Related papers: Fourier phasing with phase-uncertain mask
In the present work, a rate-dependent cohesive zone model for the fracture of polymeric interfaces is presented. Inverse calibration of parameters for such complex models through trial and error is computationally tedious due to the large…
This paper presents a detailed, numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio $\sigma=4$ determines a unique phasing…
We consider the problem of phase retrieval, i.e. that of solving systems of quadratic equations. A simple variant of the randomized Kaczmarz method was recently proposed for phase retrieval, and it was shown numerically to have a…
The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of engineering and applied physics. In this paper, we present…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
A new theoretical technique for understanding, analyzing and developing optical systems is presented. The approach is statistical in nature, where information about an object under investigation is discovered, by examining deviations from a…
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,…
The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…
In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…
A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
The classical uncertainty principle of harmonic analysis states that a nontrivial function and its Fourier transform cannot both be sharply localized. It plays an important role in signal processing and physics. This paper generalizes the…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study…
We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m \times n$ measurement matrix. We…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, sub-diffraction imaging, and…
One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian…
An important and often overlooked aspect of particle filtering methods is the estimation of unknown static parameters. A simple approach for addressing this problem is to augment the unknown static parameters as auxiliary states that are…