1
AN EFFICIENT SURVEY & COMPARISON OF IMAGE DENOISING TECHNIQUES
ANJALI KHARE, SHAHAB AHMED, PROF. L.K.VISHWAMITRA
Abstract
Removing noise from the original signal is still a challenging problem for researchers. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. Reduction of noise is essential especially in the field of image processing. Several researchers are continuously working in this direction and provide some good insights, but still there are lot of scope in this field. Noise mixed with image is harmful for image processing. In this dissertation we proposed an efficient Multithresholding approach for reducing noise and blur parameters.
Keywords: Partial Differential Equation, BER, Signal to Noise Ratio, Peak Signal To Noise Ratio, Image Restoration
1. Introduction
Vision is the most advanced of human senses, so it is not surprising that images play the single most important role in our perception. However, unlike humans, who are limited to the visual band of the electromagnetic (EM) spectrum, imaging machines cover almost the entire EM spectrum, ranging from gamma to radio waves. They can operate on images generated by sources that human are not accustomed to associating with images. These include ultrasound, electron microscopy and computer-generated images. Thus digital image processing encompasses a wide and varied field of applications.
In this context several researches apply their work in this direction. Adaptive Directional Lifting (ADL) is one of the image compressions due to the characteristics of representing the edges and textures in images efficiently [1, 2].
Several researches have shown that the application of image denoising can also benefit from this technique [3, 4]. Because of this, it can effectively decorrelate the dependencies found over image discontinuities and compact high frequency components induced by image features into the lower level or low band pass. If we think about the Wavelet transform then it can be effectively capture singular points up to two dimensions means including one dimension, but it is fail in representing the major features like edge , color ,contour and so on. There are several directional and non-directional redundant transforms which are explored in different research papers, including the curvelet, contourlet, wedgelet, bandlet, and the steerable wavelet [5-8].
2. Image Formats
2
There are various formats of the image supported by MATLAB for processing based on requirements of application. The extension of the image file shows the format of the image. The Table 2.1 describes various image formats.
Table 2.1: Image Formats supported by MATLAB
3. Image Types The toolbox supports four types of images:
a) Gray-scale images: A gray-scale image is a data matrix whose values represent shades of gray. When the elements of a gray-scale image are of class uint8, or class uint16, they have integer values in the range [0,255] or [0, 65535], respectively. If the image is of class double or single, the values are floating-point numbers (see the first two entries in Table 2.1). Values of double and single gray- scale images normally are scaled in the range [0, 1], although other ranges can be used.
b) Binary images: Binary images have a very specific meaning in MATLAB. A binary image is a logical array of 0s and1s.Thus, an array of 0s and 1s whose values are of data class, say uint8, is not considered a binary image in MATLAB. A numeric array is converted to binary using function logical. Thus, if
Format
Name Description Extension
TIFF Tagged Image File Format
.tif, .tiff
JPEG Joint
Photograph Experts Group
.jpg, .jpeg
GIF Graphics Interchange Format
.gif
BMP Window Bitmap
.bmp
PNG Portable Network Graphics
.png
3
A is a numeric array consisting of 0s and 1s, we create a logical array B using the statement.
B = logical (A)
If A contains elements other than 0s and 1s, the logical function converts all nonzero quantities to logical 1s and all entries with value 0 to logical 0s. The use of relational and logical operators can also result in logical arrays. To test if an array is logical we use the is logical function:
islogical (C)
If C is a logical array, this function returns a 1.Otherwise returns a 0.
Logical arrays can be converted to numeric arrays using the general class conversion
syntax:
B = class_name (A)
were class name is im2uint8, im2uint16, im2double, im2single, or mat2gray.Toolbox function mat2gray converts an image to an array of class double scaled to the range [0, 1]. The calling syntax is:
g = mat2gray (A, [Amin, Amax])
where image g has values in the range 0 (black) to 1 (white).
c) RGB Image: An RGB color image is an M×N×3 array of color pixels, where each color pixel is a triplet corresponding to the red, green and blue components of an RGB image at a specific spatial location. An RGB image may be viewed as a
“stack” of three gray-scale images that, when fed into the red, green and blue inputs of a color monitor, produce a color image on the screen. By convention, the three images forming an RGB color image are referred to as the red, green and blue component images. The data class of the component images determines their range of values. If an RGB image is of class double, the range of values is [0, 1].
