# Learning Point Spread Function Invertibility Assessment for Image Deconvolution

arXiv: https://arxiv.org/abs/2405.16343 · HTML: https://mlsanity.com/paper/2405.16343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Connecting Image Denoising and High-Level Vision Tasks via Deep Learning](https://mlsanity.com/paper/1809.01826/) (2018)
- [Recent Progress in Image Deblurring](https://mlsanity.com/paper/1409.6838/) (2014)
- [Deep Optical Coding Design in Computational Imaging](https://mlsanity.com/paper/2207.00164/) (2022)
- [Gaussian process deconvolution](https://mlsanity.com/paper/2305.04871/) (2023)

## Abstract (arXiv)

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.