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arXiv:2207.02448 · Scientific Reports

A highly accurate quantum optimization algorithm for CT image reconstruction based on sinogram patterns

Kyungtaek Jun

Published Sep 1, 2023• 24 citations
arXivHTMLPDF

Abstract

Computed tomography (CT) has been developed as a nondestructive technique for observing minute internal images in samples. It has been difficult to obtain photorealistic (clean or clear) CT images due to various unwanted artifacts generated during the CT scanning process, along with the limitations of back-projection algorithms. Recently, an iterative optimization algorithm has been developed that uses an entire sinogram to reduce errors caused by artifacts. In this paper, we introduce a new quantum algorithm for reconstructing CT images. This algorithm can be used with any type of light source as long as the projection is defined. Assuming an experimental sinogram produced by a Radon transform, to find the CT image of this sinogram, we express the CT image as a combination of qubits. After acquiring the Radon transform of the undetermined CT image, we combine the actual sinogram and the optimized qubits. The global energy optimization value used here can determine the value of qubits through a gate model quantum computer or quantum annealer. In particular, the new algorithm can also be used for cone-beam CT image reconstruction and for medical imaging.

DOI
10.1038/s41598-023-41700-6

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Computed tomography (CT) has been developed as a nondestructive technique for observing minute internal images in samples. It has been difficult to obtain photorealistic (clean or clear) CT images due to various unwanted artifacts generated during the CT scanning process, along with the limitations of back-projection algorithms. Recently, an iterative optimization algorithm has been developed that uses an entire sinogram to reduce errors caused by artifacts. In this paper, we introduce a new quantum algorithm for reconstructing CT images. This algorithm can be used with any type of light source as long as the projection is defined. Assuming an experimental sinogram produced by a Radon transform, to find the CT image of this sinogram, we express the CT image as a combination of qubits. After acquiring the Radon transform of the undetermined CT image, we combine the actual sinogram and the optimized qubits. The global energy optimization value used here can determine the value of qubits through a gate model quantum computer or quantum annealer. In particular, the new algorithm can also be used for cone-beam CT image reconstruction and for medical imaging.
Computed tomography (CT) is a non-destructive technique for observing internal images and has proven highly valuable in medical diagnostics. Recent advances in quantum computing have begun to influence tomographic reconstruction techniques. The quantum tomographic reconstruction algorithm is less affected by artifacts or noise than classical algorithms by using the square function of the difference between pixels obtained by projecting CT images in quantum superposition states and pixels obtained from experimental data. In particular, by using quantum linear systems, a fast quadratic unconstrained binary optimization (QUBO) model formulation for quantum tomographic reconstruction is possible. In this paper, we formulate the QUBO model for quantum compressed sensing tomographic reconstruction, which is a linear combination of the QUBO model for quantum tomographic reconstruction and the QUBO model for total variation in quantum superposition-state CT images. In our experiments, we used sinograms obtained by using the Radon transform of Shepp-Logan images and body CT images. We evaluate the performance of the new algorithm by reconstructing CT images using a hybrid solver with the QUBO model computed from each sinogram. The new algorithm was able to obtain a solution within 5 projection images for 30 × 30 image samples and within 6 projection images for 60 × 60 image samples, reconstructing error-free CT images. We anticipate that quantum compressed sensing tomographic reconstruction algorithms could significantly reduce the total radiation dose when quantum computing performance advances.
Computed tomography (CT) is an important imaging technique used in medical analysis of the internal structure of the human body. Previously, image segmentation methods were required after acquiring reconstructed CT images to obtain segmented CT images which made it susceptible to errors from both reconstruction and segmentation algorithms. However, this paper introduces a new approach using an advanced quantum optimization algorithm called quadratic unconstrained binary optimization (QUBO) for CT image segmentation. This algorithm allows CT image reconstruction and segmentation to be performed simultaneously. This algorithm segments CT images by minimizing the difference between a sinogram in a superposition state with qubits, obtained using the mathematical projection including the Radon transform, and the experimentally acquired sinogram from X-ray images for various angles. Furthermore, we leveraged X-ray mass attenuation coefficients to reduce the number of logical qubits required for our quantum optimization algorithm, and we employed D-Wave's hybrid solver to solve the optimization problem. We compared the segmentation results of our algorithm with those of classical algorithms using X-ray images of actual tooth samples to validate the results of our algorithm. The comparison revealed that, after undergoing appropriate image post-processing, our algorithm's segmentation results matched those of classical algorithms that perform segmentation after reconstruction, except for some pixels at the boundary. We expect that the new quantum optimization CT algorithm will bring about great advancements in medical imaging.