Similarly, the range of values is [0,255] or [0, 65535] for RGB images of class uint8 or uint16, respectively. The number of bits used to represent the pixel values of the component images determines the bit depth of an RGB image. For example, if each component image is an 8-bit image, the corresponding RGB image is said to be 24 bits deep. Generally, the number of bits in all component images is the same. In this case, the number of possible colors in an RGB image is (2b) 3 where b is the number of bits in each component image. For an 8-bit image, the number is 16,777,216 colors.
Let fR, fG, and fB represent three RGB component images. An RGB Image is formed from these images by using the cat (concatenate) operator to stack the images:
rgb_image = cat (3, fR, fG, fB)
d) Indexed Images: An indexed image has two components:
i) A data matrix of integers, x.
ii) A color map matrix, map.
4
Matrix map is an m×3 array of class double containing floating-point values in the range [0, 1].The length of the map is equal to the number of colors it defines. Each row of map specifies the red, green and blue components of a single color (if the three columns of map are equal, the color map becomes a gray-scale map). An indexed image uses “direct mapping” of pixel intensity values to color-map values.
The color of each pixel is determined by using the corresponding value of integer matrix X as an index (hence the name indexed image) into map. If X is of class double, then value 1 points to the first row in map, value 2 points to the second row, and so on. If X is of class uint8 or uint16, then value 0 points to the first row in map. Most monochrome image processing operations are carried out using binary or gray-scale images, so our initial focus is on these two images.
4. Noise
Most denoising algorithms assume zero mean additive white Gaussian noise (AWGN) because it is symmetric, continuous, and has a smooth density distribution. However, many other types of noise exist in practice. Correlated noise with a Guassian distribution is an example. Noise can also have different distributions such as Poisson, Laplacian, or non-additive Salt-and-Pepper noise.
Salt-and-Pepper noise is caused by bit errors in image transmission and retrieval as well as in analog-to-digital converters. A scratch in a picture is also a type of noise. Noise can be signal dependent or signal independent. For example, the process of quantization (dividing a continuous signal into discrete levels) adds signal-dependent noise. In digital image processing, a little bit of random noise is deliberately introduced to avoid false contouring or posterization. This is termed dithering. Discretizing a continuously varying shade may make it look isolated, resulting in posterization. The above facts suggest that it is not easy to model all types of practical noise into one model.
5. Evolution of Image Denoising Research
Image Denoising has remained a fundamental problem in the field of image processing. Wavelets give a superior performance in image denoising due to properties such as sparsity and multiresolution structure. With Wavelet Transform gaining popularity in the last two decades various algorithms for denoising in wavelet domain were introduced. The focus was shifted from the Spatial and Fourier domain to the Wavelet transform domain. Ever since Donoho‟s Wavelet based thresholding approach was published in 1995, there was a surge in the denoising papers being published. Although Donoho‟s concept was not revolutionary, his methods did not require tracking or correlation of the wavelet maxima and minima across the different scales as proposed by Mallat . Thus, there was a renewed interest in wavelet based denoising techniques since Donoho demonstrated a simple approach to a difficult problem. Researchers published different ways to compute the parameters for the thresholding of wavelet coefficients. Data adaptive thresholds were introduced to achieve optimum value of threshold. Later efforts found that substantial improvements in perceptual
5
quality could be obtained by translation invariant methods based on thresholding of an Undecimated Wavelet Transform . These thresholding techniques were applied to the nonorthogonal wavelet coefficients to reduce artifacts. Multiwavelets were also used to achieve similar results. Probabilistic models using the statistical properties of the wavelet coefficient seemed to outperform the thresholding techniques and gained ground. Recently, much effort has been devoted to Bayesian denoising in Wavelet domain. Hidden Markov Models and Gaussian Scale Mixtures have also become popular and more research continues to be published. Tree Structures ordering the wavelet coefficients based on their magnitude, scale and spatial location have been researched. Data adaptive transforms such as Independent Component Analysis (ICA) have been explored for sparse shrinkage. The trend continues to focus on using different statistical models to model the statistical properties of the wavelet coefficients and its neighbors. Future trend will be towards finding more accurate probabilistic models for the distribution of non-orthogonal wavelet coefficients.
In 2010, Saeid Fazli et al. [18] presents a new approach for image denoising based on Partial Differential Equations (PDE) using Artificial Intelligence (AI) techniques.
The Nonlinear Diffusion techniques and PDE-based variation models are very popular in image restoring and processing but in this proposed heuristic method, Particle Swarm Optimization (PSO) is used for Complex PDE parameter tuning by minimizing the Structural SIMilarity (SSIM) measure. Complex diffusion is a generalization of diffusion and free Schrodinger equations which has properties of both forward and inverse diffusion. The proposed method by the author is confirmed by obtained simulation results of standard images.
In 2011, Jia Liu et al. [22] proposed an image denoising method using partial differential equation and bi-dimensional empirical mode decomposition. The bi- dimensional empirical mode decomposition transforms the image into intrinsic mode function and residue. Different components of the intrinsic mode functions present different frequency of the image. The different with the classic method of partial differential equation denoising is that we use partial differential equation of the intrinsic mode functions to filter noise. Finally, they reconstruct the image with the filtered intrinsic mode functions and residue.
In 2011, Changsheng Lang et al. [19] propose a combined transform image denoising algorithm based on morphological component analysis (MCA). Author suggests that the MCA method is used to separate the image into natural scene and linear singular structure. Curvelet transform threshold denosing is used in linear singular structure while wavelet transform deals with smooth part. This algorithm makes full use of respective advantages of the wavelet transform and curvelet transform. Experiment results show that the algorithm can better maintain the details characteristics in dealing with the image with linear singularity, and it has a better denosing performance for image than a simple wavelet thresholding or curvelet thresholding.
In 2012, Meenal et al. [14] survey and analysed different traditional image denoising method using different methods. They also suggest a new approach which provides a heterogeneous way of the above challenging issue. Their approach is the combination of three different approaches first is for blur, second
6
is for noise and finally for blur and noise. After analysing several research works they analyse that not a single method can provide better method for blur and noise both. So their proposed solution can provides betterment in this issue.
In 2012, Meenal et al. [15] proposed an image denoising method using partial differential equation. In their proposed approach they proposed three different approaches first is for blur, second is for noise and finally for blur and noise.
These approaches are compared by Average absolute difference, signal to noise ratio (SNR), peak signal to noise ratio (PSNR), Image Fidelity and Mean square error. They achieve result on different scenario. They also compare our result on the basis of the above five parameters and the result is better in comparison to the traditional technique.
In 2012, Kehua Su et al. [20] introduce a sparse and redundant representations algorithm based on over complete learned dictionary to process different types of images. They use the K-SVD denoising framework and modify its initial dictionary, and then mainly focus on using it to study its denoising performance and suitability for different types of Images, and then compare it with some other image denoising algorithms. As to the remote sensing images denoising, the experiment results show that the K-SVD algorithm can leads to the state-of-art denoising performance at low noisy levels, but for high noisy levels, its performance isn‟t good on PSNR and visual effect, that is it cannot retain the local details of images.
In 2012, Guo-Duo Zhang et al. [21] proposes an image denoising method based on support vector regression; also this paper describes several other methods of image denoising. Simulation results show that the method can save the image detail better, restore the original image and remove noise.
Zhang and Karim have developed a new impulse detector [53] for switching median filter. It is based on the minimum absolute value of four convolutions obtained using one-dimensional Laplacian operators. For a „bridge‟ image corrupted with 10 % impulse noise, this scheme achieves an output MSE of 0.0011 as compared to the MED filters performance of 0.0027. This may be classified as a good filter; not a very good filter.
D.V.D. Ville, et al. [55] has developed an image filter for the noise reduction of images corrupted with additive noise. The filter consists of two stages. The first stage computes a fuzzy derivative for 8 directions. The second stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Both the stages are based on fuzzy rules.
6. Discussion
Performance of denoising algorithms is measured using quantitative performance measures such as peak signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR) as well as in terms of visual quality of the images. Many of the current techniques assume the noise model to be Gaussian. In reality, this assumption may not always hold true due to the varied nature and sources of noise. An ideal denoising procedure requires a priori knowledge of the noise, whereas a practical procedure
7
may not have the required information about the variance of the noise or the noise model. Thus, most of the algorithms assume known variance of the noise and the noise model to compare the performance with different algorithms. Gaussian Noise with different variance values is added in the natural images to test the performance of the algorithm. Not all researchers use high value of variance to test the performance of the algorithm when the noise is comparable to the signal strength. Use of FFT in filtering has been restricted due to its limitations in providing sparse representation of data. Wavelet Transform is the best suited for performance because of its properties like sparsity, multiresolution and multiscale nature. In addition to performance, issues of computational complexity must also be considered. Thresholding techniques used with the Discrete Wavelet Transform are the simplest to implement. Non-orthogonal wavelets such as UDWT and Multiwavelets improve the performance at the expense of a large overhead in their computation. HMM based methods seem to be promising but are complex. When using Wavelet Transform, Nason emphasized that issue such as choice of primary resolution (the scale level at which to begin thresholding) and choice of analyzing wavelet also have a large influence on the success of the shrinkage procedure.
