CRT Image Filter

Decompose pixel values into 5 CRT channels. Filter independently. Reconstruct. L=11 denoises for free. CC0.

How It Works

Every pixel value (0-255) maps to a ring element mod 256.
But 256 = 2^8 has only ONE prime factor. Boring.

CRT TRICK: map pixel value v to residues in Z/N where N is CRT-friendly:
  v -> (v mod 8, v mod 9, v mod 25, v mod 49, v mod 11)

Now each pixel lives in 5 INDEPENDENT channels.
Filter each channel separately — no cross-channel artifacts.
CRT-reconstruct to get filtered pixel.

DENOISING: L=11 channel = integrity check.
  Corrupt a pixel? L=11 residue breaks. Detect AND correct.
  This is error-correcting image filtering — for FREE.

BLOCK-DIAGONAL: each channel's convolution is independent.
  5 tiny convolutions instead of 1 big one.
  No cross-channel bleed. The ring structure IS the filter bank.

1. Generate Test Image

Size: 64x64 pixels. Each pixel = ring element mod 970200.

Original

2. CRT Decomposition

Each pixel decomposed into 5 independent channel views.

Z/8 (D)

Z/9 (K)

Z/25 (E)

Z/49 (b)

Z/11 (L)

3. Per-Channel Filtering

Apply filters to individual CRT channels — no cross-channel bleed.

Filter: Channel:

Filtered (CRT)

Filtered (direct)

4. L=11 Denoising

Add noise. L=11 detects corrupted pixels. CRT corrects them.

Noise %: 10%

Noisy

L=11 Denoised

Corrupted

Detected

Corrected