulty or absent sources and/or receivers result in missing data. Several developments in seismic acquisition and interpolation…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
Dark-field images are formed by small-angle scattering of x-ray photons. The small-angle scattering signal is particularly sensitive to structural variations and density fluctuation on a length scale of several ten to hundred nanometers,…
In many image processing tasks it occurs that pixels or blocks of pixels are missing or lost in only some channels. For example during defective transmissions of RGB images, it may happen that one or more blocks in one color channel are…
Phase retrieval aims to recover a signal from intensity-only measurements, a fundamental problem in many fields such as imaging, holography, optical computing, crystallography, and microscopy. Although there are several well-known phase…
We proposed a novel approach to coherent imaging of dynamic samples. The inter-frame similarity of the sample's local structures is found to be a powerful constraint in phasing a sequence of diffraction patterns. We devised a new image…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…
Machine learning is attracting surging interest across nearly all scientific areas by enabling the analysis of large datasets and the extraction of scientific information from incomplete data. Data-driven science is rapidly growing,…
Undersampled images, such as those produced by the HST WFPC-2, misrepresent fine-scale structure intrinsic to the astronomical sources being imaged. Analyzing such images is difficult on scales close to their resolution limits and may…
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop…
In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
A lensless digital holography enables wide-field microscopic imaging without the limitations imposed by optical lens performance. However, conventional holographic imaging often relies on magnifying optical systems to compensate for the low…
We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…
X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…