Overview
This research presents a framework for grayscale computed tomography (CT) reconstruction utilizing Quadratic Unconstrained Binary Optimization (QUBO) within a quantum computing context. The framework integrates dynamic interval encoding with prior-balanced optimization to address limitations associated with binary-variable budgets in existing QUBO-based CT reconstruction methods. The approach aims to enhance the fidelity of reconstructed structures and gray-level distributions in CT images.
Research Context
Quantum computed tomography (CT) based on QUBO formulates image reconstruction as a binary quadratic problem compatible with quantum annealing and hybrid quantum-classical solvers. A recurring challenge in grayscale CT is the constraint imposed by the binary-variable budget for image encoding. Fixed global bit-plane encodings lead to an increase in QUBO size and coupling complexity as the desired gray-level precision improves. Conversely, the use of low-bit encodings introduces quantization errors, compromising image quality. This trade-off between QUBO complexity/size and grayscale precision necessitates alternative encoding strategies.
Approach
The proposed QUBO-based grayscale CT reconstruction framework incorporates two primary mechanisms: dynamic interval encoding and prior-balanced optimization. Each refinement round of the reconstruction process encodes active pixels exclusively within local gray-level intervals, which are defined around the current estimated values. An adaptive update rule, guided by boundary-hit information, facilitates switching between search expansion and local refinement phases.
To improve the stability of the optimization process, the method balances two components before constructing the final QUBO: projection-domain data consistency and an edge-preserving quadratic prior. This balancing act is intended to mitigate instability that can arise during optimization. The framework enables execution on hybrid quantum-classical backends, as demonstrated by experiments conducted on a D-Wave hybrid binary quadratic model (BQM) solver.
Findings
- The proposed method, integrating dynamic interval encoding and prior-balanced optimization, recovers structures and gray-level distributions more faithfully in sparse-view and limited-angle fan-beam CT experiments.
- This performance improvement was observed in comparison to evaluated analytic, iterative, variational, and representation-based baseline methods.
- Expressivity analysis and ablation studies indicate that the observed improvements primarily stem from the effective representation of gray levels facilitated by dynamic local encoding.
- Further contributing to the method's performance is a more stable coupling between data fidelity and the prior in the optimization process.
- Experiments confirm that the formulation is executable on a hardware-backed hybrid quantum-classical backend, specifically the D-Wave hybrid BQM solver.
Why This Matters
The development of QUBO-based CT reconstruction methods capable of faithfully representing gray-level information without excessive computational burden or quantization error is significant for medical imaging and other applications requiring high-fidelity volumetric reconstruction from projections. The ability to execute such formulations on hybrid quantum-classical hardware indicates progress towards practical applications of quantum computing in this domain.