Signal processing after quadratic random sketching with optical units

TL;DR

This paper demonstrates how optical units can perform quadratic random sketching to enable direct signal processing and classification in the sketched domain, reducing the need for access to original data.

Contribution

It introduces a novel method for signal processing using quadratic random projections via optical units, extending sketching techniques beyond linear methods.

Findings

Successful estimation of local image variations using quadratic projections

Effective data classification directly in the sketched domain

Experimental validation confirms 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.