The emergence of quantum annealers has catalyzed the development of quantum optimization algorithms across various fields. The formulation of a quadratic unconstrained binary optimization (QUBO) model for quantum linear systems suggests that quantum optimization algorithms can play an important role in science and engineering. Recently, a QUBO model was developed by applying a quantum linear system to computed tomography (CT) image reconstruction to clearly show the internal structure of the sample. To date, ultra-clear CT images have not been reconstructed using quantum optimization algorithms owing to limitations in logical qubits. However, the quantum CT image reconstruction algorithm using a quantum linear system provides confidence in the accuracy of the CT image by leveraging the difference between the global and theoretical minimum energies. In this paper, we propose an algorithm that can use two or more QUBO models for CT image reconstruction. The proposed algorithm formulates several QUBO models from CT image reconstruction and verifies them using the hybrid solver of the D-Wave system. The proposed algorithm suggests that quantum-optimized CT algorithms can make greater progress in the future.
We propose a quantum-assisted reconstruction framework for high-resolution tomographic imaging that reduces qubit/variable requirements by combining sinogram downsampling and region-wise iterative refinement. Previous quantum optimization–based CT reconstruction methods require solving QUBO (Quadratic Unconstrained Binary Optimization) problems over full-resolution image grids, which limits scalability under current hardware constraints. Our method addresses this by combining sinogram downscaling with region-wise iterative refinement, allowing reconstruction to begin from a reduced-resolution sinogram and image, and then to be progressively upscaled and optimized region by region. Each region is independently transformed into a compact QUBO problem and solved via a D-Wave hybrid quantum-classical solver while keeping the surrounding image fixed. The framework supports both full-view and sparse-view sinograms and is compatible with diverse acquisition geometries, including parallel-beam, fan-beam, cone-beam, synchrotron tomography, and electron tomography (ET). Adaptive region selection (including overlapping or boundary-covering subregions) enables targeted refinement of residual-error under a limited qubit/variable budget. Experimental validation on binary and integer-valued Shepp-Logan phantoms, together with an additional chest CT slice experiment, demonstrates accurate reconstructions under both dense-view and sparse-view angular sampling using reduced qubit/variable budgets. We observed that nearest-neighbor interpolation may cause edge artifacts that hinder convergence, which can be mitigated by smoother interpolation and Gaussian filtering. Sparse-view experiments indicate that the refinement pipeline can remain effective under angular undersampling in our discrete setting, suggesting potential relevance to low-dose imaging scenarios, while a dose–quality trade-off analysis is left for future work. These findings highlight the practicality of QUBO-based, quantum-assisted refinement for high-resolution tomographic reconstruction under current hardware constraints and provide a pathway for scaling as hybrid quantum optimization capabilities evolve.
Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of quantum supremacy, which signifies the ability of quantum processors to surpass classical systems in specific tasks. In the context of tomographic image reconstruction, quantum optimization algorithms enable faster processing and clearer imaging than conventional methods. This study further substantiates quantum supremacy by reducing the required projection angles for tomographic reconstruction while enhancing robustness against image artifacts. Notably, our experiments demonstrated that the proposed algorithm accurately reconstructed tomographic images without artifacts, even when up to 50% error was introduced into the sinogram to induce ring artifacts. Furthermore, it achieved precise reconstructions using only 50% of the projection angles from the original sinogram spanning 0° to 180°. These findings highlight the potential of quantum algorithms to revolutionize tomographic imaging by enabling efficient and accurate reconstructions under challenging conditions, paving the way for broader applications in medical imaging, material science, and advanced tomography systems as quantum computing technologies continue to advance.
Computed tomography (CT) is an important diagnostic technique used to analyze the inner structure of the human body. Various reconstruction methods of CT images have been proposed and utilized for a long time. The existing optimization methods for CT reconstruction images, however, usually suffer from substantial computational complexities. To circumvent this difficulty, a quadratic unconstrained binary optimization (QUBO) model for fast and accurate reconstruction of CT images was recently developed. In this paper, we apply the QUBO model to the 15-by-15 sized Shepp-Logan phantom image sample of the largest computable image in the D-Wave Advantage System. Herein, we reconstructed the CT image of the QUBO model in the D-Wave system using a QPU solver and a hybrid solver. Here are our results.