Image Noise Removal – The New Approach Anna Fabijańska, Dominik Sankowski Abstract – This paper is about reducing noise in digital rapidly. Moreover in case of real time processing all averaged images. Traditional methods of random noise removal are images have to be stored in image processing system memory. discussed. New noise reduction algorithm is proposed. In the following part of this paper the new approach to Results of introduced method are presented and compared image noise removal is presented. with results achieved with traditional approach. Keywords – Digital Image Processing, SNR, Random II. SIGNAL TO NOISE RATIO Noise, Noise Reduction, Image Enhancement. Each digital image has two main components: a stable signal and a random noise [8][9] in accordance with equation: I. INTRODUCTION L'(x, y) = L(x, y) + N(x, y) (1) Noise can seriously affect quality of digital images. There where: are numerous potential sources of noise. However, three L' digital image (noisy image); primary components of noise in CCD imaging systems [1 4] are: L signal component (signal only image); • photon noise N noise component; is fundamental property of the quantum nature of light and x, y is irreducible due to poissonian nature of counting pixel coordinates. photons; In case of multiple exposures the signal component of the • readout noise image remains the same but the noise component differs from is generated by the on chip output amplifier; can not be one image frame to another. completely removed from image; In order to quantify noise level signal to noise ratio (SNR) is used. The higher SNR value the better quality of the • dark noise analyzed image. Signal to noise ratio can be defined as is thermally generated charge that can be measured and follows: subtracted form the output image. σ 2 (L) Photon noise and readout noise in connection with SNR(L, L )' = 10log [dB] (2) erroneous signal fluctuations (due to CCD camera electronic 10 MSE(L, L )' components properties) can be considered as a random noise where: because it varies from image to image. Random noise presence 2 can seriously degrade the spatial resolution of digital images σ image variance; and can be a problem that often arises in case of low light MSE mean square error defined by equation 3. images. 1 Methods of random noise removal are to reconstruct the MSE(L, L )' = ∑ d 2 ()L(x, y), L (' x, y) (3) original (signal only) image. They can be divided into two K K main groups: image filtration and image averaging [5 7]. In Symbols used in equation 3 denotes respectively: the first method image is either convolved with Gaussian mask number of pixels in the image; or non linearly filtered (for example with median filter). K However, filtration affects with blurred appearance of an d the distance between signal only image image and in result compromises the level of details. and noisy image. Averaging the second method of random noise removal is In the following part of this paper signal to noise ratio is said to reduce noise level without compromising details. used to quantify and compare qualities of different noise However it involves at least several images of observed scene removal algorithms. and in consequence can not be used when view field changes III. ITERATIVE NOISE REMOVAL ALGORITHM Anna Fabijańska Technical University of Lodz, Computer Noise in digital images is intensity fluctuations. It manifests Engineering Department, Stefanowskiego Str., 18/22, Lodz, itself as single pixels much brighter or much darker than the 90 924, POLAND, E mail: [email protected] neighborhood. It means that erroneous pixels can be Dominik Sankowski Technical University of Lodz Computer considered as local extremes of image intensity. Particularly, Engineering Department, Stefanowskiego Str., 18/22, Lodz, pixels much brighter than their neighbors are local intensity 90 924, POLAND, E mail: [email protected] maxima and pixels much darker than their surrounding are
CADSM’2007, February 20-24, 2007, Polyana, UKRAINE local intensity minima. The new approach to noise removal is Experiments led to conclusion that the smaller the mask based upon afore mentioned remark. The algorithm block size, the faster algorithm works. In consequence mask size was diagram is presented in figure 1. set to 3x3. Proposed algorithm works iteratively. Every iteration Maps of local extremes indicate pixels which intensity consists of two stages. In the first stage maps of image should be changed. In consequence, intensities of local intensity local extremes are built. The first map ( Lmax ) maxima are decreased and analogously intensities of local indicates local maxima of image intensity, the second one minima are increased. ( L ) – local minima. The maps are given by equations (4) In successive iterations, processes of local extremes maps min construction and intensity values correction are repeated until and (5) respectively. the required image quality is achieved. 1 for L(x, y) ≥ L(x + i, y + j) max IV. RESULTS AND DISCUSSION −a≤i≤a;−b≤ j≤b (4) Lmax (x, y) = 0 for L(x, y) < max L(x + i, y + j) Results of iterative noise removal algorithm applied to −a≤i≤a;−b≤ j≤b exemplary image are shown in figure 2. Sub figure 2a presents original (signal only) image. In sub figure 2b image corrupted 1 for L(x, y) ≤ min L(x + i, y + j) by noise is presented. Following sub figures present results of −a≤i≤a;−b≤ j≤b noise removal. Different number of iterations is considered. L (x, y) = (5) min Number of iterations performed to remove noise is indicated 0 for L(x, y) > min L(x + i, y + j) −a≤i≤a;−b≤ j≤b in the figure description. Table 1 presents corresponding values of SNR obtained for increasing number of iterations. where: Iteration 0 indicates original noisy image (Fig. 2b).
