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A Review Paper: Noise Models in Digital Image Processing
Ajay Kumar Boyat, Brijendra Kumar Joshi
TL;DR
Noise enters digital images during acquisition, coding, transmission, and processing, and denoising is difficult without prior knowledge of its model. This paper reviews noise models using statistical concepts and their origins, covering common model types and their quantitative descriptions. It concludes that noise models can be identified by origin and designed through probability density functions using mean, variance, and gray levels.
Problem
Noise disturbs image information, and effective denoising requires prior knowledge of the associated noise model.
Method
The paper reviews digital-image noise models through statistical noise theory and analysis of their origins.
Results
The review presents various digital-image noise models and describes their identification by origin and probability density functions using mean, variance, and gray levels.
Takeaways & Limitations
The review is intended as reference material for researchers and beginners studying image processing and denoising.
Abstract
from arXiv · showhide
Noise is always presents in digital images during image acquisition, coding, transmission, and processing steps. Noise is very difficult to remove it from the digital images without the prior knowledge of noise model. That is why, review of noise models are essential in the study of image denoising techniques. In this paper, we express a brief overview of various noise models. These noise models can be selected by analysis of their origin. In this way, we present a complete and quantitative analysis of noise models available in digital images.
1. INTRODUCTION
The introduction frames noise as a pervasive source of image distortion and identifies noise-model knowledge as necessary for denoising. The paper reviews noise models using their statistical properties and origins.
- Noise can arise during image acquisition, coding, transmission, and processing, disturbing original signal information.
- The resulting research questions concern corruption magnitude, signal reconstruction, and identifying the noise model associated with a noisy image.
- The paper presents a review intended to reinforce theoretical and practical understanding of noises in digital images.
- The review covers fundamental digital-image noise types including Gaussian, Poisson, Speckle, and Salt and Pepper noise.
- Noise sources include environmental conditions, faulty memory locations, and imperfections in image-capture devices.
2. NOISE MODELS
The paper introduces noise as unwanted image information and surveys models characterized by physical origins, probability distributions, and image statistics. Gaussian noise is described through its PDF and gray-value behavior, while white noise is distinguished from Gaussianity.
- Digital noise produces artifacts, unrealistic edges, unseen lines, corners, blurred objects, and disturbed background scenes.
- Gaussian Noise Model: Gaussian noise is electronic noise associated with amplifiers or detectors and can also arise from thermal vibration and radiation.
- Gaussian Noise Model: Gaussian noise disturbs gray values and is characterized using a probability density function or normalized histogram.
- Gaussian Noise Model: The Gaussian model described uses mean zero, variance 0.1, and 256 gray levels.
- Gaussian Noise Model: The normalized Gaussian curve is bell-shaped, with 70% to 90% of noisy pixel values lying between µ − σ and µ + σ.
- Gaussian noise and white noise are distinct properties: white noise has constant noise power spectrum and zero autocorrelation.
2.3 Brownian Noise (Fractal Noise)
This section describes colored and impulse-valued noise through their physical or statistical origins and their effects on image pixels. Brownian noise follows a fractal, nonstationary process, whereas salt-and-pepper noise replaces selected pixels with extreme values.
- Brownian Noise (Fractal Noise): Brownian noise, also called pink, flicker, or 1/f noise, is caused by random Brownian motion of suspended particles in fluid.
- Brownian Noise (Fractal Noise): Fractional Brownian noise follows a nonstationary stochastic process with a normal distribution and is also called fractal noise.
- Brownian Noise (Fractal Noise): Fractional Brownian motion is represented mathematically as a zero-mean Gaussian process, with its expected value specified in the associated equations.
- Impulse Valued Noise (Salt and Pepper Noise): Salt-and-pepper noise, also called data-drop noise, changes some image pixels while leaving neighboring pixels potentially unchanged.
- Impulse Valued Noise (Salt and Pepper Noise): During transmission, corrupted pixels may be replaced by minimum or maximum values, 0 or 255 for 8-bit images.
