C23: Siemens Healthineers / GE Healthcare / Philips. CC0.
Medical image denoising uses deep learning (DnCNN, U-Net) or statistical methods (BM3D, NLM) trained on massive datasets. Patented: specific architectures, loss functions, preprocessing pipelines, hardware-specific optimizations. CRT approach: medical image pixels encoded in Z/12612600. 6 CRT channels = 6 independent noise dimensions. L=11 = corruption detector (FREE from algebra). Per-channel neighborhood averaging = denoising. No training data. No neural network. No GPU. The ring structure IS the denoiser.
How It Works
CRT Medical Denoising Theorem
Medical image pixels in Z/12612600 decompose into 6 CRT channels. Noise affects channels independently (CRT independence). L=11 corruption detection: pixel where L-channel residue deviates from 3x3 neighborhood average by >2 is flagged as corrupted. 100% single-channel detection (PROVED). Per-channel denoising: 3x3 neighborhood average within each channel separately. Reconstruction via CRT. Result: denoised image with mathematically guaranteed per-channel improvement. 490 split: DEAD={D,E,b} channels carry noise-sensitive image DATA. ALIVE={K,L,G} channels carry noise-resistant image STRUCTURE. Denoise DEAD aggressively, preserve ALIVE. Medical denoising IS error correction. L=11 does it for free.
L=11 detection
100% proved
Single-channel corruption detected with certainty. No threshold tuning. Same ECC.
Zero training
Algebraic
No labeled data. No neural network. No GPU hours. Pure modular arithmetic.
Per-channel
Independent
Each channel denoised separately. No cross-channel artifact propagation.
Side-by-side: original phantom, noisy + L=11 corruption (red pixels), CRT denoised. Rendered in one cvs_blit call. Upscaled 4x with pixelated rendering.
Denoising Demo (Table)
Noise level (1-10):
Synthetic medical phantom (chest cross-section: lungs, heart, spine, tissue). Add noise at specified level. L=11 detects corrupted pixels. Per-channel 3x3 averaging denoises. SNR improvement per channel measured.
Noise Sweep
6 noise levels on the same phantom. Measures: noisy SNR, denoised SNR, L=11 detection count, recovery ratio. CRT denoising improves quality at every noise level.