Wang and Colleagues Proposes Dynamic Interval Encoding for Grayscale Quantum Computed Tomography

A new framework for grayscale computed tomography (CT) reconstruction, based on quadratic unconstrained binary optimisation (QUBO), has been presented by Ao Wang and colleagues at Peking University, in collaboration with Pattern Recognition Lab. The approach tackles limitations in existing image encoding techniques by using dynamic interval encoding, concentrating computational effort on active pixels within local gray-level intervals. This method balances data consistency with an edge-preserving prior, and it recovers structures and gray-level distributions more accurately than current analytic, iterative, and variational techniques. Importantly, the set of tools is executable on a hardware-backed hybrid quantum, classical backend such as the D-Wave BQM solver.

Dynamic interval encoding enhances computed tomography image reconstruction fidelity

A 3.2dB improvement in peak signal-to-noise ratio (PSNR) was observed with the new framework compared to existing analytic, iterative, variational, and representation-based baselines. Previously unattainable fidelity levels are now possible due to improved representation of grayscale information within a constrained binary-variable budget. The approach, utilising dynamic interval encoding and prior-balanced optimisation, overcomes challenges posed by fixed encoding methods that increase computational complexity, or low-bit encodings which introduce errors into the reconstructed images.

Experiments utilising sparse-view and limited-angle fan-beam CT demonstrate the method’s ability to recover structures and gray-level distributions more faithfully than current techniques. Expressivity analysis confirms this improvement stems from effective gray-level representation and stable data-fidelity-prior coupling. Further analysis revealed average SSIM scores of 0.89 and NRMSE values of 0.06 across four representative images, including clinical datasets from the American Association of Physicists in Medicine (AAPM). This enhanced fidelity stems from a novel dynamic interval encoding method, which focuses computational effort on active pixels within local gray-level ranges, coupled with a balanced optimisation strategy prioritising both data consistency and edge preservation. Experiments utilising a D-Wave hybrid binary quadratic model (BQM) solver confirmed the framework’s executability on quantum-classical hardware; however, the current proof-of-concept evaluations limited the scope to 32×32 images, and substantial work remains to scale the method to clinically relevant image sizes and assess its performance with realistic noise levels.

Traditional CT reconstruction methods often rely on iterative algorithms or analytic techniques which can be computationally expensive, particularly when dealing with limited or incomplete projection data. These methods can also struggle to accurately represent subtle grayscale variations, leading to blurred images or inaccurate diagnoses. The QUBO-based approach offers a fundamentally different paradigm by formulating the reconstruction problem as a binary quadratic optimisation problem, suitable for solution using quantum annealing or hybrid quantum-classical algorithms. The core challenge lies in efficiently encoding the grayscale image data into a binary representation that can be processed by the quantum solver. Fixed global bit-plane encodings, while straightforward, rapidly increase the size and complexity of the QUBO problem as the desired gray-level precision increases. This is because each additional bit-plane requires a corresponding increase in the number of binary variables and coupling terms within the QUBO formulation. Conversely, low-bit encodings, although reducing computational burden, introduce significant quantization errors, resulting in a loss of image detail and accuracy. Dynamic interval encoding addresses this trade-off by adaptively adjusting the encoding resolution based on the local gray-level characteristics of the image. Pixels within uniform regions represent data with fewer bits, while pixels exhibiting rapid gray-level changes assign a higher resolution, thereby concentrating computational resources where they are most needed.

The data consistency term in the QUBO formulation ensures that the reconstructed image is consistent with the measured projection data. This is typically achieved by minimising the difference between the forward projection of the reconstructed image and the original measurements. The edge-preserving prior, on the other hand, encourages the reconstructed image to have smooth transitions between adjacent pixels, thereby reducing noise and enhancing image quality. Balancing these two competing objectives is crucial for achieving optimal reconstruction performance. The researchers employed a carefully tuned weighting scheme to ensure that both data consistency and edge preservation contribute equally to the overall cost function. The SSIM scores of 0.89 and NRMSE values of 0.06 demonstrate the effectiveness of this balanced optimisation strategy, indicating a high degree of similarity between the reconstructed images and the ground truth, with minimal root mean squared error. The use of clinical datasets from the AAPM further validates the method’s potential for real-world applications.

Quantum reconstruction from limited data shows promise for improved medical scans

This work represents a valuable step forward in medical imaging technology, allowing for more efficient use of quantum resources and potentially clearer images created from limited data. Reducing radiation exposure for patients and lowering scan times are important benefits of this advancement. The team at Peking University and collaborators have created a new computed tomography (CT) image reconstruction framework utilising principles from quantum computing, specifically quadratic unconstrained binary optimisation, or QUBO. While the method excels at reconstructing images from sparse or incomplete data, a comprehensive performance comparison against all possible reconstruction techniques remains to be completed.

The current proof-of-concept evaluations limited the scope to 32×32 images, and substantial work remains to scale the method to clinically relevant image sizes and assess its performance with realistic noise levels. Dynamically adjusting how grayscale information is encoded overcomes limitations of earlier techniques that either demanded excessive computational power or introduced inaccuracies. The framework focuses computational effort on relevant areas of the scan rather than processing every pixel equally. By balancing data consistency with an edge-preserving technique, the framework demonstrably improves the fidelity of reconstructed images, particularly when scan data is limited or incomplete. Further research will focus on expanding the scope of comparisons to other reconstruction methods and refining the method for larger datasets and more complex noise models.

The potential benefits of this approach extend beyond improved image quality. By enabling accurate reconstruction from sparse-view or limited-angle CT scans, the method could significantly reduce patient radiation exposure.

This research successfully demonstrated a new method for reconstructing grayscale computed tomography images using quantum computing principles. By employing dynamic interval encoding and prior-balanced optimisation, the framework improves image fidelity, especially when reconstructing from limited or incomplete scan data. The technique focuses computational resources on active pixels, overcoming limitations of previous approaches that struggled with either accuracy or computational cost. The authors intend to expand comparisons to other reconstruction methods and refine the technique for larger datasets, suggesting ongoing development of this approach.