📂Machine Learning

Difference between Noise and Artifacts in Images (Signals, Data)

Overview

Noise and artifacts are common factors that degrade the original signal (data) and need to be removed. This document explains the characteristics of these two elements and how they differ from each other.

Definition

In an image, noise refers to any values that degrade the original image, typically caused by random, unpredictable, and unremovable factors.

On the other hand, the degradation caused by removable, regular, or predictable factors is called an artifact.

Description

Both noise and artifacts are factors that degrade the original image and need to be removed. They differ in several ways; noise is a ‘value’, whereas an artifact refers to the ‘phenomenon’ of the image being degraded itself. Mathematically, noise can be considered a vector $\mathbf{n} \in \mathbb{R}^{n}$, and while not always the case, an artifact might be regarded as an operator (function) $A : \mathbb{R}^{n} \to \mathbb{R}^{n}$.

In summary, the characteristics of noise and artifacts are as follows.

Noise	Artifact
Random	Regular
Not predictable	Predictable
Cannot remove cause	Can remove cause
Localized	Spreads over a wide area

Types

• Noise
  • Salt-and-pepper noise
• Artifacts
  • Blur

Removal Techniques

• Noise
  • Total Variation
• Artifacts
  • Deconvolution

Noise

Noise typically occurs randomly and is the result of unremovable causes. For example, when taking a photo with a digital camera, the heat of the sensor detecting light can affect the measured values. In such cases, it is impossible to remove the fundamental cause of noise, making it unpredictable and random. Therefore, noise is often modeled as a random variable and assumed to follow a normal distribution. Let $\mathbf{x}$ be the original image and $\mathbf{n} \sim N_{n}(\mathbf{0},\Sigma)$ be the noise. Mathematically, the noisy image $\mathbf{y}$ can be expressed as follows.

$$\mathbf{y} = \mathbf{x} + \mathbf{n} \qquad(\mathbf{x}, \mathbf{y}, \mathbf{n} \in \mathbb{R}^{n})$$

Since vector addition is defined as the sum of individual components, the degradation of the image by noise occurs on a pixel-by-pixel basis, and assuming the components of noise are independent, the image degradation can be considered local.

Removing noise from an image (signal) is referred to as denoising. Ideally, one could compute $\mathbf{y} - \mathbf{n} = \mathbf{x}$ to obtain the original image, but since $\mathbf{n}$ is unknown, this is not feasible. Denoising, therefore, is about estimating two unknowns $\mathbf{x}$ and $\mathbf{n}$ from a single value $\mathbf{y}$.

Below is an example of an original image mixed with Gaussian noise.

Artifacts

Artifacts are typically regular, appear over a comparatively wide area, and are often caused by removable factors. For example, when taking a CT scan of teeth, the presence of metal in the teeth can cause significant degradation in the CT image. This kind of degradation is called an artifact. The left photo below shows a CT image without artifacts, while the right photo shows a CT image with artifacts caused by an overlay of amalgam on teeth.

Blurriness caused by hand tremor is also considered an artifact. This is commonly mathematically expressed using convolution. Let $\mathbf{x}$ be the original image and $\mathbf{k}$ be an arbitrary kernel. A blurry image can then be expressed as follows.

$$\mathbf{y} = \mathbf{k} \ast \mathbf{x}$$

The process of restoring a sharp image from a blurry one is called the deconvolution problem. Below is an example of an original image and an image with Gaussian blur applied.

Lines such as horizontal or vertical ones appearing in an image are also called artifacts. (Left: original image, Right: image with artifacts)

Motion artifacts are another form of image degradation in medical imaging such as CT or MRI, caused when a patient moves during an imaging session.¹