# Three Dimensional Sums of Character Gabor Systems

In deterministic compressive sensing, one constructs sampling matrices that recover sparse signals from highly incomplete measurements. However, the so-called square-root bottleneck limits the usefulness of such matrices, as they are only able to recover exceedingly sparse signals with respect to the matrix dimension. In view of the flat restricted isometry property (flat RIP) proposed by Bourgain et al., we provide a partial solution to the bottleneck problem with the Gabor system of Legendre symbols. When summing over consecutive vectors, the estimate gives a nontrivial upper bound required for the bottleneck problem.

## Authors

• 4 publications
10/21/2020

### On Compressed Sensing Matrices Breaking the Square-Root Bottleneck

Compressed sensing is a celebrated framework in signal processing and ha...
10/19/2020

### On the restricted isometry property of the Paley matrix

In this paper, we prove that the Paley graph conjecture implies that the...
05/29/2018

### Explicit construction of RIP matrices is Ramsey-hard

Matrices Φ∈^n× p satisfying the Restricted Isometry Property (RIP) are a...
06/26/2020

### Recovery of Binary Sparse Signals from Structured Biased Measurements

In this paper we study the reconstruction of binary sparse signals from ...
05/14/2020

### Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs

We study sparse recovery with structured random measurement matrices hav...
01/01/2018

### Statistical and Computational Limits for Sparse Matrix Detection

This paper investigates the fundamental limits for detecting a high-dime...
11/29/2021

### Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimension

In this paper, we consider recovering n dimensional signals from m binar...
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