Machine learning with sub-diffraction resolution in the photon-counting regime

TL;DR

This paper demonstrates that combining physical optical pre-processing with machine learning enables sub-diffraction resolution image classification, surpassing traditional limits in optical imaging.

Contribution

It introduces a hybrid approach integrating spatial-mode demultiplexing with neural networks for improved classification of blurred images.

Findings

Successfully classified highly blurred MNIST images using the method.

Achieved sub-diffraction resolution in image classification tasks.

Showed physical pre-processing enhances neural network performance.

Abstract

The resolution of optical imaging is classically limited by the width of the point-spread function, which in turn is determined by the Rayleigh length. Recently, spatial-mode demultiplexing (SPADE) has been proposed as a method to achieve sub-Rayleigh estimation and discrimination of natural, incoherent sources. Here we show that SPADE yields sub-diffraction resolution in the broader context of image classification. To achieve this goal, we outline a hybrid machine learning algorithm for image classification that includes a physical part and a computational part. The physical part implements a physical pre-processing of the optical field that cannot be simulated without essentially reducing the signal-to-noise ratio. In detail, a spatial-mode demultiplexer is used to sort the transverse field, followed by mode-wise photon detection. In the computational part, the collected data are fed into an artificial neural network for training and classification. As a case study, we classify images from the MNIST dataset after severe blurring due to diffraction. Our numerical experiments demonstrate the ability to classify highly blurred images that would be otherwise indistinguishable by direct imaging without the physical pre-processing of the optical field.