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The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…

We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…

Joint analyses of the large-scale distribution of galaxies, and their motions under the gravitational influence of this density field, allow powerful tests of the cosmological model, including measurement of the growth rate of cosmic…

In ultrasound nondestructive testing, a widespread approach is to take synthetic aperture measurements from the surface of a specimen to detect and locate defects within it. Based on these measurements, imaging is usually performed using…

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…

We consider the recovery of sparse signals that share a common support from multiple measurement vectors. The performance of several algorithms developed for this task depends on parameters like dimension of the sparse signal, dimension of…

In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal…

Fourier ptychographic microscopy (FPM) is a recently proposed quantitative phase imaging technique with high resolution and wide field-of-view (FOV). In current FPM imaging platforms, systematic error sources come from the aberrations, LED…

Quarter sampling is a novel sensor design that allows for an acquisition of higher resolution images without increasing the number of pixels. When being used for video data, one out of four pixels is measured in each frame. Effectively,…

In this paper, we address the inverse problem of fast, stable, and high-quality wavefront reconstruction from pyramid wavefront sensor data for Adaptive Optics systems on Extremely Large Telescopes. For solving the indicated problem we…

We introduce a dual-wavelength Fourier ptychographic topography (FPT) method that extends the lambda/2 height-range limit of single-wavelength FPT. By reconstructing complex fields at two illumination wavelengths and exploiting their phase…

This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…

In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…

Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a system performance beyond the limit defined by its optical elements. The FPM technique applies a novel…

Sound propagation in the ocean is considered. We demonstrate a novel algorithm for full wavefield reconstruction using pointwise measurements by means of a vertical array. The algorithm is based on the so-called discrete variable…

Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…

In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…

The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…

Recent attempts to constrain cosmological variation in the fine structure constant, alpha, using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently…

Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…