Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

ECALL: Expectation-calibrated learning for unsupervised blind deconvolution

Markus Haltmeier, Gyeongha Hwang

TL;DR

This work tackles blind deconvolution with an unknown kernel by proposing ECALL, an unsupervised learning framework that learns both the kernel $\mathbf k^\star$ and a reconstruction operator $\mathbf R^\star$ from unpaired image collections. The core idea is a loss that combines cycle-consistency with expectation-calibrated statistics in the Fourier domain to guide kernel estimation and reconstruction, enabling virtual supervised data generation once the kernel is estimated. Empirical results on FFHQ images with synthetic Gaussian blur demonstrate that ECALL achieves kernel recovery and deblurring performance close to supervised methods, even in the presence of noise, indicating practical viability when paired data are unavailable. The approach provides a principled, unsupervised alternative for blind deconvolution with potential extensions to other inverse problems and comparisons with GAN-based strategies.

Abstract

Blind deconvolution aims to recover an original image from a blurred version in the case where the blurring kernel is unknown. It has wide applications in diverse fields such as astronomy, microscopy, and medical imaging. Blind deconvolution is a challenging ill-posed problem that suffers from significant non-uniqueness. Solution methods therefore require the integration of appropriate prior information. Early approaches rely on hand-crafted priors for the original image and the kernel. Recently, deep learning methods have shown excellent performance in addressing this challenge. However, most existing learning methods for blind deconvolution require a paired dataset of original and blurred images, which is often difficult to obtain. In this paper, we present a novel unsupervised learning approach named ECALL (Expectation-CALibrated Learning) that uses separate unpaired collections of original and blurred images. Key features of the proposed loss function are cycle consistency involving the kernel and associated reconstruction operator, and terms that use expectation values of data distributions to obtain information about the kernel. Numerical results are used to support ECALL.

ECALL: Expectation-calibrated learning for unsupervised blind deconvolution

TL;DR

This work tackles blind deconvolution with an unknown kernel by proposing ECALL, an unsupervised learning framework that learns both the kernel and a reconstruction operator from unpaired image collections. The core idea is a loss that combines cycle-consistency with expectation-calibrated statistics in the Fourier domain to guide kernel estimation and reconstruction, enabling virtual supervised data generation once the kernel is estimated. Empirical results on FFHQ images with synthetic Gaussian blur demonstrate that ECALL achieves kernel recovery and deblurring performance close to supervised methods, even in the presence of noise, indicating practical viability when paired data are unavailable. The approach provides a principled, unsupervised alternative for blind deconvolution with potential extensions to other inverse problems and comparisons with GAN-based strategies.

Abstract

Blind deconvolution aims to recover an original image from a blurred version in the case where the blurring kernel is unknown. It has wide applications in diverse fields such as astronomy, microscopy, and medical imaging. Blind deconvolution is a challenging ill-posed problem that suffers from significant non-uniqueness. Solution methods therefore require the integration of appropriate prior information. Early approaches rely on hand-crafted priors for the original image and the kernel. Recently, deep learning methods have shown excellent performance in addressing this challenge. However, most existing learning methods for blind deconvolution require a paired dataset of original and blurred images, which is often difficult to obtain. In this paper, we present a novel unsupervised learning approach named ECALL (Expectation-CALibrated Learning) that uses separate unpaired collections of original and blurred images. Key features of the proposed loss function are cycle consistency involving the kernel and associated reconstruction operator, and terms that use expectation values of data distributions to obtain information about the kernel. Numerical results are used to support ECALL.
Paper Structure (14 sections, 1 theorem, 8 equations, 1 figure, 4 tables)

This paper contains 14 sections, 1 theorem, 8 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Prior work
  3. Main contributions
  4. Outline
  5. Proposed ECALL method
  6. Problem formulation
  7. Theory
  8. Empirical estimation
  9. Numerical simulations
  10. Datasets and data generation
  11. Training
  12. Results
  13. Conclusion
  14. Acknowledgments

Key Result

Theorem 2.4

Suppose $\mathbb{E}[ \widehat{\mathbf x}] (\xi) \neq 0$ for almost every $\xi \in \operatorname{supp}(\widehat{\mathbf k^\star})$. Then $(\mathbf k^\star, \mathbf R^\star)$ is the unique solution of

Figures (1)

  • Figure 3.1: U-net architecture $(\mathbf{R}_\theta)_{\theta \in \Theta}$ for representing the reconstruction operator $\mathbf R^\star$ used in all presented numerical results.

Theorems & Definitions (3)

  • Remark 2.3
  • Theorem 2.4: Uniqueness results
  • proof