Fourier optical preprocessing in lieu of deep learning

Deep learning convolutional neural networks generally involve multiple-layer, forward-backward propagation machine-learning algorithms that are computationally costly. In this work, we demonstrate an alternative scheme to convolutional neural nets that reconstructs an original image from its optically preprocessed, Fourier-encoded pattern. The scheme is much less computationally demanding and more noise robust, and thus suited for high-speed and low light imaging. We introduce a vortex phase transform with a lenslet-array to accompany shallow, dense, small-brain neural networks. Our single-shot coded-aperture approach exploits the coherent diffraction, compact representation, and edge enhancement of Fourier-transformed spiral phase gradients. With vortex encoding, a small brain is trained to deconvolve images at rates 5-20 times faster than those achieved with random encoding schemes, where greater advantages are gained in the presence of noise. Once trained, the small brain reconstructs an object from intensity-only data, solving an inverse mapping without performing iterations on each image and without deep learning schemes. With vortex Fourier encoding, we reconstruct MNIST Fashion objects illuminated with low-light flux (5 nJ/cm2) at a rate of several thousand frames per second on a 15 W central processing unit. We demonstrate that Fourier optical preprocessing with vortex encoders achieves similar accuracies and speeds 2 orders of magnitude faster than convolutional neural networks. (c) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement