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Multi-Frame Blind Manifold Deconvolution for Rotating Synthetic Aperture Imaging

Dao Lin, Jian Zhang, Martin Benning

TL;DR

This work tackles reconstructing a high-resolution latent image $X$ from rotating synthetic aperture frames $igl\

Abstract

Rotating synthetic aperture (RSA) imaging system captures images of the target scene at different rotation angles by rotating a rectangular aperture. Deblurring acquired RSA images plays a critical role in reconstructing a latent sharp image underlying the scene. In the past decade, the emergence of blind convolution technology has revolutionised this field by its ability to model complex features from acquired images. Most of the existing methods attempt to solve the above ill-posed inverse problem through maximising a posterior. Despite this progress, researchers have paid limited attention to exploring low-dimensional manifold structures of the latent image within a high-dimensional ambient-space. Here, we propose a novel method to process RSA images using manifold fitting and penalisation in the content of multi-frame blind convolution. We develop fast algorithms for implementing the proposed procedure. Simulation studies demonstrate that manifold-based deconvolution can outperform conventional deconvolution algorithms in the sense that it can generate a sharper estimate of the latent image in terms of estimating pixel intensities and preserving structural details.

Multi-Frame Blind Manifold Deconvolution for Rotating Synthetic Aperture Imaging

TL;DR

This work tackles reconstructing a high-resolution latent image from rotating synthetic aperture frames $igl\

Abstract

Rotating synthetic aperture (RSA) imaging system captures images of the target scene at different rotation angles by rotating a rectangular aperture. Deblurring acquired RSA images plays a critical role in reconstructing a latent sharp image underlying the scene. In the past decade, the emergence of blind convolution technology has revolutionised this field by its ability to model complex features from acquired images. Most of the existing methods attempt to solve the above ill-posed inverse problem through maximising a posterior. Despite this progress, researchers have paid limited attention to exploring low-dimensional manifold structures of the latent image within a high-dimensional ambient-space. Here, we propose a novel method to process RSA images using manifold fitting and penalisation in the content of multi-frame blind convolution. We develop fast algorithms for implementing the proposed procedure. Simulation studies demonstrate that manifold-based deconvolution can outperform conventional deconvolution algorithms in the sense that it can generate a sharper estimate of the latent image in terms of estimating pixel intensities and preserving structural details.

Paper Structure

This paper contains 15 sections, 4 theorems, 47 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. MAP blind deconvolution: XK-procedure
  4. MAP blind manifold deconvolution: IMR-procedure
  5. IX-step
  6. MF-step
  7. RC-step
  8. Numerical results
  9. Dataset
  10. Implementation details
  11. Simulation results and discussion
  12. Conclusion
  13. Appendix A: Convolution, DFT and Proof of Proposition \ref{['proposition2.1']}
  14. Appendix B: Half-quadratic Splitting
  15. Appendix C: Converting the optimisation problems in equation \ref{['eqQ']} and equation (\ref{['eqQ']}) with $\nabla_jy_i$ and $\nabla_j\widehat{x}$ replaced by $y_i$ and $\widehat{x}$ into the problems of Lasso regression

Key Result

Proposition A.1

Figures (9)

  • Figure 1: Process of blurring. (a) The ground-truth sharp image $x$; (b) one simulated PSF $k_i$; (c) one ground-truth convolved image $k_i \ast x$; (d) one blurred image $y_i = k_i \ast x + n_i$.
  • Figure 2: First row: $12$ estimated blur kernels; second row: the associated real (simulated) blur kernels.
  • Figure 3: First row: $4$ deconvolved images; second row: the associated enhanced deconvolved images. The baseline image is the ground-truth sharp image $x$. The PSNR (peak signal-to-noise ratio) and SSIM (structural similarity) values of each showed image are calculated with respect to the ground-truth image $x$.
  • Figure 4: (a) Comparison of PSNR values of deconvolved images $\{\widetilde{x}_i\}_{i=1}^n$ and those of enhanced (denoised) deconvolved images $\{\widehat{x}_i^{\ast}\}_{i=1}^n$. (b) Comparison of SSIM values of deconvolved images $\{\widetilde{x}_i\}_{i=1}^n$ and those of enhanced (denoised) deconvolved images $\{\widehat{x}_i^{\ast}\}_{i=1}^n$. The baseline image is the ground-truth sharp image $x$, i.e., the PSNR (peak signal-to-noise ratio) and SSIM (structural similarity) values of each $\widetilde{x}_i$ and $\widehat{x}_i^{\ast}$ are calculated with respect to the ground-truth image $x$.
  • Figure 5: Process of denoising. (a) One blurred image $y_i$; (b) the associated deconvolved image $\widehat{x}_i$; (c) the associated enhanced deconvolved image $\widehat{x}^{\ast}_i$; (d) the associated enhanced convolved image $\widetilde{y_i}$.
  • ...and 4 more figures

Theorems & Definitions (6)

  • Proposition A.1
  • Lemma A.1
  • Lemma A.2
  • proof
  • Lemma C.1
  • proof