Image denoising
Encyclopedia
Image denoising refers to the recovery of a digital image that has been contaminated by additive white Gaussian noise
(AWGN).
or Poisson noise) have also been studied in the literature of image processing, the term “image denoising” is usually devoted to the problem associated with AWGN. Mathematically, if we use Y=X+W to denote the degradation process (X: clean image, Y: noisy image, W~N(0,σw2)), the image denoising algorithm
attempts to obtain the best estimate of X from Y. The optimization criterion can be mean squared error
(MSE)-based or perceptual quality driven (though image quality assessment itself is a difficult problem, especially in the absence of an original reference).
Nasser Nahi at USC
and computer vision
pioneers such as S. Zucker and Azriel Rosenfeld
. In 1980, J. S. Lee published an important paper titled "Digital image enhancement and noise filtering by use of local statistics". The invention of wavelet transforms in late 1980s has led to dramatic progress in image denoising in 1990s. The Bayesian
view towards image denoising was put forward by Simoncelli & Adelson in 1996 and since then, many wavelet-domain denoising techniques have been proposed. The simple yet elegant Gaussian scalar mixture (GSM) algorithm published by Portilla et al. in 2003 and the nonlocal mean (NLM) algorithm by Buades et al. in 2005 have renewed the interest into this classical inverse problem
. In the past three years, many more powerful denoising algorithms have appeared - among them the patch-based nonlocal schemes, such as BM3D, have shown outstanding performance and its theoretic interpretation has been given by an expectation-maximization (EM)-based inference on stochastic
factor graphs.
Additive white Gaussian noise
Additive white Gaussian noise is a channel model in which the only impairment to communication is a linear addition of wideband or white noise with a constant spectral density and a Gaussian distribution of amplitude. The model does not account for fading, frequency selectivity, interference,...
(AWGN).
Technical description
Although other types of noise (e.g., impulseBurst noise
Burst noise is a type of electronic noise that occurs in semiconductors. It is also called popcorn noise, impulse noise, bi-stable noise, or random telegraph signal noise....
or Poisson noise) have also been studied in the literature of image processing, the term “image denoising” is usually devoted to the problem associated with AWGN. Mathematically, if we use Y=X+W to denote the degradation process (X: clean image, Y: noisy image, W~N(0,σw2)), the image denoising algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
attempts to obtain the best estimate of X from Y. The optimization criterion can be mean squared error
Mean squared error
In statistics, the mean squared error of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or...
(MSE)-based or perceptual quality driven (though image quality assessment itself is a difficult problem, especially in the absence of an original reference).
History
In the 1970s, image denoising was studied by control theoristControl theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
Nasser Nahi at USC
University of Southern California
The University of Southern California is a private, not-for-profit, nonsectarian, research university located in Los Angeles, California, United States. USC was founded in 1880, making it California's oldest private research university...
and computer vision
Computer vision
Computer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...
pioneers such as S. Zucker and Azriel Rosenfeld
Azriel Rosenfeld
Professor Dr. Azriel Rosenfeld was an American Research Professor, a Distinguished University Professor, and Director of the Center for Automation Research at the University of Maryland in College Park, Maryland, where he also held affiliate professorships in the Departments of Computer Science,...
. In 1980, J. S. Lee published an important paper titled "Digital image enhancement and noise filtering by use of local statistics". The invention of wavelet transforms in late 1980s has led to dramatic progress in image denoising in 1990s. The Bayesian
Thomas Bayes
Thomas Bayes was an English mathematician and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes' theorem...
view towards image denoising was put forward by Simoncelli & Adelson in 1996 and since then, many wavelet-domain denoising techniques have been proposed. The simple yet elegant Gaussian scalar mixture (GSM) algorithm published by Portilla et al. in 2003 and the nonlocal mean (NLM) algorithm by Buades et al. in 2005 have renewed the interest into this classical inverse problem
Inverse problem
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in...
. In the past three years, many more powerful denoising algorithms have appeared - among them the patch-based nonlocal schemes, such as BM3D, have shown outstanding performance and its theoretic interpretation has been given by an expectation-maximization (EM)-based inference on stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
factor graphs.