When comparing algorithms, it is very important that researchers do not omit these comparison details. Several papers did not specify the wavelet used neither the level of decomposition of the wavelet transform was mentioned. It is expected that the future research will focus on building robust statistical models of non- orthogonal wavelet coefficients based on their intra scale and inter scale correlations. Such models can be effectively used for image denoising and compression.
7. References
[1] W. P. Ding and F. Wu, “Adaptive directional lifting based wavelet transform for image coding,” IEEE Trans. Image Processing, vol. 16, no. 2, pp. 416–684, 2007
[2] Y. Liu and K. N. Ngan, “Weighted adaptive lifting-based wavelet transform,”IEEE Trans.
Image Processing, vol. 17, no. 4, pp. 500–511, 2008.
[3] X. T. Wang, G. M. Shi, and Y. Niu, “Image denoising based on improved adaptive directional lifting wavelet transform,” in International Conference on Signal Processing, 2008, vol. 2, pp. 1112–
1116.
[4] X. T. Wang, G. M. Shi, Y. Niu, and L. Zhang, “Robust adaptive directional lifting wavelet transform for image denoising,” IET Image Process (Accepted), 2009.
[5] G. Y. Chen, B. Kegl, “Image denoising with complex ridgelets,”Pattern Recognition, vol. 40, 2007,pp. 578-585,.
[6] Z. Liu, H. Xu, “Image Denoising with Nonsubsampled Wavelet-Based Contourlet Transform,” Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 2008, pp.
301-305.
[7] J. R. Sveinsson, Z. Semar, J. A. Benediktsson, “Speckle Reduction of SAR Images in the Bandlet Domain,” IEEE International Geoscience and Remote Sensing Symposium, 2008, pp.
1158-1161.
[8] B. Fisch and E.L. Schowart, "Iearning an Integral Equation Approximation to Nonlinear Anisotropic Diffusion in Image processing", Dept. cognitive and Neural Systems Boston University.
[9] Perona. P and Ma[ik. J, "Sca[e-space and edge detection using anisotropic diffusion," in Proceeding of IEEE Computer Society workshop on Computer Vision, 1987, pp. 16-27.
[10] Y. You, W. Xu, A. Tannenbaum and M. Kaveh, "Behaviora[ analysis of an isotropic diffusion in image processing", IEEE Trans. Image Processing, vol. 5, 1996, pp. 1539-1553.
8
[11] D. Strong and T. Chan, "Edge-preserving and scale-dependent properties of total variation regularization", Inverse Problems, vol. 19, 2003, pp. 165-187.
[12] Sujata, R. B. Dubey,R. Dhiman T. J. Singh Chugh, “An Evaluation of Two Mammography Segmentation Techniques”, International Journal of Advanced Computer Research (IJACR) Volume- 2 Number-4 Issue-7 December-2012.
[13] Meenakshi, R. B. Dubey, “Vehicle License Plate Recognition System”, International Journal of Advanced Computer Research (IJACR) Volume-2 Number-4 Issue-7 December-2012.
[14] Meenal Jain, Sumit Sharma, Ravi Mohan Sairam, “Effect of Blur and Noise on Image Denoising based on PDE”, International Journal of Advanced Computer Research (IJACR) Volume- 3 Number-1 Issue-8 March-2013.
[15] Meenal Jain, Sumit Sharma, Ravi Mohan Sairam, “Result Analysis of Blur and Noise on Image Denoising based on PDE”, International Journal of Advanced Computer Research (IJACR) Volume-2 Number-4 Issue-7 December-2012.
[16] David L.Donoho and Iain M.Johnstone, 1994, “Ideal spatial adaptation via waveletshrinkage”, Biometrika, Vol.81, pp.425-455.
[17] Raghuveer M.Rao and Ajit S.Bobaradikar, 1998, “Wavelet transforms: Introduction to theory and applications”, Addison Wesley Longman Inc.pp.183-189.
[18] Saeid Fazli, Hamed Bouzari and Hamed Moradi pour, “Complex PDE Image Denoising Based on Particle Swarm Optimization”, 2010 International Congress on Ultra-Modern Telecommunications and Control Systems and Workshops (ICUMT).
[19] Changsheng Lang, Guangzheng Li , Jianhong Li, Xiujuan Zhao,” Combined Transform Image Denoising based on Morphological Component Analysis”, IEEE 2011.
[20] Kehua Su, Hongbo Fu, Bo Du, Hong Cheng, Haofeng Wang and Dengyi Zhang, “Image Denoising based on Learning Over-complete Dictionary”, 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2012).
