hesameddin
عضو جدید
Automatic Underwater Image Pre-Processing
St´ephane Bazeille(1), Isabelle Quidu(1), Luc Jaulin(1), Jean-Phillipe
Malkasse(2)
(1) Laboratoire E3I2 EA-3876, ENSIETA, 2 rue Fran¸cois Verny, 29806 BREST Cedex 9
FRANCE
(2) Thales Underwater Systems S.A S. Route de Sainte Anne du Portzic Site Amiral Nomy CS
43814 29238 BREST Cedex 3 FRANCE
SHORT ABSTRACT: A novel pre-processing filter is proposed for underwater image restoration.
Because of specific transmission properties of light in the water, underwater image suffers from
limited range, non uniform lighting, low contrast, color diminished, important blur. . .Today preprocessing
methods typically only concentrates on non uniform lighting or color correction and
often require additional knowledge of the environment. The algorithm proposed in this paper is an
automatic algorithm to pre-process underwater images. It reduces underwater perturbations, and
improves image quality. It is composed of several successive independent processing steps which
correct non uniform illumination, suppress noise, enhance contrast and adjust colors. Performances
of filtering will be assessed using an edge detection robustness criterion.
Keywords: Image processing, contrast enhancement, denoising, color correction.
R´ESUM´E COURT: L’obstacle majeur dans le traitement des images sous marines r´esulte des
ph´enom`enes d’absorption et de diffusion dus aux propri´et´es optiques particuli`eres de la lumi`ere
dans l’eau. Ces deux ph´enom`enes auxquels s’ajoute le probl`eme de turbidit´e, impose de travailler
sur des images tr`es bruit´ees, avec souvent une illumination non uniforme, des contrastes faibles, des
couleurs att´enu´ees. . .Cet article pr´esente une nouvelle m´ethode de pr´etraitement des images sous
marines. L’algorithme propos´e qui ne n´ecessite ni param´etrage manuel ni information a priori,
permet d’att´enuer les d´efauts pr´ec´edemment cit´es et d’am´eliorer de fa¸con significative la qualit´e
des images. L’approche utilis´ee est bas´ee sur le rehaussement, l’´eclairage, le bruit, les contrastes
puis les couleurs sont corrig´es s´equentiellement.
Mots-cl´es: Traitement d’image, rehaussement de contraste, d´ebruitage, compensation colorim´etrique.
1 INTRODUCTION
Underwater vehicles are used to survey the ocean floor, much often with acoustic sensors for their
capability of remote sensing. Optical sensors have been introduced into these vehicles and the use
of video is well integrated by the underwater community for short range operations. However, these
vehicles are usually remotely operated by human operators : the automated processing and analysis
of video data is only emerging and first suffers from a poor quality of the images due to specific
propagation properties of the light in the water. To summarize underwater images suffer from
limited range, non uniform lighting, low contrast, diminished colors, important blur. . .Moreover
many parameters can modify the optical properties of the water and underwater images show
large temporal and spatial variations. So, it is necessary to pre-process those images before using
usual image processing methods. Today pre-processing methods typically only concentrate on non
uniform lighting or color correction and often require additional knowledge of the environment:
as depth, distance object/camera or water quality [6][7]. The algorithm proposed in this paper is
a parameter-free algorithm which reduces underwater perturbations, and improves image quality
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
without using any knowledge and without any human parameter adjustment. It is composed of
several successive independent processing steps which respectively correct non uniform illumination,
suppress noise, enhance contrast and adjust colors [3][4][5][8]. The pre-processing step occurs
before the segmentation. In most cases, a great improvement is observed while filtering, as it is
showed by the edge detection criterion.
The remaining of the paper is organized as follows: Section II details underwater characteristic
perturbations. Section III describes the complete filter bank composed of five different processes :
homomorphic filtering to reduce illumination problems and to enhance the contrast, wavelet denoising
and anisotropic filtering to cancel out the noise and enhance edges, contrast adjustment and,
color compensation to suppress the predominant color. Section IV then details one by one those
algorithms and explains our choices, Section V presents results on real underwater images. Finally
Section VI shows qualitative improvements of our filter for the following step of segmentation.
