Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Blind source separation for imaging

Randy Bartels, Olivier Pinaud

TL;DR

This work extends blind source separation (BSS) theory to imaging in diffusive media by providing separability criteria and an explicit error bound for correlated complex-valued sources. It formulates a two-phase imaging pipeline: (1) separate the fields from different scatterers using BSS (± ICA) and (2) remove random phases to form diffraction-limited images, building on an improved DORT approach. The authors verify separability in speckle and Random Geometrical Optics (RGO) regimes and demonstrate improved image reconstruction for SHG and linear scattering scenarios, reducing the number of illuminations needed in some cases. The results broaden the applicability of BSS in imaging through highly scattering media and offer practical advantages over classical DORT in terms of resolution and robustness to noise.

Abstract

This work is concerned with the problem of blind source separation and its applications to imaging. We first establish a theoretical result that we stated in our previous article on imaging in diffusive environments. This result is a generalization of separability criteria found in the literature to arbitrary correlated complex-valued sources with additive noise. In a second step, we verify these separability conditions in two propagation regimes frequently encountered in imaging: the speckle regime and the random geometrical optics regime. Finally, we propose a new imaging method based on the blind source separation problem that improves on images obtained with the classical decomposition of the time reversal operator method.

Blind source separation for imaging

TL;DR

This work extends blind source separation (BSS) theory to imaging in diffusive media by providing separability criteria and an explicit error bound for correlated complex-valued sources. It formulates a two-phase imaging pipeline: (1) separate the fields from different scatterers using BSS (± ICA) and (2) remove random phases to form diffraction-limited images, building on an improved DORT approach. The authors verify separability in speckle and Random Geometrical Optics (RGO) regimes and demonstrate improved image reconstruction for SHG and linear scattering scenarios, reducing the number of illuminations needed in some cases. The results broaden the applicability of BSS in imaging through highly scattering media and offer practical advantages over classical DORT in terms of resolution and robustness to noise.

Abstract

This work is concerned with the problem of blind source separation and its applications to imaging. We first establish a theoretical result that we stated in our previous article on imaging in diffusive environments. This result is a generalization of separability criteria found in the literature to arbitrary correlated complex-valued sources with additive noise. In a second step, we verify these separability conditions in two propagation regimes frequently encountered in imaging: the speckle regime and the random geometrical optics regime. Finally, we propose a new imaging method based on the blind source separation problem that improves on images obtained with the classical decomposition of the time reversal operator method.
Paper Structure (28 sections, 4 theorems, 97 equations, 5 figures, 1 table)

This paper contains 28 sections, 4 theorems, 97 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Acknowledgment.
  3. Blind source separation
  4. Notation.
  5. Generalities
  6. Optimality result
  7. Applications to imaging
  8. Measurement setting
  9. The incoming field
  10. The outgoing field
  11. Isoplanaticity.
  12. Blind source separation
  13. Separability in the speckle regime
  14. Separability in the random geometrical optics regime
  15. Imaging procedure
  16. ...and 13 more sections

Key Result

Theorem 2.1

Assume that $\mathbb E \{|s_1|^4\}-2-|\mathbb E\{s_1^2\}|^2\neq 0$. Then, there exists $\varepsilon>0$ such that the estimate holds under the condition $M^{(s)}+M^{(n)} \leq \varepsilon$.

Figures (5)

  • Figure 1: Measurement setting
  • Figure 2: SHG imaging with BSS based on $V$. Left: Improved DORT method. Right: DORT method. The red dots represent the exact position of the scatterers.
  • Figure 3: SHG imaging with BSS based on $V$. Upper row: Improved DORT method with $\eta_F=0.5,0.7,0.9$. Lower row: DORT method with $\eta_F=0.5,0.7,0.9$. The red dots represent the exact position of the scatterers.
  • Figure 4: SHG imaging with BSS based on $U$. Left: Improved DORT method. Right: DORT method. The red dots represent the exact position of the scatterers.
  • Figure 5: Linear scattering imaging with BSS based on $U$. Left: Improved DORT method. Right: DORT method. The red dots represent the exact position of the scatterers.

Theorems & Definitions (7)

  • Theorem 2.1
  • Lemma A.1
  • proof
  • Lemma A.2
  • proof
  • Lemma A.3
  • proof