Related papers: Approximation of Non-Decaying Signals From Shift-I…
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…
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
Stability perserving is an important topic in approximation of systems, e.g.\ model reduction. If the original system is stable, we often want the approximation to be stable. But even if an algorithm preserves stability the resulting system…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
Given any domain $X\subseteq \mathbb{R}^d$ and a probability measure $\rho$ on $X$, we study the problem of approximating in $L^2(X,\rho)$ a given function $u:X\to\mathbb{R}$, using its noiseless pointwise evaluations at random samples. For…
We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match…
In this paper we study the recovery conditions of weighted $l_{1}$ minimization for signal reconstruction from incomplete linear measurements when partial prior support information is available. We obtain that a high order RIP condition can…
We study the phase reconstruction of signals $f$ belonging to complex Gaussian shift-invariant spaces $V^\infty(\varphi)$ from spectrogram measurements $|\mathcal{G} f(X)|$ where $\mathcal{G}$ is the Gabor transform and $X \subseteq…
In this paper, we consider recovering $n$ dimensional signals from $m$ binary measurements corrupted by noises and sign flips under the assumption that the target signals have low generative intrinsic dimension, i.e., the target signals can…
The method of stable random projections is popular for efficiently computing the Lp distances in high dimension (where 0<p<=2), using small space. Because it adopts nonadaptive linear projections, this method is naturally suitable when the…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…
In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…
Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the…
Convergence rates for $L_2$ approximation in a Hilbert space $H$ are a central theme in numerical analysis. The present work is inspired by Schaback (Math. Comp., 1999), who showed, in the context of best pointwise approximation for radial…