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Synthetic Aperture Radar Image Segmentation with Quantum Annealing

Timothe Presles, Cyrille Enderli, Gilles Burel, El Houssain Baghious

TL;DR

The paper tackles the NP-hard problem of segmenting high-resolution SAR images by formulating Markov Random Field-based segmentation as Quadratic Unconstrained Binary Optimization (QUBO) problems suitable for quantum annealing. It introduces two QUBO variants for binary and multi-class segmentation and couples them with an EM-inspired parameter estimation loop, plus an adaptation to SAR data using Weibull/Generalized Gaussian models. Experimental validation on the D-Wave Advantage, complemented by simulated annealing with d-wave neal, demonstrates potential speedups and competitive accuracy, while highlighting hardware limitations in qubit count and embedding. The work suggests a viable hybrid quantum–classical pipeline for scalable SAR segmentation and ATR classifier training, pending advances in quantum hardware and embedding techniques.

Abstract

In image processing, image segmentation is the process of partitioning a digital image into multiple image segment. Among state-of-the-art methods, Markov Random Fields (MRF) can be used to model dependencies between pixels, and achieve a segmentation by minimizing an associated cost function. Currently, finding the optimal set of segments for a given image modeled as a MRF appears to be NP-hard. In this paper, we aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of Synthetic Aperture Radar images. For that purpose, we propose an hybrid quantum annealing classical optimization Expectation Maximization algorithm to obtain optimal sets of segments. After proposing suitable formulations, we discuss the performances and the scalability of our approach on the D-Wave quantum computer. We also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimization problems.

Synthetic Aperture Radar Image Segmentation with Quantum Annealing

TL;DR

The paper tackles the NP-hard problem of segmenting high-resolution SAR images by formulating Markov Random Field-based segmentation as Quadratic Unconstrained Binary Optimization (QUBO) problems suitable for quantum annealing. It introduces two QUBO variants for binary and multi-class segmentation and couples them with an EM-inspired parameter estimation loop, plus an adaptation to SAR data using Weibull/Generalized Gaussian models. Experimental validation on the D-Wave Advantage, complemented by simulated annealing with d-wave neal, demonstrates potential speedups and competitive accuracy, while highlighting hardware limitations in qubit count and embedding. The work suggests a viable hybrid quantum–classical pipeline for scalable SAR segmentation and ATR classifier training, pending advances in quantum hardware and embedding techniques.

Abstract

In image processing, image segmentation is the process of partitioning a digital image into multiple image segment. Among state-of-the-art methods, Markov Random Fields (MRF) can be used to model dependencies between pixels, and achieve a segmentation by minimizing an associated cost function. Currently, finding the optimal set of segments for a given image modeled as a MRF appears to be NP-hard. In this paper, we aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of Synthetic Aperture Radar images. For that purpose, we propose an hybrid quantum annealing classical optimization Expectation Maximization algorithm to obtain optimal sets of segments. After proposing suitable formulations, we discuss the performances and the scalability of our approach on the D-Wave quantum computer. We also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimization problems.
Paper Structure (16 sections, 19 equations, 7 figures, 2 tables)

This paper contains 16 sections, 19 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Mathematical Background
  3. Markov Random Fields
  4. MRF for Image Segmentation
  5. Expectation Maximisation Algorithm
  6. Problem Implementation
  7. QUBO formulation for 2-classes segmentation
  8. QUBO formulation for Q-classes segmentation
  9. EM inspired approach for parameter estimation
  10. Adaptation for SAR image processing
  11. Results
  12. Experimental context
  13. Results for Gaussian distributions
  14. Results for SAR images
  15. Discussion on optimal parameters and limits of the model
  16. ...and 1 more sections

Figures (7)

  • Figure 1: Variation of the accuracy depending on the value of $\lambda_{P}$. These results are obtained by simulating the multi-class segmentation approach on a (40, 40) image with $Q = 4$.
  • Figure 2: Qualitative results of the EM algorithm for images with additional Gaussian noise: (a) and (e) corresponds the original image, (b) and (f) corresponds to the original image with the addition of a gaussian noise, (c) and (g) correspond to the segmentation obtained with the simulated annealing approach. (d) and (h) corresponds to the segmentation obtained with the region smoothing algorithm region_smoothing
  • Figure 3: Example of MSTAR SAR image: (1) corresponds to the vehicle, (2) corresponds to the shadow of the vehicle, (3) corresponds to the (noisy) background of the image.
  • Figure 4: Qualitative results of the EM algorithm on M-STAR SAR images. (a/e/i) correspond to the original image. (b/f/j) correspond to the results obtained with our approach. (c/g/k) corresponds to the results obtained with the region smoothing algorithm. (d/h/l) corresponds to the results obtained with the fuzzy clustering algorithm.
  • Figure 5: Qualitative results of the EM algorithm on SSDD dataset images. (a/e/i) correspond to the original image. (b/f/j) correspond to the results obtained with our approach. (c/g/k) corresponds to the results obtained with the region smoothing algorithm. (d/h/l) corresponds to the results obtained with the fuzzy clustering algorithm.
  • ...and 2 more figures