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.
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.
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.
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.
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.
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical computers. Notably, the hybrid solver provided by the D-wave system can leverage up to two million variables. By exploiting this technology, quantum optimization models based on quadratic unconstrained binary optimization (QUBO) have been proposed for applications, such as linear systems, eigenvalue problems, RSA cryptosystems, and CT image reconstruction. The formulation of QUBO typically involves straightforward arithmetic operations, presenting significant potential for future advancements as quantum computers continue to evolve. A prevalent approach in these developments is the binarization of variables and their mapping to multiple qubits. These methods increase the required number of qubits as the range and precision of each variable increase. Determining the optimal value of a QUBO model becomes more challenging as the number of qubits increases. Furthermore, the accuracies of the existing Qiskit simulator, D-Wave system simulator, and hybrid solver are limited to two decimal places. Problems arise because the qubits yielding the optimal value for the QUBO model may not necessarily correspond to the solution of a given problem. To address these issues, we propose a new iterative algorithm. The novel algorithm sequentially progresses from the highest to the lowest exponent in binarizing each number, whereby each number is calculated using two variables, and the accuracy can be computed up to a maximum of 16 decimal places.
Quantum-optimization-based computed tomography (CT) reconstruction has demonstrated quantum supremacy in reconstruction accuracy over conventional classical methods under sparse-view and corrupted-sinogram conditions. However, scaling this approach remains challenging because larger images require increasingly many binary variables and interactions in the underlying quadratic unconstrained binary optimization (QUBO) model. Even with iterative region-of-interest (ROI) refinement, a 60 by 60 ROI with three X-ray mass attenuation coefficients requires 10,800 binary variables under our encoding. As an initial step toward larger quantum CT images, we investigate simulated annealing (SA) followed by spin-error mitigation for optimisation (SEMO), without altering the CT-QUBO objective. We evaluate three 54-view ROI reconstruction instances and nine-view reconstruction with detector-row corruption, comparing SA and SEMO with selected hybrid quantum-classical solver results. For the ROI cases, SEMO reduced the numbers of incorrectly reconstructed pixels in low-budget SA outputs from 13 to 1, 38 to 0, and 54 to 15. With 20 percent detector-row corruption, three of four selected SA and SEMO pairs achieved exact reconstruction. Applying SEMO to one hybrid-solver output reduced its ROI error from 78 to 1 pixel. Improvements were instance-dependent: in one corrupted-sinogram case, QUBO energy decreased while image-domain error increased slightly; in one ROI case, the refined image retained 15 incorrect pixels despite having lower QUBO energy than ground truth. At the evaluated problem sizes, SA and SEMO attained reconstruction accuracy comparable to or better than selected unmitigated hybrid-solver results, providing an initial solution-quality benchmark for future larger-scale, parallelized quantum CT image reconstruction.