Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Imaging with super-resolution in changing random media

Alexander Christie, Matan Leibovich, Miguel Moscoso, Alexei Novikov, George Papanicolaou, Chrysoula Tsogka

TL;DR

The paper tackles high-resolution imaging from array data when the ambient medium changes across measurements, requiring joint estimation of medium realizations and source configurations. It introduces a four-step approach—sparse dictionary learning to estimate the block sensing matrix $\mathcal{G}^B$, clustering to remove noise, graph-based separation to assign columns to each medium, and multidimensional scaling to order columns for imaging with $\ell_1$ or $\ell_2$ methods. Key contributions include a modified MOD dictionary-learning scheme that converges without a good initialization, DBSCAN-based denoising, graph-based medium separation, and MDS-based grid reconstruction, enabling robust super-resolution imaging. Results on synthetic Foldy-Lax data show that the proposed method yields high-resolution images even when media are correlated or independent, with the $\ell_1$-based reconstruction using the full block matrix performing best.

Abstract

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional scaling. Starting from random initializations, the algorithm reliably extracts the unknown medium properties necessary for accurate imaging using back-propagation, $\ell_2$ or $\ell_1$ methods. Remarkably, scattering enhances resolution beyond homogeneous medium limits. When abundant data are available, the algorithm allows the realization of super-resolution in imaging.

Imaging with super-resolution in changing random media

TL;DR

The paper tackles high-resolution imaging from array data when the ambient medium changes across measurements, requiring joint estimation of medium realizations and source configurations. It introduces a four-step approach—sparse dictionary learning to estimate the block sensing matrix , clustering to remove noise, graph-based separation to assign columns to each medium, and multidimensional scaling to order columns for imaging with or methods. Key contributions include a modified MOD dictionary-learning scheme that converges without a good initialization, DBSCAN-based denoising, graph-based medium separation, and MDS-based grid reconstruction, enabling robust super-resolution imaging. Results on synthetic Foldy-Lax data show that the proposed method yields high-resolution images even when media are correlated or independent, with the -based reconstruction using the full block matrix performing best.

Abstract

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional scaling. Starting from random initializations, the algorithm reliably extracts the unknown medium properties necessary for accurate imaging using back-propagation, or methods. Remarkably, scattering enhances resolution beyond homogeneous medium limits. When abundant data are available, the algorithm allows the realization of super-resolution in imaging.

Paper Structure

This paper contains 16 sections, 23 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Array imaging with data from multiple random media
  3. The four-step imaging algorithm
  4. Formulation of the imaging problem
  5. Data generation with the Foldy-Lax model
  6. Imaging with data from the Foldy-Lax model
  7. Analytical description of the imaging algorithm
  8. Sparse dictionary learning
  9. Related work
  10. Introduction of a modified MOD algorithm
  11. Improved estimate of sensing matrix by clustering
  12. Separating the medium realizations using graphs
  13. Grid reconstructions using multidimensional scaling
  14. On the coherence of the columns of the block sensing matrix $\hbox{\boldmath{${\cal G}$}}^B\,$
  15. Numerical simulations
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Schematic view of how super-resolution can be explained by the idea of a larger effective aperture Borcea_2002. On the left the point spread function in the strongly scattering medium is illustrated and on the right the one obtained using the same array and bandwidth in the homogeneous medium.
  • Figure 2: Schematic of the imaging problem setup in a scattering medium. On the left, an array of receivers at locations $\vec{r}_j$, $j=1, \ldots,N$. The central square region contains randomly distributed scatterers at positions $\boldsymbol{\xi}_j$, $j=1,\ldots, J$. On the right, the imaging window (IW) is depicted, with discrete grid of points $\left\{ \vec{z}_l \right\}_{l=1}^K$ where the image will be reconstructed.
  • Figure 3: $\ell_1$- and KM-images for $L=3$nearby (correlated) media.Top row: the solution $\bm{x}^{\ell_1}$ obtained with $\ell_1$ minimization . Center row: Locations of top $4$$\ell_1$-norm coefficients plotted with blue $x$'s and the true sources locations plotted with red circles. Bottom row: KM-images. Left column: Images produced using the actual medium from which the data originated. Right column: Images produced using the combined sensing matrix $\hbox{\boldmath{$\hat{{\cal G}}$}}^B$. In the KM images the true sources locations are indicated with red x's
  • Figure 4: $\ell_1$ and KM images for $L=3$independent media.Top row: the solution $\bm{x}^{\ell_1}$ obtained with $\ell_1$ minimization. Center row: Locations of top $4$$\ell_1$-norm coefficients plotted with blue $x$'s and the true sources locations plotted with red circles. Bottom row: KM-images. Left column: Images produced using the actual medium from which the data originated. Right column: Images produced using the combined sensing matrix $\hbox{\boldmath{$\hat{{\cal G}}$}}^B$. In the KM images the true sources locations are indicated with red x's