Related papers: Robust Spectral Recovery for Dynamical Sampling
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…
The identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…
This paper considers the problem of recovering the delays and amplitudes of a weighted superposition of pulses. This problem is motivated by a variety of applications such as ultrasound and radar. We show that for univariate and bivariate…
We study the recovery of an unknown three-dimensional band-limited signal from multiple noisy observations that are randomly rotated by latent elements of SO(3), where the rotations are drawn from an unknown, non-uniform distribution.…
Band selection has a great impact on the spectral recovery quality. To solve this ill-posed inverse problem, most band selection methods adopt hand-crafted priors or exploit clustering or sparse regularization constraints to find most…
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…
In this paper, we study the problem of robust phase recovery. We investigate a novel approach based on extremely quantized (one-bit) phase-less measurements and a corresponding recovery scheme. The proposed approach has surprising…
For the first time, this paper investigates the phase retrieval problem with the assumption that the phase (of the complex signal) is sparse in contrast to the sparsity assumption on the signal itself as considered in the literature of…
This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite…
This contribution proposes a two stage strategy to allow for phase retrieval in state of the art sub-Nyquist sampling schemes for sparse multiband signals. The proposed strategy is based on data acquisition via modulated wideband converters…
We consider the problem of spatiotemporal sampling in which an initial state $f$ of an evolution process $f_t=A_tf$ is to be recovered from a combined set of coarse samples from varying time levels $\{t_1,\dots,t_N\}$. This new way of…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…
In this paper we study a realistic setup for phase retrieval, where the signal of interest is modulated or masked and then for each modulation or mask a diffraction pattern is collected, producing a coded diffraction pattern (CDP) [CLM13].…
We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here we develop a two-stage super-resolution method using spectral filtering to restore the high-wavenumber…
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak)…
Phase retrieval (PR) is an inverse problem about recovering a signal from phaseless linear measurements. This problem can be effectively solved by minimizing a nonconvex amplitude-based loss function. However, this loss function is…