2 UNDERWATER DEGRADATION
A major difficulty to process underwater images comes from light attenuation. Light attenuation
limits the visibility distance, at about twenty meters in clear water and five meters or less in turbid
water. The light attenuation process is caused by the absorption (which removes light energy) and
scattering (which changes the direction of light path). Absorption and scattering effects are due
to the water itself and to other components such as dissolved organic matter or small observable
floating particles. We simulate blur and unequal illumination using Jaffe and McGlamery’s model [14][16], gaussian and
particles noise as additive contributions to the images and finally reduced color range by histogram
operation.
3 ALGORITHM DESCRIPTION
The algorithm proposed corrects each underwater perturbations sequentially.
1. Removing potential moir´e effect. A moir´e effect has the appearance of a wavy repetitive
pattern on the image. It is not an underwater perturbation, and it is often considered
as aliasing phenomena. Sampling moir´e mainly occurs in the analog to digital conversion
process. Moir´e pattern is removed via spectral analysis by detecting peaks in the Fourier
transform and deleting them assuming that they represent the moir´e effect [13]. Only few
images suffer from moir´e degradation but removing it is important because the following
processes enhance contrast so enhance the moir´e effect and consequently highly degrade
results.
2. Resizing and extending symmetrically the image to get a squared image whose
size is a power of two. Symmetric extension prevents from potential border effects and
resizing to squared image speeds up the following process by enabling to use fast Fourier
transform and fast wavelet transform algorithms.
3. Converting color space from RGB to YCbCr (Luminance Chrominance). This
color space conversion allows us to work only on one channel instead of processing the three
RGB channels. In YCbCr color space we process only the luminance channel (Y) corresponding
to intensity component (gray scale image). The two other components correspond
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
to chroma color-difference. This step speeds up again all the following processings avoiding
to process each time each RGB channels.
4. Homomorphic filtering. The homomorphic filtering is used to correct non uniform illumination
and to enhance contrasts in the image. It’s a frequency filtering, preferred to others
techniques [4][8] because it corrects non uniform lighting and sharpens the edges at the same
time.
5. Wavelet denoising. As explained in the previous part gaussian noise (i.e noise acquisition)
is always present in natural images. This noise currently important is further amplified by
homomorphic filtering. A step of denoising is so necessary to suppress it. This wavelet
denoising method was preferred to many others algorithms [15] because of it performances
of speed in comparison of its denoising quality.
6. Anisotropic filtering. Anisotropic filtering allows us to simplify image features to improve
image segmentation. This filter smooths the image in homogeneous area but preserves edges
and enhance them. It is used to smooth textures and reduce artifacts by deleting small edges
amplified by homomorphic filtering.
7. Adjusting image intensity. This step increases contrast by adjusting image intensity values.
It suppresses eventually outliers pixels to improve contrast stretching. It then stretches
contrast to use the whole range of intensity channel and if necessary it saturates some low
or high values.
8. Converting from YCbCr to RGB and reverse symmetric extension. After this step
luminance channel has been preprocessed, so to regain colors we convert back the image the
RGB space, and cut out the symmetric extension part of the image to recover the image with
original size.
9. Equalizing color mean. In underwater imaging color channels are rarely balanced correctly.
This step enables to suppress predominant color by equalizing RGB channels means.
• Inversion of the multiscale decomposition to reconstruct the filtered image.
• Modification of the pixel value using (Eq.9)
• Color correction is preformed by equalizing each color means. In underwater image colors
are rarely balanced correctly, this processing step suppresses prominent blue or green color
without taking into account absorption phenomena (results using absorption’s law are better
but a priori knowledge is required [7]). This algorithm is a linear translation of the histogram.
We add to each pixel the difference between desired mean value and the mean of the channel.
We do that for each RGB channel.
5 RESULTS
The computation time to pre-process a color image 512 × 512 is about 1.5 seconds on pentium 4,
3Ghz using Matlab 7.0. The prefilter is studied to be very fast and is optimized for Matlab.
Fig. 2: Pairs of images before (left) and after preprocessing (right), the first four images come
from the web, and others are images extracted from TOPVISION videos.
Fig. 3: Images with additional underwater noise (average blur, gaussian white noise, spot effect
and color range reduced) on the left and the same images after pre-processing on the right.
* The information contained in this publication are derived from data property of the French State that have been provided by the GESMA
(Groupe d’Etudes Sous-Marines de l’Atlantique) within TOPVISION project coordinated by Thales Underwater Systems SAS. This project is
related to Techno-Vision Programme launched by french Ministry of Research and french Ministry of Defense.
