Integrating a Physical Prior into a Machine Learning Model for Quantum Noise Reduction in X-ray Imaging

Deep learning methods for X-ray image denoising are predominantly data-driven, they learn a statistical mapping between noisy observations and reference images without making use of the deterministic physical laws governing signal formation. We present Héméra, a machine learning model in which a strong physical prior, the differential attenuation relationship between two spectrally separated detection channels, enters both the training dataset (Beer-Lambert law [3], XCOM/NIST cross-sections [4]) and the composite loss function. The MLP network (7 inputs → 64 → 64 → 32 → 16 → 2 outputs), trained on 27 compounds spanning Zeff ∈ [5.4; 16] and d ∈ [1; 30] cm with realistic Poisson noise simulation [1], reduces the variance of the attenuation ratio R estimator by 98.0 % (σ: 0.01895 → 0.00038) and the median relative error by 79.9 % within the training domain, without increasing photon flux or relying on inter-pixel spatial correlation. The gain remains stable across the dose range (mean factor ×2.90 over N₀ ∈ [3,308; 16,543] photons/pixel), with the largest advantage at low flux. The results admit a Bayesian reading [13,14]. The physical prior contracts the posterior distribution of R by drawing on inter-channel Fisher information that the naive Poisson estimator ignores. Compared with PWLS (Penalized Weighted Least Squares) filtering, Héméra preserves local contrast where PWLS over-smooths. Strictly pixel-by-pixel processing (~14,000 FLOPs/pixel) allows real-time GPU execution on current hardware.