[21] Guo-Duo Zhang, Xu-Hong Yang, Hang Xu, DongQing Lu, Yong-Xiao Liu, “Image Denoising Based On Support Vector Machine”, IEEE 2012.
[22] Jia Liu, Caicheng Shi and Meiguo Gao, “Image Denoising Based on BEMD and PDE”, IEEE 2011.
[23] R. G. Baraniuk, “Optimal tree approximation with wavelets,” in Proc. SPIE Tech. Conf.Wavelet Applications Signal Processing VII, vol. 3813, Denver, CO, 1999, pp. 196-207.
[24] J. Lu, J. B.Weaver, D.M. Healy, and Y. Xu, “Noise reduction with multiscale edge representation and perceptual criteria,” in Proc. IEEE-SP Int. Symp. TimeFrequency and Time- Scale Analysis, Victoria, BC, Oct. 1992, pp. 555–558.
[25] D. L. Donoho, “CART and best-ortho-basis: A connection,” Ann. Statist., pp. 1870–1911, 1997.
[26]. R. W. Buccigrossi, and E. P. Simoncelli, „Image compression via joint statistical characterization in the wavelet domain‟, IEEE Image Process., Vol. 8, No 12, Dec.1999, pp. 1688- 1701.
[27]. J. K. Romberg, H. Choi, and R. G. Baraniuk, “Bayesian tree-structured image modeling using wavelet-domain hidden Markov models”, IEEE Image Process., Vol. 10, No 7, Jul. 2001, pp. 1056- 1068.
[28]. H. A. Chipman, E. D. Kolaczyk, and R. E. McCulloch: “Adaptive Bayesian wavelet shrinkage”, J. Amer. Stat. Assoc., Vol. 92, No 440, Dec. 1997, pp. 1413-1421.
[29]. P. Moulin and J. Liu, “Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors”, IEEE Infor. Theory, Vol. 45, No 3, Apr. 1999, pp. 909-919.
[30] M. K. Mihcak, I. Kozintsev, K. Ramchandran, and P. Moulin, "Low-Complexity Image Denoising Based on Statistical Modeling of Wavelet Coefficients," IEEE Signal Processing Lett. (to appear).
[31] Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.P., “Image Denoising using Gaussian Scale Mixtures in the Wavelet Domain”, TR2002-831, Computer Science Dept, New York University.
2002.
[32] V. Strela, J. Portilla, and E. P. Simoncelli, “Image denoising via a local Gaussian scale mixture model in the wavelet domain,” in Proc. SPIE 45th Annu. Meeting, San Diego, CA, Aug. 2000.
9
[33] E. P. Simoncelli and E. Adelson, “Noise removal via Bayesian wavelet coring,” in Proc. IEEE International Conference on Image Processing, Lausanne, Switzerland, September 1996, pp. 279–
382.
[34] S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Processing, vol. 9, pp. 1522–1531, Sept. 2000.
[35]J. Romberg, H. Choi and R. G. Baraniuk, "Bayesian wavelet domain image modeling using hidden Markov models," IEEE Transactions on Image Processing, vol. 10, pp. 1056-1068, July 2001.
[36] M. Malfait and D. Roose, “Wavelet based image denoising using a Markov Random Field a priori model,” IEEE Transactions on Image Processing, vol. 6, no. 4, pp. 549–565, 1997.
[37] M. Jansen and A. Bulthel, “Empirical bayes approach to improve wavelet thresholding for image noise reduction,” Journal of the American Statistical Association, vol. 96, no. 454, pp. 629–
639, June 2001.
[38] A. Jung, “An introduction to a new data analysis tool: Independent Component Analysis”, Proceedings of Workshop GK "Nonlinearity" - Regensburg, Oct. 2001.
[39] A. Hyvärinen, E. Oja, P. Hoyer, and J. Hurri, “Image feature extraction by sparse coding and independent component analysis”, In Proc. Int. Conf. on Pattern Recognition (ICPR'98), pp. 1268-1273, Brisbane, Australia, 1998.
[40] Nason, G.P., “Fast cross-validatory choice of wavelet smoothness, primary resolution and threshold in wavelet shrinkage using the KovacSilverman algorithm”, Technical report, Department of Mathematics, University of Bristol, United Kingdom.
Anjali Khare received the B.E. degree from the Department of Information Technology Engineering, Rajiv Gandhi Prodhougiki Vishwavidhyalaya Bhopal. Her research interests include image processing, computer graphics, and associated VLSI architectures.
