# ROP inception: signal estimation with quadratic random sketching

@article{Delogne2022ROPIS, title={ROP inception: signal estimation with quadratic random sketching}, author={R'emi Delogne and Vincent Schellekens and Laurent Jacques}, journal={ArXiv}, year={2022}, volume={abs/2205.08225} }

Rank-one projections (ROP) of matrices and quadratic random sketching of signals support several data processing and machine learning methods, as well as recent imaging applications, such as phase retrieval or optical processing units. In this paper, we demonstrate how signal estimation can be operated directly through such quadratic sketches--equivalent to the ROPs of the"lifted signal"obtained as its outer product with itself--without explicitly reconstructing that signal. Our analysis relies…

## One Citation

### Signal Processing with Optical Quadratic Random Sketches

- Computer ScienceICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2023

This work shows how to estimate simple signal processing tasks (such as deducing local variations in a image) directly using random quadratic projections achieved by an optical processing unit and allows for naive data classification methods directly operated in the sketched domain.

## 16 References

### Random projections through multiple optical scattering: Approximating Kernels at the speed of light

- Computer Science2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2016

This work proposes an analog, optical device that performs the random projections literally at the speed of light without having to store any matrix in memory, and shows that, on the MNIST database, the experimental results closely match the theoretical performance of the corresponding kernel.

### Signal Processing With Compressive Measurements

- Computer ScienceIEEE Journal of Selected Topics in Signal Processing
- 2010

This paper takes some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved.

### ROP: Matrix Recovery via Rank-One Projections

- Computer ScienceArXiv
- 2013

A rank-one projection model for low-rank matrix recovery is introduced and a constrained nuclear norm minimization method for stable recovery of low- rank matrices in the noisy case is proposed.

### Jointly low-rank and bisparse recovery: Questions and partial answers

- Computer ScienceAnalysis and Applications
- 2019

This paper investigates the problem of recovering jointly low-rank and bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements, and suggests an iterative-hard-thresholding algorithm modified to exploit the nonstandard restricted isometry property obeyed by this type of measurements.

### Exact and Stable Covariance Estimation From Quadratic Sampling via Convex Programming

- Computer ScienceIEEE Transactions on Information Theory
- 2015

This paper explores a quadratic (or rank-one) measurement model which imposes minimal memory requirements and low computational complexity during the sampling process, and is shown to be optimal in preserving various low-dimensional covariance structures.

### Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements

- Computer ScienceIEEE Transactions on Information Theory
- 2011

It is shown that properly constrained nuclear-norm minimization stably recovers a low-rank matrix from a constant number of noisy measurements per degree of freedom; this seems to be the first result of this nature.

### Weighted Sums of Random Kitchen Sinks : Replacing minimization with randomization in learning

- Computer Science
- 2008

This work considers architectures that compute a weighted sum of their inputs after passing them through a bank of arbitrary randomized nonlinearities, and identifies conditions under which these networks exhibit good classification performance, and bound their test error in terms of the size of the dataset and the number of random non linearities.

### Flavors of Compressive Sensing

- Computer Science
- 2016

This survey presents an overview of the field of compressive sensing, accentuating elements from approximation theory, but also highlighting connections with other disciplines that have enriched the theory, e.g., statistics, sampling theory, probability, optimization, metagenomics, graph theory, frame theory, and Banach space geometry.

### Quantized Iterative Hard Thresholding: Bridging 1-bit and High-Resolution Quantized Compressed Sensing

- Computer ScienceArXiv
- 2013

In this work, we show that reconstructing a sparse signal from quantized compressive measurement can be achieved in an unified formalism whatever the (scalar) quantization resolution, i.e., from…

### PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming

- Computer ScienceArXiv
- 2011

It is shown that in some instances, the combinatorial phase retrieval problem can be solved by convex programming techniques, and it is proved that the methodology is robust vis‐à‐vis additive noise.