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Frequency-resolved optical gating (FROG) is probably the most popular technique for complete characterization of ultrashort laser pulses. In FROG, a reconstruction algorithm retrieves the pulse from a measured spectrogram, yet current FROG…
Ptychography has become prominent at synchrotron facilities worldwide for characterizing biological and material specimens' topological structures and properties at the nanometer or atomic scale, due to its lens - less, highly quantitative…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
We present eMAGPIE (extended Multilevel-Adaptive-Guided Ptychographic Iterative Engine), a stochastic multigrid method for blind ptychographic phase retrieval that jointly recovers the object and the probe. We recast the task as the…
Ptychography is an imaging technique that captures multiple overlapping snapshots of a sample, illuminated coherently by a moving localized probe. The image recovery from ptychographic data is generally achieved via an iterative algorithm…
Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the…
Sample-induced aberrations and optical imperfections limit the resolution of fluorescence microscopy. Phase diversity is a powerful technique that leverages complementary phase information in sequentially acquired images with deliberately…
Ptychography, a form of Coherent Diffractive Imaging, is used with short wavelengths (e.g. X-rays, electron beams) to achieve high-resolution image reconstructions. One of the limiting factors for the reconstruction quality is the accurate…
Direct ptychography enables the retrieval of information encoded in the phase of an electron wave passing through a thin sample by deconvolving the interference effects of a converged probe with known aberrations. Under the weak phase…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
Formation of a bright-field microscopic image of a transparent phase object is described in terms of elementary geometrical optics. Our approach is based on the premise that image replicates the intensity distribution (real or virtual) at…
The problem of phase retrieval is a classic one in optics and arises when one is interested in recovering an unknown signal from the magnitude (intensity) of its Fourier transform. While there have existed quite a few approaches to phase…
Phase unwrapping is the process of recovering a continuous phase signal from an original signal wrapped in the ($-\pi$,$\pi$] interval. It is a critical step of coherent signal processing, with applications such as synthetic aperture radar,…
In conventional x-ray ptychography, diffraction data is collected by scanning a sample through a monochromatic, and spatially coherent, x-ray beam. A high-resolution image is then retrieved using an iterative algorithm. Combined with a scan…
Ptychography is a technique widely used in microscopy for achieving high-resolution imaging. This method relies on computational processing of images gathered from diffraction patterns produced by several partial illuminations of a sample.…
Blind image deblurring is the process of recovering a sharp image from a blurred one without prior knowledge about the blur kernel. It is a small data problem, since the key challenge lies in estimating the unknown degrees of blur from a…
The resolution of optical imaging is classically limited by the width of the point-spread function, which in turn is determined by the Rayleigh length. Recently, spatial-mode demultiplexing (SPADE) has been proposed as a method to achieve…