Related papers: Signal Reconstruction from Modulo Observations
This study addresses the blind deconvolution problem with modulated inputs, focusing on a measurement model where an unknown blurring kernel $\boldsymbol{h}$ is convolved with multiple random modulations…
Magnetic resonance imaging (MRI) is known to be a slow imaging modality and undersampling in k-space has been used to increase the imaging speed. However, image reconstruction from undersampled k-space data is an ill-posed inverse problem.…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
This study provides a computationally effective deconvolution algorithm capable to reconstruct piled-up events in scintillating detector systems with high count rate where fully digitized waveforms are available. A fixed-point iteration…
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…
Although image restoration has advanced significantly, most existing methods target only a single type of degradation. In real-world scenarios, images often contain multiple degradations simultaneously, such as rain, noise, and haze,…
We consider the problem of recovering a continuous-time bandlimited signal from the discrete-time signal obtained from sampling it every $T_s$ seconds and reducing the result modulo $\Delta$, for some $\Delta>0$. For $\Delta=\infty$ the…
In this paper, we propose a framework for output tracking control of both minimum phase (MP) and non-minimum phase (NMP) systems {as well as systems with transmission zeros on the unit circle}. Towards this end, we first address the problem…
We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives,…
The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In…
Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…
We describe and experimentally validate an algorithm to reconstruct an unknown extended object from through-focus measured image intensities blurred by unknown aberrations. It is shown that the method can recover diffraction-limited image…
The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…
Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
Learning a graph from data is the key to taking advantage of graph signal processing tools. Most of the conventional algorithms for graph learning require complete data statistics, which might not be available in some scenarios. In this…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
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…
We consider the problem of signal reconstruction for a system under sparse signal corruption by a malicious agent. The reconstruction problem follows the standard error coding problem that has been studied extensively in the literature. We…
In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding…