A Review of Nonlinear Image-Denoising
Techniques
Ayman M. Abdalla, Mohammed S. Osman, Hanadi AlShawabkah, Osaid Rumman, Mutaz Mherat
Faculty of Science and Information Technology
Al-Zaytoonah University of Jordan
Amman, Jordan
ayman@zuj.edu.jo, m.s.e@msn.com, hanade83@yahoo.com, osaidrumman@gmail.com, mherat93@gmail.com
Abstract—This paper discusses different nonlinear
techniques for removing noise from images; i.e., image
denoising. These techniques differ in terms of algorithm
design, purpose, effectiveness, and efficiency. In this paper,
different denoising techniques are described briefly where
their advantages and disadvantages are discussed. The
performances of these techniques are analyzed and compared
according to different implementations using statistical
methods. Finally, the paper infers when each denoising method
is most effective what type of noise each method can handle
effectively.
Keywords—Denoising filter, Bilateral filter, Anisotropic
diffusion, Nonlocal means filter, Median filter, Block-matching
3D transform
I. I
NTRODUCTION
Image enhancement is one of the most important and
challenging fields in digital image processing. Image
enhancement techniques, also known as image enhancement
filter, include eliminating noise, adjusting colors, and
adjusting light intensity.
There are two main purposes for image enhancement
filters. The first is filter smoothing, which usually focuses on
noise reduction. The other purpose is sharpening the image,
by improving its fine details such as lines and edges. These
two purposes often contradict one another. For example,
smoothing an image may have a blurring effect and could
remove fine details. Therefore, a tradeoff between smoothing
and sharpening must be realized.
Image noise is an unwanted variation of brightness or
color information in an image that degrades its quality. The
noise affecting an image may take a random or a nonrandom
pattern, depending on the source of that noise. For example,
Gaussian noise is usually caused by variations of
illumination and temperature during image acquisition, and it
is characterized by a probability density function. Variations
of this type of noise include white Gaussian and thermal
noise. If the noise follows a Rice probability distribution, it is
called Rician noise. Illumination problems may also create
fog noise, which appears as a white blur shadowing the
image. Salt and pepper noise appears as dark and bright
spots, and it is often caused by image conversion errors.
When noise is significantly related to image orientation, such
as row noise or column noise, it is called an anisotropic
noise. Speckle or granular noise appears in images acquired
using radar, ultrasound, or optical coherence tomography
devices due to the effect that different objects have on the
image acquisition process.
As there are many types of noise affecting images, there
are many techniques used to enhance the quality of these
images and remove the noise. To remove the noise, the
denoising processes should use one or more techniques,
usually known as denoising filters. This paper discusses and
compares different nonlinear filters that reduce noise without
removing important details from the image such as edges and
lines.
A Bilateral Filter (BF) is a nonlinear and non-iterative
filter that considers neighboring pixels’ geometric closeness
and gray level similarities to determine the modified value of
the pixel in its neighborhood.
An Anisotropic Diffusion (AD) filter, also known as
Perona–Malik diffusion, is a technique that attempts to
remove noise by smoothing or blurring the image without
degrading significant contents. Similarly, a Median Filter
(MF) attempts to preserve significant contents while
removing the noise.
A Non-Local Means (NLM) filter is a denoising image-
processing algorithm that uses weighted averages computed
using all pixel values in the image.
A Wiener filter is an adaptive filter that involves linear
estimation of a non-noisy signal sequence using a noisy one.
It is successful in removing additive noise when the noise
consists of stationary linear random processes with known
spectral characteristics, and less effective in general cases
[1]. It is a linear filter, but it may be enhanced with a
nonlinear extension or combined with nonlinear filters.
A Block-Matching Three-Dimensional (BM3D) filter
groups image fragments of the same size based on similarity.
The BM3D algorithm was extended to perform decoupled
deblurring and denoising.
In the next section, each of the above filters is described
briefly with its advantages and disadvantages, and the
differences among the filters are highlighted. Then, different
variations and implementations of the filters are evaluated
using measures that include Peak Signal-to-Noise Ratio
(PSNR) and Structural Similarity Index (SSIM).
The MSE for two images, stored in matrices A and B, is
computed as in (1):
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==
−
=
m
i
n
j
jiBjiA
mn
MSE
11
2
)(
],[],[
1
. (1)
The Root MSE and Normalized Root MSE are commonly
used variations of MSE. In addition, PSNR is a meaningful
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