A BEMD-Based Quaternion Filtering Approach Sharp-to-Soft Kernel CT Image Conversion

Image denoising is a crucial task in image processing, focused on improving image quality by minimizing noise while maintaining essential structural elements. This study presents a hybrid denoising framework that combines several decomposition techniques, including empirical mode decomposition (EMD), variational mode decomposition (VMD), multichannel EMD (MEMD), and bidimensional EMD (BEMD), with curvelet transform thresholding. Each decomposition mode undergoes processing through both soft and hard thresholding, and the denoised modes are combined to rebuild the final image. Comprehensive evaluations of standard CT image datasets reconstructed with various kernels (B50, B46, B41, B36) reveal substantial enhancements in denoising efficacy. VMD consistently achieves the highest peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), signifying exceptional noise reduction and feature preservation. The study analyses the trade-offs between soft and hard thresholding: soft thresholding maintains intricate visual details, whilst harsh thresholding provides enhanced noise reduction. The suggested method surpasses traditional techniques in both reference and non-reference quality criteria, indicating its potential for broader application in medical imaging and future incorporation with adaptive thresholding algorithms.

Objective. Existing quadratic unconstrained binary optimization (QUBO)-based sparse-view computed tomography (CT) reconstruction neglects photon-counting statistics and anatomical heterogeneity. We address both limitations within the QUBO framework.Approach. We propose a quantum compressed-sensing CT method combining penalized weighted least squares (PWLS) and guided total variation (GTV). PWLS weights projection residuals by photon-count reliability, whereas GTV uses gradients from a prior image reconstructed by the simultaneous algebraic reconstruction technique (SART) to preserve edges and suppress noise in homogeneous regions. After binary encoding, both terms form a unified QUBO model. Experiments used four 40 times 40 CT images under a 10-view fan-beam geometry with Poisson noise. Comparisons included conventional reconstruction methods, QUBO variants, gradient descent, simulated annealing, and a D-Wave hybrid quantum-classical solver.Main results. PWLS-GTV achieved the best reconstruction quality across all cases. In the representative chest case, it reached a peak signal-to-noise ratio (PSNR) of 36.64 dB, compared with 22.48 dB for SART, the best conventional baseline. GTV consistently outperformed conventional total variation. Simulated annealing and the D-Wave hybrid solver produced similar reconstructions, whereas gradient descent was ineffective. Repeated hybrid-solver runs showed stable performance.Significance. The framework incorporates photon-statistical weighting and structure-guided regularization into QUBO-based CT reconstruction without changing its quadratic form, providing a proof of concept for quantum-assisted sparse-view CT reconstruction.

Quadratic unconstrained binary optimization (QUBO)-based quantum computed tomography (CT) casts reconstruction as a binary quadratic problem for quantum annealing and hybrid quantum--classical solvers. For grayscale CT, however, image encoding is constrained by the binary-variable budget: fixed global bit-plane encodings increase QUBO size and coupling complexity as gray-level precision improves, whereas low-bit encodings introduce quantization error. We propose a QUBO-based grayscale CT reconstruction framework that combines dynamic interval encoding with prior-balanced optimization. Each refinement round encodes active pixels only within local gray-level intervals around the current estimate, and a boundary-hit-guided update rule adaptively switches between search expansion and local refinement. To improve optimization stability, the method balances projection-domain data consistency and an edge-preserving quadratic prior before forming the final QUBO. Sparse-view and limited-angle fan-beam CT experiments show that the proposed method recovers structures and gray-level distributions more faithfully than the evaluated analytic, iterative, variational, and representation-based baselines. Expressivity analysis and ablation studies further indicate that the improvement mainly arises from effective gray-level representation through dynamic local encoding and more stable data-fidelity--prior coupling. Experiments on the D-Wave hybrid binary quadratic model (BQM) solver further demonstrate that the formulation is executable on a hardware-backed hybrid quantum--classical backend.