Quantum Compressed Sensing CT Reconstruction Algorithm Based on Penalized Weighted Least Squares and Guided Total Variation

Sparse-view computed tomography (CT) is an ill-posed inverse problem where limited projection data leads to significant noise and artifacts. While quantum annealing has been proposed as a tool for solving the resulting combinatorial optimization problems, existing frameworks often ignore the statistical nature of photon-counting noise and the anatomical heterogeneity of the scanned objects, leading to suboptimal reconstruction quality.

The authors introduce a quantum compressed-sensing framework that incorporates two key improvements into the QUBO model:

1. Penalized Weighted Least Squares (PWLS): Instead of assuming uniform noise, this term weights projection residuals based on photon-count reliability, effectively down-weighting low-signal, high-noise measurements.
2. Guided Total Variation (GTV): Unlike standard total variation, which applies uniform smoothing, GTV uses gradients from a prior image (reconstructed via SART) to adaptively adjust regularization strength. This preserves structural edges while suppressing noise in homogeneous regions.

These terms are combined into a single quadratic objective function, which is then binary-encoded and solved using a D-Wave hybrid quantum-classical solver.

In experiments using 40x40 pixel CT images under sparse-view (10-view) and Poisson-noisy conditions, the PWLS-GTV framework consistently outperformed conventional reconstruction methods (FBP, SART, SIRT, EM) and other QUBO variants. Specifically, the proposed method achieved a peak signal-to-noise ratio (PSNR) of 36.64 dB in a chest CT case, compared to 22.48 dB for the best conventional baseline. The study also demonstrated that continuous gradient-based optimization fails in this highly quantized, sparse-view setting, highlighting the necessity of the discrete QUBO approach.