  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.
