Related papers: On phase retrieval for continuous and discrete Fou…
In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear…
This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…
Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm,…
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set…
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…
An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model.…
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…
The Phase Retrieval problem is dealt with for the challenging case where just a single set of (phaseless) radiated field data is available. In particular, even still emulating the solution of crosswords puzzles, we provide decisive…
We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering…
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found…
We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical "noise free" projection in any…
Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging.…
We study theoretical limits of \emph{descending} phase retrieval algorithms. Utilizing \emph{Random duality theory} (RDT) we develop a generic program that allows statistical characterization of various algorithmic performance metrics.…
Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
Fusion frames are extensively studied due to their effectiveness in recovering signals from large-scale data. They are applicable in distributed processing, wireless sensor networks, and packet encoding systems due to their robustness and…