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
Fig. 4: Gradient magnitude histogram of the eight previous images (Fig. 2) before pre-processing
(solid line) and after pre-processing (dotted line).
6 ROBUSTNESS
Fig. 5: Mean of gradient magnitude histogram on the
eight previous images with and without additional synthetic
degradations.
This pre-processing algorithm is the preliminary
step of a feature point extraction
or an edge detection. In order to illustrate
our results we use gradient magnitude
histogram Fig.4 and Fig. 5 (gradient
histograms are plotted between 0
and 0.4 so each value greater than 0.
Also we have assess quality of our
restoration procedure using the robustness
criterion of [11]. This criterion assumes
that a well contrasted and noisefree
image has a distribution of the gradient
magnitude histogram close to exponential,
it attributes a mark from zero to one. Following results presented in the table are the
mean values of the criterion on the previous eight images before and after pre-processing. Each
value corresponds to a curve Fig.5.
Before After
Without additional synthetic degradations 0.398 0.539
With additional synthetic degradations 0.313 0.538
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
7 CONCLUSION AND FUTURE WORK.
In this paper we present a novel underwater pre-processing algorithm. This algorithm is automatic
and requires no parameter adjustment and no a priori knowledge of the acquisition conditions.
Many adjustments can still be done to improve the whole pre-processing algorithms. We will be
able to investigate notably curvelets-based methods for contrast enhancement and image denoising
which seems to give very good results [10], and also deconvolution methods. Inverse filtering gives
good results but generally requires a priori knowledge on the environment [12]. Our filtering needs
no parameters adjustment so it can be used systematically on underwater images before every
pre-processing algorithms.
References
[1] M. Arredondo and K. Lebart, “A methodology for the systematic assessment of underwater
video processing algorithms,” IEEE OCEANS 05 Europe Conference. June 2005.
[2] A. Farras Abdelmour, Ivan W. Selesnick, “Symmetric Nearly Orthogonal, and Orthogonal
Nearly Symmetric Wavelets,” Research Report February 2003.
[3] L. Sendur and I. W. Selesnick, “Bivariate shrinkage functions for wavelet-based denoising
exploiting interscale dependency,” IEEE Trans on Signal Processing, November 2002.
[4] R. Garcia, T. Nicosevici and X. Cufi, “On the way to solve lighting problems in underwater
imaging,” IEEE OCEAN 02, 1018-1024, October 2002.
[5] P. Perona and J.Malik, “Scale space and edge detection using anisotropic diffusion,” IEEE
Trans on Pattern Analysis and Machine Intelligence, 629-639, July 1990.
[6] A. O. Olmos Antillon, “Detecting underwater man-made objects in unconstrained video image,”
Thesis, Department of Computing and Electrical Engineering, December 2002
[7] J. Ahlen, “Color correction of underwater images using spectral data,” Thesis, Uppsala University,
Centre for Image Analysis, 2005.
[8] A. Arnold-Bos, J. P. Malkasse and Gilles Kervern, “Towards a model-free denoising of underwater
optical image,” IEEE OCEANS 05 EUROPE, June 2005.
[9] P. Kovesi, “Phase preserving denoising of images,” Proceeding of the Australian Pattern Recognition
Society Conference, December 1999.
[10] J. L. Starck, Fionn Murtagh, Emmanuel J. Cand´es and David L. Donoho, “ The curvelet
transform for image denoising,” IEEE Transactions on image processing, June 2002.
[11] A. Arnold-Bos, J. P. Malkasse and Gilles Kervern, “A preprocessing framework for automatic
underwater images denoising,”European Conference on Propagation and Systems, March 2005.
[12] Z. Liu, Y. Yu, K. Zhang and H. Huang, “Underwater image transmission and blurred image
restoration,” SPIE Journal of optical Engineering, June 2001.
[13] D. N. Sidorov and ANil C. Kokaram, “Suppression of moir´e patterns via spectral analysis,”
Proceedings of SPIE in Visual Communications and Image Processing, January 2002.
[14] J.S Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE
Journal of oceanic Eng., April 1990.
[15] A. Buades, B. Coll, J.M Morel, “A review of image denoising algorithms, with a new one,”
Multiscale Modeling and Simulation (SIAM interdisciplinary journal), 2005.
