Deep Convolutional Autoencoders for Image Reconstruction from Incomplete Fourier Amplitude Measurements

Giovanni Pellegrini and Jacopo Bertolotti

https://slides.com/giovannipellegrini/icton2024

HOW THIS COLLABORATION WAS BORN

THE PROBLEM

Scattering

Autocorr

Autocorr

Inversion

Inversion

THE IDEA: NEURAL NETWORK VS ITERATIVE METHODS

ALSO: We want to erode the correlation information!!!

THE FUNDAMENTALS: DEFINING THE DATASET

• We devise a synthetic dataset based on the MNIST handwritten digits as a benchmark for the reconstruction performance

A PRELIMINARY CHECK: DO ITERATIONS WORK?

• Current phase retrieval techniques adopt iterative approaches to recover phase information from the modulus of the Fourier transform

• We apply a circular erosion mask to the Fourier autocorrelation, in order to assess the performance of traditional methods in presence of partial information

• We observe that traditional approaches struggle in the presence of incomplete information. We employ a deep neural network to overcome these limitations, and show that such and approach vastly over-performs traditional methods in a large variety of scenarios 

DEFINING THE NEURAL NETWORK ARCHITECTURE

• We adopt a deep convolutional autoencoder based on the DeepLabV3+ architecture with a L1 loss computed on the input and reconstructed autocorrelations

TAILORING THE TRAINING PROCESS

• Phase 1: We train the network on full autocorrelation

• Phase 2: We progressively erode the input autocorrelation, and train the network to reconstruct the missing information

• Phase 3: We perform a final stabilization training

DEEP LEARNING: RESULTS 

Deep Learning Vs Iterative

Deep Learning: exploration

CONCLUSIONS

• Neural network reconstructions routinely outperform traditional ones, especially in scenarios where large chunks of the autocorrelation information are missing

• The neural network can perform phase retrieval on out of distribution samples.

• The neural network performance degrades once the information is not just incomplete, but completely missing from the input

1. Pellegrini, G. & Bertolotti, J. Phase-Retrieval with Incomplete Autocorrelations Using Deep Convolutional Autoencoders. Preprint at https://doi.org/10.48550/arXiv.2304.09303 (2023).