Related papers: On the Injectivity of STFT Phase Retrieval with su…
Recognizing degraded faces from low resolution and blurred images are common yet challenging task. Local Frequency Descriptor (LFD) has been proved to be effective for this task yet it is extracted from a spatial neighborhood of a pixel of…
A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here we consider the continuous…
This paper addresses the task of anomaly diagnosis when the underlying data generation process has a complex spatio-temporal (ST) dependency. The key technical challenge is to extract actionable insights from the dependency tensor…
We study the problem of recovering a function of the form $f(x) = \sum _{k\in \mathbb{Z} } c_k e^{-(x-k)^2}$ from its phaseless samples $|f(\lambda )|$ on some arbitrary countable set $\Lambda \subseteq \mathbb{R} $. For real-valued…
Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics, quantum mechanics, and astronomy. This…
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions…
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…
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…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
The aim of this work is to prove existence and uniqueness of $L^{2}-$solutions of stochastic fractional partial differential equations in one spatial dimension. We prove also the equivalence between several notions of $L^{2}-$solutions. The…
This study introduces a short-time Fourier transform-based method for reconstructing signals encoded using modulo analog-to-digital converters with 1-bit folding information. In contrast to existing Fourier-based reconstruction approaches…
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…
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…
Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a…
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…