---
id: wiki-2026-0508-noise
title: Noise
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Noise, 노이즈, Random-Noise]
duplicate_of: none
source_trust_level: A
confidence_score: 0.92
verification_status: applied
tags: [noise, signals, data-quality, information-theory, statistics]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: python
  framework: numpy
---

# Noise

## 매 한 줄
> **"매 signal은 noise와 함께 살아간다"**. Noise는 measurement·channel·process에 섞이는 unwanted variation으로, 매 statistical structure (Gaussian, Poisson, 1/f 등)을 가진다. 2026 ML 시대에서도 매 denoising diffusion model의 핵심 도구로 부활.

## 매 핵심

### 매 분류 (by spectrum)
- **White noise**: flat power spectrum, 매 사실상 i.i.d.
- **Pink (1/f) noise**: 매 자연계 보편 — neural firing, music, finance.
- **Brownian (1/f²)**: 매 random walk integral.
- **Shot noise (Poisson)**: 매 photon counting, low-light imaging.
- **Quantization noise**: ADC bit depth 한계.

### 매 noise model
- Additive: y = x + n (대부분 가정).
- Multiplicative: y = x · n (speckle, fading).
- Convolutive: 매 reverberation.

### 매 응용
1. Denoising diffusion (Stable Diffusion 3, FLUX) — noise를 학습 시그널로 사용.
2. Differential privacy — Laplace/Gaussian noise 추가.
3. Stochastic optimization — SGD의 noise가 generalization 도움.

## 💻 패턴

### Gaussian noise 추가
```python
import numpy as np
def add_gaussian(x, sigma=0.1):
    return x + np.random.normal(0, sigma, x.shape)
```

### Pink noise 생성 (Voss-McCartney)
```python
def pink_noise(n, num_sources=16):
    array = np.zeros((num_sources, n))
    for i in range(num_sources):
        step = 2 ** i
        array[i, ::step] = np.random.randn((n + step - 1) // step)
    return array.sum(axis=0)
```

### SNR 계산
```python
def snr_db(signal, noise):
    return 10 * np.log10(np.var(signal) / np.var(noise))
```

### Wiener filter (optimal linear denoise)
```python
from scipy.signal import wiener
denoised = wiener(noisy, mysize=5)
```

### DP-noise (differential privacy)
```python
def laplace_dp(value, sensitivity, epsilon):
    return value + np.random.laplace(0, sensitivity / epsilon)
```

### Diffusion forward process
```python
def forward_diffuse(x0, t, betas):
    alpha_bar = np.cumprod(1 - betas)[t]
    eps = np.random.randn(*x0.shape)
    return np.sqrt(alpha_bar) * x0 + np.sqrt(1 - alpha_bar) * eps, eps
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Sensor 측정 | Gaussian assumption + Kalman |
| Photon-limited | Poisson MLE |
| Privacy preserve | Laplace/Gaussian DP |
| Generative model | Diffusion (DDPM/EDM) |

**기본값**: Additive Gaussian (most analyzable).

## 🔗 Graph
- 부모: [[Entropy in Information Theory|Information Theory]] · [[Statistics]]
- 응용: [[Kalman-Filter-and-State-Tracking]] · [[Differential-Privacy]]

## 🤖 LLM 활용
**언제**: Data augmentation, robustness training, generative modeling, privacy.
**언제 X**: Deterministic exact computation 필요 시.

## ❌ 안티패턴
- **Noise blindness**: noise model 가정 없이 deterministic 처리.
- **SNR 무시**: low-SNR 데이터로 high-precision claim.
- **Whiteness 가정**: 매 실제는 colored noise인데 white로 모델링.

## 🧪 검증 / 중복
- Verified (Papoulis "Probability, Random Variables, and Stochastic Processes").
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — Noise taxonomy + DP/diffusion patterns |
