Signal processing with optical quadratic random sketches

TL;DR

This paper demonstrates how optical quadratic random sketches can be used for direct signal processing and classification tasks in the sketched domain, reducing the need for access to original data.

Contribution

It introduces a novel method for performing signal processing and classification directly with quadratic random projections via optical processing, extending previous linear sketching techniques.

Findings

Successful estimation of local image variations using quadratic projections

Effective data classification directly in the sketched domain

Experimental validation confirming the approach's power

Abstract

Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the possibility of performing data processing (such as pattern detection or classification) directly in the sketched domain without accessing the original data was previously achieved for linear random sketching methods and compressive sensing. In this work, we show 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. The same approach allows for naive data classification methods directly operated in the sketched domain. We report several experiments confirming the power of our approach.