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Learning Point Spread Function Invertibility Assessment for Image Deconvolution

Romario Gualdrón-Hurtado, Roman Jacome, Sergio Urrea, Henry Arguello, Luis Gonzalez

TL;DR

The paper tackles the lack of quantitative PSF invertibility metrics for DL-based image deconvolution and introduces a differentiable score based on a neural network that maps a PSF $\mathbf{h}$ to a unit impulse $\boldsymbol{\delta}$ by minimizing $\|\boldsymbol{\delta}-\mathcal{N}_{\beta}(\mathbf{h})\|_2$. This metric correlates with reconstruction quality across Wiener, variational, and DL-based methods and offers a computationally cheaper, differentiable alternative to condition-number analyses. It further serves as a regularizer in end-to-end DOE design, enabling the optimization of a diffractive optical element jointly with a reconstruction network to yield invertible PSFs and improved recovery, demonstrated by RGB imaging with PSNR gains of about $1$ dB at appropriate regularization levels. The work provides a practical, differentiable means to assess and enforce PSF invertibility, with potential extensions to spatially variant 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.

Learning Point Spread Function Invertibility Assessment for Image Deconvolution

TL;DR

The paper tackles the lack of quantitative PSF invertibility metrics for DL-based image deconvolution and introduces a differentiable score based on a neural network that maps a PSF to a unit impulse by minimizing . This metric correlates with reconstruction quality across Wiener, variational, and DL-based methods and offers a computationally cheaper, differentiable alternative to condition-number analyses. It further serves as a regularizer in end-to-end DOE design, enabling the optimization of a diffractive optical element jointly with a reconstruction network to yield invertible PSFs and improved recovery, demonstrated by RGB imaging with PSNR gains of about dB at appropriate regularization levels. The work provides a practical, differentiable means to assess and enforce PSF invertibility, with potential extensions to spatially variant 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.
Paper Structure (11 sections, 7 equations, 5 figures, 1 table)

This paper contains 11 sections, 7 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Image Deconvolution Background
  3. Wiener Deconvolution
  4. Variational Methods
  5. Deep Learning-based Deconvolution
  6. Learning Invertibility Assessment
  7. Metric as Regularizer for DOE Design
  8. Differentiable Physical modeling
  9. End to End Optimization
  10. Results
  11. Conclusion

Figures (5)

  • Figure 1: a) Employed Gaussian filters. b) Comparison of proposed vs. traditional invertibility assessment in Gaussian filters.
  • Figure 2: Running time comparison of proposed vs. traditional invertibility assessment in Gaussian filters with different kernel sizes.
  • Figure 3: Correlation matrix between reconstruction performance in MSE, the proposed metric, and the condition number of the convolution matrix.
  • Figure 4: Correlation matrix for different noise levels in a data-driven scheme.
  • Figure 5: Comparative results illustrating the impact of incorporating the proposed invertibility metric into the E2E optimization loss function for ID.