[16] B.L McGlamery,
St´ephane Bazeille(1), Isabelle Quidu(1), Luc Jaulin(1), Jean-Phillipe
Malkasse(2)
(1) Laboratoire E3I2 EA-3876, ENSIETA, 2 rue Fran¸cois Verny, 29806 BREST Cedex 9
FRANCE
(2) Thales Underwater Systems S.A S. Route de Sainte Anne du Portzic Site Amiral Nomy CS
43814 29238 BREST Cedex 3 FRANCE
SHORT ABSTRACT: A novel pre-processing filter is proposed for underwater image restoration.
Because of specific transmission properties of light in the water, underwater image suffers from
limited range, non uniform lighting, low contrast, color diminished, important blur. . .Today preprocessing
methods typically only concentrates on non uniform lighting or color correction and
often require additional knowledge of the environment. The algorithm proposed in this paper is an
automatic algorithm to pre-process underwater images. It reduces underwater perturbations, and
improves image quality. It is composed of several successive independent processing steps which
correct non uniform illumination, suppress noise, enhance contrast and adjust colors. Performances
of filtering will be assessed using an edge detection robustness criterion.
Keywords: Image processing, contrast enhancement, denoising, color correction.
R´ESUM´E COURT: L’obstacle majeur dans le traitement des images sous marines r´esulte des
ph´enom`enes d’absorption et de diffusion dus aux propri´et´es optiques particuli`eres de la lumi`ere
dans l’eau. Ces deux ph´enom`enes auxquels s’ajoute le probl`eme de turbidit´e, impose de travailler
sur des images tr`es bruit´ees, avec souvent une illumination non uniforme, des contrastes faibles, des
couleurs att´enu´ees. . .Cet article pr´esente une nouvelle m´ethode de pr´etraitement des images sous
marines. L’algorithme propos´e qui ne n´ecessite ni param´etrage manuel ni information a priori,
permet d’att´enuer les d´efauts pr´ec´edemment cit´es et d’am´eliorer de fa¸con significative la qualit´e
des images. L’approche utilis´ee est bas´ee sur le rehaussement, l’´eclairage, le bruit, les contrastes
puis les couleurs sont corrig´es s´equentiellement.
Mots-cl´es: Traitement d’image, rehaussement de contraste, d´ebruitage, compensation colorim´etrique.
1 INTRODUCTION
Underwater vehicles are used to survey the ocean floor, much often with acoustic sensors for their
capability of remote sensing. Optical sensors have been introduced into these vehicles and the use
of video is well integrated by the underwater community for short range operations. However, these
vehicles are usually remotely operated by human operators : the automated processing and analysis
of video data is only emerging and first suffers from a poor quality of the images due to specific
propagation properties of the light in the water. To summarize underwater images suffer from
limited range, non uniform lighting, low contrast, diminished colors, important blur. . .Moreover
many parameters can modify the optical properties of the water and underwater images show
large temporal and spatial variations. So, it is necessary to pre-process those images before using
usual image processing methods. Today pre-processing methods typically only concentrate on non
uniform lighting or color correction and often require additional knowledge of the environment:
as depth, distance object/camera or water quality [6][7]. The algorithm proposed in this paper is
a parameter-free algorithm which reduces underwater perturbations, and improves image quality
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
without using any knowledge and without any human parameter adjustment. It is composed of
several successive independent processing steps which respectively correct non uniform illumination,
suppress noise, enhance contrast and adjust colors [3][4][5][8]. The pre-processing step occurs
before the segmentation. In most cases, a great improvement is observed while filtering, as it is
showed by the edge detection criterion.
The remaining of the paper is organized as follows: Section II details underwater characteristic
perturbations. Section III describes the complete filter bank composed of five different processes :
homomorphic filtering to reduce illumination problems and to enhance the contrast, wavelet denoising
and anisotropic filtering to cancel out the noise and enhance edges, contrast adjustment and,
color compensation to suppress the predominant color. Section IV then details one by one those
algorithms and explains our choices, Section V presents results on real underwater images. Finally
Section VI shows qualitative improvements of our filter for the following step of segmentation.
