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Quantum medical image encoding and compression using Fourier-based methods

Taehee Ko, Inho Lee, Hyeong Won Yu

TL;DR

This work tackles the challenge of encoding large medical images into quantum circuits by introducing FAQPIE, a Fourier-based approximate quantum probability image encoding that uses a no-ancilla FSL circuit to load significant Fourier coefficients. The method leverages a truncation parameter $m\le n-2$ to balance image fidelity against circuit resources, achieving a gate-count scaling of $\mathcal{O}(4^{m+2}+n^2)$ and enabling substantial efficiency gains for compressible images. Two compression strategies—compression of uniformly-controlled rotations (CUCR) and image partition (IP)—further reduce gate counts and pre-processing time, with combined use delivering up to about $80\%$ maximal gate reduction and preserving critical surgical details in $1024\times1024$ medical images. The results suggest FAQPIE as a practical option for scalable quantum image processing in medical imaging and potentially compatible with quantum edge detection and matrix-product-state based approaches for additional circuit compression.

Abstract

Quantum image processing (QIMP) has recently emerged as a promising field for modern image processing applications. In QIMP algorithms, encoding classical image informaiton into quantum circuit is important as the first step. However, most of existing encoding methods use gates almost twice the number of pixels in an image, and simulating even a modest sized image is computationally demanding. In this work, we propose a quantum image encoding method that effectively reduces gates than the number of pixels by a factor at least 4. We demonstrate our method for various 1024 by 1024 high-quality medical images captured during the Bilateral Axillo-Breast Approach (BABA) robotic thyroidectomy surgery. Additionally, two compression techniques are proposed to further reduce the number of gates as well as pre-processing time with negligible loss of image quality. We suggest our image encoding strategy as a valuable option for large scale medical imaging.

Quantum medical image encoding and compression using Fourier-based methods

TL;DR

This work tackles the challenge of encoding large medical images into quantum circuits by introducing FAQPIE, a Fourier-based approximate quantum probability image encoding that uses a no-ancilla FSL circuit to load significant Fourier coefficients. The method leverages a truncation parameter to balance image fidelity against circuit resources, achieving a gate-count scaling of and enabling substantial efficiency gains for compressible images. Two compression strategies—compression of uniformly-controlled rotations (CUCR) and image partition (IP)—further reduce gate counts and pre-processing time, with combined use delivering up to about maximal gate reduction and preserving critical surgical details in medical images. The results suggest FAQPIE as a practical option for scalable quantum image processing in medical imaging and potentially compatible with quantum edge detection and matrix-product-state based approaches for additional circuit compression.

Abstract

Quantum image processing (QIMP) has recently emerged as a promising field for modern image processing applications. In QIMP algorithms, encoding classical image informaiton into quantum circuit is important as the first step. However, most of existing encoding methods use gates almost twice the number of pixels in an image, and simulating even a modest sized image is computationally demanding. In this work, we propose a quantum image encoding method that effectively reduces gates than the number of pixels by a factor at least 4. We demonstrate our method for various 1024 by 1024 high-quality medical images captured during the Bilateral Axillo-Breast Approach (BABA) robotic thyroidectomy surgery. Additionally, two compression techniques are proposed to further reduce the number of gates as well as pre-processing time with negligible loss of image quality. We suggest our image encoding strategy as a valuable option for large scale medical imaging.
Paper Structure (10 sections, 9 equations, 5 figures, 3 tables)

This paper contains 10 sections, 9 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Method description
  3. Approximate quantum probability image encoding via FSL circuit
  4. Compression strategies for FAQPIE
  5. Compression of UCRs
  6. Image partition
  7. Numerical experiments
  8. Conclusion
  9. Acknowledgment
  10. Author contributions

Figures (5)

  • Figure 1: Workflow of the FAQPIE of RGB image and two options for reducing circuit resource
  • Figure 2: (a) Illustration of 2d FSL circuit with uniformly-controlled rotations (UCRs) (b): Illustration of compression of a cascade of UCRs that are reformulated with rotation gates (RGs) and CNOT gates (CXs) (c): Image partition with reduced circuits for multiple FAQPIEs
  • Figure 3: Illustration of the change of image quality of FAQPIE for a surgical image with increasing values of truncation order $m$ in \ref{['eq: imagrepm']} from left to right ($m=3,4,5,6,7$).
  • Figure 4: We zero pad the original medical images (a) to one of size $1024\times 1024$ (b). Then, we encode the zero-padded surgical image using FAQPIE for the simulation (c). The figures (d), (e), and (f) are obtained with one of the compression techniques or both in \ref{['sec: parallel']}. For short, we call compression of UCRs CUCR and image partition IP.
  • Figure 5: Comparison of original medical images (left), the corresponding reconstructed images via FAQPIE with no compression technique (middle) and the two compression techniques applied as in \ref{['fig:frames']} (right).