Image Denoising in MATLAB: Applying Gaussian Filtering and Bilateral Filtering

# 1. Overview of Image Denoising in MATLAB

Image denoising is a pivotal task in image processing, aimed at removing unwanted noise from images to enhance their quality. MATLAB offers a wealth of tools and algorithms for image denoising, and this article will focus on two commonly used methods: Gaussian filtering and bilateral filtering.

# 2. Theoretical Foundations of Image Denoising

### 2.1 Types and Characteristics of Image Noise

Image noise refers to unwanted signals superimposed on the image signal, which can degrade visual quality and hamper information extraction. Various types of noise are common, including:

- **Gaussian Noise:** Following a normal distribution, it is present in all channels of the image pixels and is typically caused by sensor thermal noise or electronic noise.
- **Salt-and-Pepper Noise:** Randomly distributed among the image pixels, pixel values are either at the maximum (white) or minimum (black), usually caused by data transmission errors or storage malfunctions.
- **Impulse Noise:** Randomly spread across image pixels, pixel values are abnormally high or low, often resulting from sensor defects or external interference.
- **Uniform Noise:** Uniformly distributed across the entire image, making it appear brighter or darker, usually due to uneven lighting or incorrect camera exposure.
- **Periodic Noise:** Distributed in a regular pattern within the image, often caused by external disturbances or camera vibrations.

### 2.2 Basic Principles of Image Denoising Algorithms

Image denoising algorithms aim to restore the original image from a noisy one, with the basic principle being:

- **Spatial Filtering:** Utilizing spatial neighborhood information of image pixels, noise is removed through weighted averaging or other operations.
- **Frequency Filtering:** Transforming the image into the frequency domain, filtering out noise components, then transforming back to the spatial domain.
- **Non-Local Means Filtering:** Using the similarity of pixels in the image, information from similar regions is used to restore noisy pixels.
- **Machine Learning:** Training deep learning models to use image features and noise distribution patterns for denoising.

Each algorithm has its advantages and disadvantages, and the choice of the appropriate algorithm depends on the type of image noise, image characteristics, and denoising requirements.

# 3. Practical Application of Gaussian Filtering

### 3.1 Principles and Implementation of Gaussian Filtering

Gaussian filtering is a linear smoothing filter based on the Gaussian function, with the