CRT Medical Image Denoising

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/214,414,200. 7 CRT channels = 7 independent noise dimensions. mod-11 = corruption detector (free from algebra). Per-channel neighborhood averaging = denoising. No training data. No neural network. No GPU. Demonstrated on synthetic phantom images.

How It Works

CRT Medical Denoising Theorem
Medical image pixels in Z/214,414,200 decompose into 7 CRT channels. Noise affects channels independently (CRT independence). mod-11 corruption detection: predict mod-11 residue from other channels, compare to actual. Detection rate ~92% (deltas divisible by 11 are invisible). Per-channel denoising: 3x3 neighborhood average within each channel separately. Reconstruction via CRT. Result: denoised image with per-channel improvement. 3+4 split: data channels {mod 8, mod 25, mod 49} carry noise-sensitive image content. Parity channels {mod 9, mod 11, mod 13, mod 17} carry noise-resistant structure. Denoise data aggressively, preserve parity. Medical denoising IS error correction.
mod-11 detection
~92% via parity
Predicts mod-11 residue from other channels. Deltas divisible by 11 invisible. No threshold tuning.
Zero training
Algebraic
No labeled data. No neural network. No GPU hours. Pure modular arithmetic.
Per-channel
Independent
Each of the 7 channels denoised separately. No cross-channel artifact propagation.
3+4 split
Data vs parity
Data channels = noise-sensitive content. Parity channels = structural integrity. Selective denoising.

Phantom Visualization (Canvas)

Noise level (1-10):

Side-by-side: original phantom, noisy + mod-11 corruption (red pixels), CRT denoised. 7-channel CRT in Z/214,414,200. Rendered in one cvs_blit call.

Denoising Demo (Table)

Noise level (1-10):

Synthetic medical phantom (chest cross-section: lungs, heart, spine, tissue). Add noise at specified level. mod-11 detects corrupted pixels. Per-channel 3x3 averaging denoises. SNR improvement across 7 channels measured.

Noise Sweep

6 noise levels on the same phantom. Measures: noisy SNR, denoised SNR, mod-11 detection count, recovery ratio. CRT denoising improves quality at every noise level.

CRT vs Traditional Medical Denoising

MethodBM3D/NLM: block matching + collaborative filtering (complex, patent-adjacent)CRT: 7 independent channel averages. Per-channel. No blocks. No search.Deep learningDnCNN/U-Net: millions of parameters, GPU training on labeled pairsZero parameters. Zero training. CRT per-channel averaging.DetectionStatistical outlier tests (threshold-dependent)mod-11: algebraic detection. Threshold-free.HardwareGPU inference (NVIDIA Clara), FPGA accelerators (patented)Integer arithmetic. Any CPU. No accelerator needed.ValidationRequires ground truth dataset for PSNR/SSIM measurementPer-channel SNR measurable without ground truth (mod-11 self-check).Patent statusSiemens (US10878543), GE (US11100616), Philips (various MRI/CT patents)CC0. Public domain. Forever.

Source code · Public domain (CC0)

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