- Impulse Valued Noise (Salt and Pepper Noise): Salt-and-pepper noise can insert dark pixels in bright regions and bright pixels in dark regions, arising from sensor, memory, digitization, or bit-transmission errors.
2.5 Periodic Noise
Periodic noise is associated with electronic interference during image acquisition and has spatially dependent, sinusoidal structure at specific frequency multiples. Its frequency-domain appearance supports narrow-band rejection filtering.
- Periodic noise is generated by electronic interference, especially in power signals during image acquisition.
- The noise is spatially dependent and sinusoidal at multiples of a specific frequency, appearing as conjugate spots in the frequency domain.
- A narrow-band reject filter or notch filter can conveniently remove periodic noise.
2.6 Quantization noise
Quantization noise arises when analog data are converted into digital amplitudes and follows a uniform distribution. Its SNR depends on pixel-value limits and noise standard deviation, with a full-amplitude sine-wave relation based on bit depth.
- Quantization noise is inherent in amplitude quantization during analog-to-digital conversion.
- Its SNR is limited by the minimum and maximum pixel values, Pmin and Pmax.
- For a full-amplitude sine wave, SNR = 6n + 1.76 dB, where n is the number of bits.
- Quantization noise follows a uniform distribution, so it is also called uniform noise.
- The paper illustrates uniform noise with the PDF shown in Figure 5.
2.8 Photon Noise (Poisson Noise)
Photon noise results from random fluctuations in photon counts in electromagnetic imaging, including x-ray and gamma-ray systems, and obeys the Poisson distribution. The reviewed model also describes Poisson-Gaussian noise for MRI images using combined Poisson and Gaussian components.
- Photon noise arises from random fluctuations in photons emitted by x-ray, visible-light, and gamma-ray sources.
- The reviewed Poisson-Gaussian model addresses noise removal in Magnetic Resonance Imaging (MRI).
- Poisson-Gaussian noise combines Poisson-distribution and Gaussian-distribution components.
- The model forms a noisy image by adding Poisson and Gaussian noise components to the underlying image.
2.10 Structured Noise
Structured noise has periodic or aperiodic behavior and may be stationary or non-stationary; it is associated with interference among electronic components. In measurement space, the resulting noise is modeled as low-rank and dependent on the physical system.
- Structured noise can be periodic, stationary, non-stationary, or aperiodic.
- Stationary structured noise has fixed amplitude, frequency, and phase.
- Interference among electronic components can cause structured noise.
- Communication-channel noise is divided into unstructured noise and structured noise, with structured noise also called low-rank noise.
- In measurement space, the resulting noise has low rank and structure dependent on the physical system.
- The structured-noise model represents a received image using a linear-system transfer function, subspace, rank, process, and signal parameters.
2.12 Rayleigh noise
Rayleigh noise is presented as a noise model occurring in radar range images. The paper identifies its probability density function but does not provide its explicit form in the supplied passages.
- Rayleigh noise occurs in radar range images.
- The paper presents Rayleigh noise through its probability density function and Figure 12.
- Figure 13 is labeled Rayleigh Noise [26].
3. CONCLUSIONS
The paper emphasizes that noise-model knowledge is important for image denoising and reviews models identifiable by their origin and statistical properties.
- Noise-model knowledge is important because denoising actions cannot be properly performed without prior knowledge of the noise model.
- The review presents various noise models found in digital images and identifies them through their origins.
- Noise models are also designed using probability density functions based on mean, variance, and gray levels.
AUTHORS
The authors are affiliated with the Electronics & Telecommunication and Computer Engineering Department at MCTE in India and work across image and signal processing fields.
- Ajay Boyat is a research scholar at MCTE and is pursuing a Ph.D. in Electronics and Telecommunication Engineering at Devi Ahiliya University, Indore.
- The authors' stated research interests include image processing, signal processing, digital communications, and wireless networks.
- Brijendra Kumar Joshi is a professor at MCTE with doctoral training in Electronics and Telecommunication Engineering.