Related papers: Exact Reconstruction using Beurling Minimal Extrap…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…
A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ allows for a linear and stable reconstruction of any vector $x\in H$ from the linear measurements $(\langle x,x_j\rangle)_{j\in J}$. However, there are many situations where some information…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We show that a tessellation generated by a small number of random affine hyperplanes can be used to approximate Euclidean distances between any two points in an arbitrary bounded set $T$, where the random hyperplanes are generated by…
We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…
We consider the extensively studied problem of $\ell_2/\ell_2$ compressed sensing. The main contribution of our work is an improvement over [Gilbert, Li, Porat and Strauss, STOC 2010] with faster decoding time and significantly smaller…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network…
In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…
This paper deals with two related problems, namely distance-preserving binary embeddings and quantization for compressed sensing . First, we propose fast methods to replace points from a subset $\mathcal{X} \subset \mathbb{R}^n$, associated…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
In the 1-dimensional multiple changepoint detection problem, we prove that any procedure with a fast enough $\ell_2$ error rate, in terms of its estimation of the underlying piecewise constant mean vector, automatically has an (approximate)…
We gain tight rigorous bounds on the renormalisation fixed point function for period doubling in families of unimodal maps with degree 2 critical point. By writing the relevant eigenproblems in a modified nonlinear form, we use these…
We proved direct and inverse theorems on B-spline quasi-interpolation sampling representation with a Littlewood-Paley-type norm equivalence in Sobolev spaces $W^r_p$ of mixed smoothness $r$, established estimates of the approximation error…
To prove that a measure, linearly representable by means of a finite set of nonnegative matrices $\mathcal M$, has the weak-Gibbs property, one check the uniform convergence (on $\mathcal M^\mathbb N$) of the sequence of vectors…
We study the problem of recovering an atomic measure on the unit 2-sphere $\mathbb{S}^2$ given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on…