Related papers: Frames and Phaseless Reconstruction
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…
In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…
One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
We consider a wireless sensor network, sampling a bandlimited field, described by a limited number of harmonics. Sensor nodes are irregularly deployed over the area of interest or subject to random motion; in addition sensors measurements…
In this paper, we consider the problem of feature reconstruction from incomplete x-ray CT data. Such problems occurs, e.g., as a result of dose reduction in the context medical imaging. Since image reconstruction from incomplete data is a…
Optoacoustic tomography image reconstruction has been a problem of interest in recent years. By exploiting the exceptional generative power of the recently proposed diffusion models we consider a scheme which is based on a conditional…
Phase retrieval is an inverse problem that, on one hand, is crucial in many applications across imaging and physics, and, on the other hand, leads to deep research questions in theoretical signal processing and applied harmonic analysis.…
Upper Mid-Band (FR3, 7-24 GHz) receivers for 6G must operate over wide bandwidths in dense spectral environments, making them particularly vulnerable to strong adjacent-band interference and front-end nonlinearities. While conventional…
This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance…
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…
The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
The paper presents a unified, flexible framework for the tasks of audio inpainting, declipping, and dequantization. The concept is further extended to cover analogous degradation models in a transformed domain, e.g. quantization of the…
Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements…