Related papers: FROG-measurement based phase retrieval for analyti…

Phase retrieval aims to recover a signal $x \in \mathbb{C}^{n}$ from its amplitude measurements $|<x, a_i > |^2$, $i=1,2,...,m$, where $a_i$'s are over-complete basis vectors, with $m$ at least $3n -2$ to ensure a unique solution up to a…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Continuous wavefront sensing benefits space observatories in on-orbit optical performance maintenance. To measure the phase of a wavefront, phase retrieval is an attractive technique as it uses multiple point spread function (PSF) images…

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…

Physics-constrained data generation is essential for machine learning in scientific domains where real data are scarce; however, existing approaches often over-constrain models without identifying which physical components are necessary. We…

Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…

Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…

The studying of anomalous diffusion by pulsed field gradient (PFG) diffusion technique still faces challenges. Two different research groups have proposed modified Bloch equation for anomalous diffusion. However, these equations have…

Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…

Path-length diversity methods may be used for adaptive optics (AO) systems to retrieve phase and amplitude information by measuring intensity across multiple planes. Observations that rely on free-space propagation, such as the nonlinear…

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered…

One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling…

Retrieval-augmented generation (RAG) is a powerful technique that enhances downstream task execution by retrieving additional information, such as knowledge, skills, and tools from external sources. Graph, by its intrinsic "nodes connected…

In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…

Pulse Doppler radars suffer from range-Doppler ambiguity that translates into a trade-off between maximal unambiguous range and velocity. Several techniques, like the multiple PRFs (MPRF) method, have been proposed to mitigate this problem.…

We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited…

While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…

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…