2 UNDERWATER DEGRADATION
A major difficulty to process underwater images comes from light attenuation. Light attenuation
limits the visibility distance, at about twenty meters in clear water and five meters or less in turbid
water. The light attenuation process is caused by the absorption (which removes light energy) and
scattering (which changes the direction of light path). Absorption and scattering effects are due
to the water itself and to other components such as dissolved organic matter or small observable
floating particles. We simulate blur and unequal illumination using Jaffe and McGlamery’s model [14][16], gaussian and
particles noise as additive contributions to the images and finally reduced color range by histogram
operation.
3 ALGORITHM DESCRIPTION
The algorithm proposed corrects each underwater perturbations sequentially.
1. Removing potential moir´e effect. A moir´e effect has the appearance of a wavy repetitive
pattern on the image. It is not an underwater perturbation, and it is often considered
as aliasing phenomena. Sampling moir´e mainly occurs in the analog to digital conversion
process. Moir´e pattern is removed via spectral analysis by detecting peaks in the Fourier
transform and deleting them assuming that they represent the moir´e effect [13]. Only few
images suffer from moir´e degradation but removing it is important because the following
processes enhance contrast so enhance the moir´e effect and consequently highly degrade
results.
2. Resizing and extending symmetrically the image to get a squared image whose
size is a power of two. Symmetric extension prevents from potential border effects and
resizing to squared image speeds up the following process by enabling to use fast Fourier
transform and fast wavelet transform algorithms.
3. Converting color space from RGB to YCbCr (Luminance Chrominance). This
color space conversion allows us to work only on one channel instead of processing the three
RGB channels. In YCbCr color space we process only the luminance channel (Y) corresponding
to intensity component (gray scale image). The two other components correspond
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
to chroma color-difference. This step speeds up again all the following processings avoiding
to process each time each RGB channels.
4. Homomorphic filtering. The homomorphic filtering is used to correct non uniform illumination
and to enhance contrasts in the image. It’s a frequency filtering, preferred to others
techniques [4][8] because it corrects non uniform lighting and sharpens the edges at the same
time.
5. Wavelet denoising. As explained in the previous part gaussian noise (i.e noise acquisition)
is always present in natural images. This noise currently important is further amplified by
homomorphic filtering. A step of denoising is so necessary to suppress it. This wavelet
denoising method was preferred to many others algorithms [15] because of it performances
of speed in comparison of its denoising quality.
6. Anisotropic filtering. Anisotropic filtering allows us to simplify image features to improve
image segmentation. This filter smooths the image in homogeneous area but preserves edges
and enhance them. It is used to smooth textures and reduce artifacts by deleting small edges
amplified by homomorphic filtering.
7. Adjusting image intensity. This step increases contrast by adjusting image intensity values.
It suppresses eventually outliers pixels to improve contrast stretching. It then stretches
contrast to use the whole range of intensity channel and if necessary it saturates some low
or high values.
8. Converting from YCbCr to RGB and reverse symmetric extension. After this step
luminance channel has been preprocessed, so to regain colors we convert back the image the
RGB space, and cut out the symmetric extension part of the image to recover the image with
original size.
9. Equalizing color mean. In underwater imaging color channels are rarely balanced correctly.
This step enables to suppress predominant color by equalizing RGB channels means.
• Inversion of the multiscale decomposition to reconstruct the filtered image.
• Modification of the pixel value using (Eq.9)
• Color correction is preformed by equalizing each color means. In underwater image colors
are rarely balanced correctly, this processing step suppresses prominent blue or green color
without taking into account absorption phenomena (results using absorption’s law are better
but a priori knowledge is required [7]). This algorithm is a linear translation of the histogram.
We add to each pixel the difference between desired mean value and the mean of the channel.
We do that for each RGB channel.
5 RESULTS
The computation time to pre-process a color image 512 × 512 is about 1.5 seconds on pentium 4,
3Ghz using Matlab 7.0. The prefilter is studied to be very fast and is optimized for Matlab.
Fig. 2: Pairs of images before (left) and after preprocessing (right), the first four images come
from the web, and others are images extracted from TOPVISION videos.
Fig. 3: Images with additional underwater noise (average blur, gaussian white noise, spot effect
and color range reduced) on the left and the same images after pre-processing on the right.
* The information contained in this publication are derived from data property of the French State that have been provided by the GESMA
(Groupe d’Etudes Sous-Marines de l’Atlantique) within TOPVISION project coordinated by Thales Underwater Systems SAS. This project is
related to Techno-Vision Programme launched by french Ministry of Research and french Ministry of Defense.
