Shevchuk V.V., Garmash V.V.
Vinnitsia national technical
university, Ukraine
Color image denoising
using “channel method”
In
real-world scenarios, noise in color images comes from many sources, such as
the underlying physics of the imaging sensor itself, sensor malfunction, flaws
in the data transmission procedure, and electronic interference. Due to the
complex nature of the noise process, the overall acquisition noise is usually
modeled as a zero mean white Gaussian noise. Aside from this, image imperfections
resulting from salt and pepper noise are generated during transmission through
a communication channel with sources ranging from human-made to natural. Thus,
noise corruption process in simulated scenarios is usually modeled using
additive Gaussian noise, salt and pepper noise, or mixed noise.
Real
images are corrupted by real, non-approximated noise which may be different in
characteristics and statistical properties depending on application. One may
argue that color images are no difference from three monochromatic images once
we consider the three channels separately and therefore to denoise a color
photo one only needs to denoise the three monochromatic channels separately.
This view, however, misses some important subtle characteristics in naturally
captured color images that, when fully utilized, yield superior results. To
denoise color photos we must understand the nature of the noise in these
images, and take full advantages of all available information.
A color
model is an abstract mathematical model describing the way colors can be
represented as tuples of numbers, typically as three or four values or color
components. The three most popular color models are RGB, Lab (used in computer
graphics); YIQ, YUV or YCrCb (used in video systems) and CMYK (used in color
printing).
All of
the color spaces are derived from the RGB information captured by devices such
as cameras and scanners.
The
red, green, and blue (RGB) color space is widely used throughout computer
graphics. Red, green, and blue are three primary additive colors and are
represented by a 3D coordinate system. The RGB data captured by digital cameras
and scanners is the raw data and has the most information. This color space is
the most prevalent choice for computer graphics because color displays use red,
green, and blue to create the desired color. RGB is a convenient color model
for computer graphics because the human visual system works in a way that is
similar though not quite identical to an RGB color space.
CIE XYZ
is a linear transformation of RGB:
A Lab
color space is a color-opponent space with dimension L for lightness (or
luminance) and a and b for the color-opponent (or chrominance) dimensions,
based on a nonlinear
transformation of CIE XYZ color space.
Lab is
a nonlinear transformation of XYZ, thus it is nonlinear of RGB:
where
YCrCb
color space decomposition is also a Luminance-Chrominance decomposition. Y is
the luminance component and Cb and Cr are the blue-difference and
red-difference chrominance components. It is often used as a part of the Color
image pipeline in video and digital photography systems.
Mathematically,
YCrCb is also a linear transformation of RGB. The basic equation to convert
between 8-bit digital RGB data with a 16-235 nominal range YCrCb is:
Due to
the similarity between the amplified noise and Gaussian noise, many of the
studies focus on normal images with artificially added Gaussian noise (or
sometimes salt and pepper noise). The results are often either misleading or
not optimal. Color images captured by digital cameras are often noisy, but the
noise profile is nothing like those that have been added artificially [1].
It has
been well studied that, for a grey value image, the natural noise distribution
is quite different between light areas and dark areas. The dominant noise in
the lighter parts of an image from an image sensor is typically caused by
statistical quantum fluctuations, that is, variation in the number of photons
sensed at a given exposure level; this noise is known as photon shot noise [2].
Shot noise has a Poisson distribution, which is usually not very different from
Gaussian.
While
there is additional shot noise from the dark leakage current in the image
sensor; this dark area noise is sometimes known as dark shot noise [2] or
dark-current shot noise [3]. Dark current is greatest at hot pixels within the
image sensor; the variable dark charge of normal and hot pixels can be
subtracted of, leaving only the shot noise, or random component, of the leakage
[4, 5]; if the exposure time is long enough that the hot pixel charge exceeds
the linear charge capacity, the noise will be more than just shot noise, and
hot pixels appear as salt-and-pepper noise.
Generally,
we have a comparison between the natural noise and artificial noise:
(1)
Additive artificial noise is homogeneous in the whole image, while real noise
is often not, especially in dark areas;
(2)
There is much more real noise in dark areas than in light areas;
(3)
Additive artificial noise is independent from pixel to pixel, while real noise
is often non-independent from pixels.
Bayer
pattern is known as a filter arrangement in an image sensor that captures
natural light in RGB model. In a Bayer filter arrangement, green is given twice
as many sensors as red and blue in order to achieve higher luminance resolution
than chrominance resolution. For every channel, missing pixels are obtained by
interpolation in the demosaicing process to build up the complete image.
In this
case, the green channel will be cleaner than the red channel and the blue
channel. What's more, due to the reason that more amplification is used in the
blue color channel than in the green or red channel, the blue channel is always
the noisiest [2]. For the same reason, in a luminance-chrominance color space
decomposition, the luminance channel is always cleaner than the chrominance
channel. Since the cleaner channel(s) have better geometric properties (which
are not annoyed by noise that much), it is natural to think that, we can use
cleaner channel(s) as a standard in denoising process to work on noisier
channels.
For a
given 3-channel color space decomposition 
a color image
(1)
and a “channel
method” will be
(2)
where 
, 
and 
are different but
correlated filters defined on 3
channels.
For
example, a naive algorithm using Lab decomposition and Gaussian filter is:
(3)
Since L
is a luminance channel, it is almost clean. We use Gaussian blur to denoise the
chrominance channels a and b.
One
thing that needs to be paid attention is, the advantage of separating luminance
from chrominance is that human vision is typically less sensitive to diffusion
in chrominance [1]. which means, when we take a strong blurring effect on
chrominance channels (a, b in Lab decomposition or Cr Cb in YCrCb
decomposition), after recomposition, there is a very little discernible
difference from the original image (except for denoising). However, to the
luminance channel (L or Y), it is a different story. In fact, even a tiny
blurring in the luminance channel will be immediately visible in the recomposed
color image. Given these characteristics of the luminance-chrominance
decomposition, we would be more aggressive in denoising the chrominance
channels while less so in denoising the luminance channel.
References
1. F. Malgouyres, A
noise selection approach of image restoration, Applications in signal and image
processing IX, Vol 4478, pp. 34-41, 2001.
2. T. Chan , Y. Wang
and H. M. Zhou, Denoising Natural Color Photos in Digital Photography,
submitted to IEEE Transcation on Image Processing.
3. Lindsay MacDonald,
Digital Heritage. Butterworth-Heinemann, 2006
4. Michael A.
Covington, Digital SLR
Astrophotography. Cambridge University Press, 2007.
5. R. E. Jacobson, S.
F. Ray, G. G. Attridge, and N. R. Axford, The Manual of Photography. Focal
Press, 2000.