Related papers: Ab initio compressive phase retrieval
We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples. Assuming the discontinuity set of the image is localized to the zero level-set of a trigonometric polynomial, we…
A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs)…
In this paper we present an extremely simple structure solution method termed charge flipping. It works ab initio on high resolution x-ray diffraction data in the manner of Fourier recycling. The real space modification simply changes the…
Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…
Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred and corrupted by various artifacts such as irregular waves, spots, etc. These disturbances, arising due to many factors such as non-idealities…
To obtain spatial information about an arbitrary object in x-ray structure analysis, the standard method is to measure the intensity in the far field, i.e., the first-order photon correlation function of the coherently scattered x-ray…
We implement a compressive quantum state tomography capable of reconstructing any arbitrary low-rank spectral-temporal optical signal with extremely few measurement settings and without any \emph{ad hoc} assumptions about the initially…
Optical and acoustical trapping has been established as a tool for holding and moving microscopic particles suspended in a liquid in a contact-free and non-invasive manner. Opposed to standard microscopic imaging where the probe is fixated,…
A new digital image encryption method based on fast compressed sensing approach using structurally random matrices and Arnold transform is proposed. Considering the natural images to be compressed in any domain, the fast compressed sensing…
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two dimensional images, and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…
We present the experimental reconstruction of sub-wavelength features from the far-field intensity of sparse optical objects: sparsity-based sub-wavelength imaging combined with phase-retrieval. As examples, we demonstrate the recovery of…
Many applications seek to measure a sample's absorption coefficient spectrum to retrieve the chemical makeup. Many real world samples are optically turbid, causing scattering confounds which many commercial spectrometers cannot address.…
The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a., compressive phase retrieval), emerges naturally in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
Terahertz microscopy has attracted attention owing to distinctive characteristics of the THz frequency region, particularly non-ionizing photon energy, spectral fingerprint, and transparency to most nonpolar materials. Nevertheless, the…
Diffraction tomography is a widely used inverse scattering technique for quantitative imaging of weakly scattering media. In its conventional formulation, diffraction tomography assumes monochromatic plane wave illumination. This…
Partial-transfer absorption imaging is a tool that enables optimal imaging of atomic clouds for a wide range of optical depths. In contrast to standard absorption imaging, the technique can be minimally-destructive and can be used to obtain…
Ultrafast nanocrystallography has the potential to revolutionize biology by enabling structural elucidation of proteins for which it is possible to grow crystals with 10 or fewer unit cells on the side. The success of nanocrystallography…