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
Fig. 4: Gradient magnitude histogram of the eight previous images (Fig. 2) before pre-processing
(solid line) and after pre-processing (dotted line).
6 ROBUSTNESS
Fig. 5: Mean of gradient magnitude histogram on the
eight previous images with and without additional synthetic
degradations.
This pre-processing algorithm is the preliminary
step of a feature point extraction
or an edge detection. In order to illustrate
our results we use gradient magnitude
histogram Fig.4 and Fig. 5 (gradient
histograms are plotted between 0
and 0.4 so each value greater than 0.
Also we have assess quality of our
restoration procedure using the robustness
criterion of [11]. This criterion assumes
that a well contrasted and noisefree
image has a distribution of the gradient
magnitude histogram close to exponential,
it attributes a mark from zero to one. Following results presented in the table are the
mean values of the criterion on the previous eight images before and after pre-processing. Each
value corresponds to a curve Fig.5.
Before After
Without additional synthetic degradations 0.398 0.539
With additional synthetic degradations 0.313 0.538
CMM’06 - CARACTERISATION DU MILIEU MARIN 16 - 19 Octobre 2006
7 CONCLUSION AND FUTURE WORK.
In this paper we present a novel underwater pre-processing algorithm. This algorithm is automatic
and requires no parameter adjustment and no a priori knowledge of the acquisition conditions.
Many adjustments can still be done to improve the whole pre-processing algorithms. We will be
able to investigate notably curvelets-based methods for contrast enhancement and image denoising
which seems to give very good results [10], and also deconvolution methods. Inverse filtering gives
good results but generally requires a priori knowledge on the environment [12]. Our filtering needs
no parameters adjustment so it can be used systematically on underwater images before every
pre-processing algorithms.
References
[1] M. Arredondo and K. Lebart, “A methodology for the systematic assessment of underwater
video processing algorithms,” IEEE OCEANS 05 Europe Conference. June 2005.
[2] A. Farras Abdelmour, Ivan W. Selesnick, “Symmetric Nearly Orthogonal, and Orthogonal
Nearly Symmetric Wavelets,” Research Report February 2003.
[3] L. Sendur and I. W. Selesnick, “Bivariate shrinkage functions for wavelet-based denoising
exploiting interscale dependency,” IEEE Trans on Signal Processing, November 2002.
[4] R. Garcia, T. Nicosevici and X. Cufi, “On the way to solve lighting problems in underwater
imaging,” IEEE OCEAN 02, 1018-1024, October 2002.
[5] P. Perona and J.Malik, “Scale space and edge detection using anisotropic diffusion,” IEEE
Trans on Pattern Analysis and Machine Intelligence, 629-639, July 1990.
[6] A. O. Olmos Antillon, “Detecting underwater man-made objects in unconstrained video image,”
Thesis, Department of Computing and Electrical Engineering, December 2002
[7] J. Ahlen, “Color correction of underwater images using spectral data,” Thesis, Uppsala University,
Centre for Image Analysis, 2005.
[8] A. Arnold-Bos, J. P. Malkasse and Gilles Kervern, “Towards a model-free denoising of underwater
optical image,” IEEE OCEANS 05 EUROPE, June 2005.
[9] P. Kovesi, “Phase preserving denoising of images,” Proceeding of the Australian Pattern Recognition
Society Conference, December 1999.
[10] J. L. Starck, Fionn Murtagh, Emmanuel J. Cand´es and David L. Donoho, “ The curvelet
transform for image denoising,” IEEE Transactions on image processing, June 2002.
[11] A. Arnold-Bos, J. P. Malkasse and Gilles Kervern, “A preprocessing framework for automatic
underwater images denoising,”European Conference on Propagation and Systems, March 2005.
[12] Z. Liu, Y. Yu, K. Zhang and H. Huang, “Underwater image transmission and blurred image
restoration,” SPIE Journal of optical Engineering, June 2001.
[13] D. N. Sidorov and ANil C. Kokaram, “Suppression of moir´e patterns via spectral analysis,”
Proceedings of SPIE in Visual Communications and Image Processing, January 2002.
[14] J.S Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE
Journal of oceanic Eng., April 1990.
[15] A. Buades, B. Coll, J.M Morel, “A review of image denoising algorithms, with a new one,”
Multiscale Modeling and Simulation (SIAM interdisciplinary journal), 2005.
[16] B.L McGlamery,
