Learning Point Spread Function Invertibility Assessment for Image Deconvolution

TL;DR

This paper introduces a neural network-based metric to assess the invertibility of point spread functions, improving image deconvolution quality by predicting PSF suitability for deep learning recovery and enabling optimized optical element design.

Contribution

It proposes a novel non-linear metric for PSF invertibility assessment using neural networks, facilitating better deconvolution and optical element design.

Findings

The metric correlates with high recovery performance in DL and traditional methods.

It reduces computational complexity compared to condition number assessments.

It enables end-to-end optimization of optical elements for invertible PSFs.

Abstract

Deep-learning (DL)-based image deconvolution (ID) has exhibited remarkable recovery performance, surpassing traditional linear methods. However, unlike traditional ID approaches that rely on analytical properties of the point spread function (PSF) to achieve high recovery performance - such as specific spectrum properties or small conditional numbers in the convolution matrix - DL techniques lack quantifiable metrics for evaluating PSF suitability for DL-assisted recovery. Aiming to enhance deconvolution quality, we propose a metric that employs a non-linear approach to learn the invertibility of an arbitrary PSF using a neural network by mapping it to a unit impulse. A lower discrepancy between the mapped PSF and a unit impulse indicates a higher likelihood of successful inversion by a DL network. Our findings reveal that this metric correlates with high recovery performance in DL and traditional methods, thereby serving as an effective regularizer in deconvolution tasks. This approach reduces the computational complexity over conventional condition number assessments and is a differentiable process. These useful properties allow its application in designing diffractive optical elements through end-to-end (E2E) optimization, achieving invertible PSFs, and outperforming the E2E baseline framework.