m (6) a) b) a = 2
n (7) b = 2 Symbols m and n denote dimensions of image areas searched for local extremes. The areas are determined by mask that passes through the whole image row by row (or column by column) in accordance with the image filtration mechanism. c) d) START
Build map of intensity local minima
Build map of intensity local maxima Increase intensity e) f) of local minima
Decrease intensity of local maxima
Satisfying image quality YES NO Fig.2. Iterative noise removal; a) original signal only image; STOP b) original noisy image; c) noise removal result, 3 iterations; d) noise removal result, 5 iterations; e) noise removal result, 7 iterations; Fig.1. Block diagram of iterative noise removal algorithm. f) noise removal result, 10 iterations.
CADSM’2007, February 20-24, 2007, Polyana, UKRAINE Analysis of the results presented in figure 2 and table 1 leads to conclusion that for appropriately selected number of iterations presented algorithm improves significantly SNR SNR = 71.17 dB value. Experiments have shown that maximum signal to noise ratio is achieved for 3 4 iterations. For higher number of iterations quality of reconstructed image decreases. The details are lost. (4 iterations) TABLE 1
Iterative noise removal ITERATIVE NOISE REMOVAL – SNR VALUES OBTAINED FOR DIFFERENT NUMBER OF ITERATIONS .
Number of iterations SNR [dB] SNR=43.16 dB 0 47.67 1 56.59 2 64.60 3 69.81 4 71.17 (mask size: 3x3) Median filtration 5 69.47 7 61.84 10 46.16 In the following section of this paper, proposed algorithm is SNR=36.75 dB compared with common methods of image noise removal. V. COMPARISON WITH TRADITIONAL APPROACH Table 2 presents results of noise reduction due to different algorithms usage. The first column indicates method used for (mask size: 5x5) Median filtration noise removal. Author’s method, median filtration and Gaussian filtration are considered. In the second column, result of algorithm usage can be seen. Exemplary image from figure 2b was used as an original noisy image. Comparison of algorithms qualities is made by means of SNR value that is placed in the last one column. SNR=80.60 dB It can be easily seen that author’s approach to noise removal affects with significant signal to noise ratio improvement. Achieved results are far better than in case of median filtration (SNR value is almost twice higher). Only Gaussian filtration
using 3x3 size mask results with signal to noise ratio higher (mask size: 3x3) Gaussian filtration than the one achieved with presented method. However, it should be pointed out that Gaussian filtration compromises TABLE 2
NOISE REMOVAL ALGORITHMS COMPARISON
SNR=71.09 dB Method Noise removal effect SNR
SNR = 47.67 dB (mask size: 5x5) Gaussian filtration
details much more than the iterative approach. Moreover
Original noisy image Gaussian filter makes image looks blurry. In case of author’s method sharpness of reconstructed image is far better. Furthermore more details are visible.
CADSM’2007, February 20-24, 2007, Polyana, UKRAINE REFERENCES CONCLUSIONS [1] H. F. Michael, F. Wilkinson, F. Schut (ed): “Digital In this paper problem of noise in digital images was image analysis of microbes”, John Wiley and Sons, 1998. discussed. Particular attention was paid to random noise. [2] R. D. Goldman, D. L. Spector: “Live cell imaging: Custom methods of random noise removal were mentioned. a laboratory manual”, CSHL Press, 2004. The author’s algorithm of random noise removal was [3] S. F. Ray: “Scientific Photography and Applied Imaging”, introduced. Proposed method in successive iterations Focal Press, 1999. constructs consecutive approximations of image signal [4] J. R Janesick: “Scientific Charge Coupled Devices” component. Results of author’s method were presented and SPIE International Society for Optical Engine, 2001. compared with those achieved with traditional approach to noise removal. Median and Gaussian filtration were [5] R.C. Gonzalez, R. E. Woods: “Digital Image Processing considered. (2nd Edition)”, Prentice Hall, 2002. Analysis of obtained results leads to conclusion that for [6] B. Jähne: “Digital image processing“, Springer, 1991. appropriately selected number of iterations presented [7] R. A. Schowengerdt: “Remote sensing models and algorithm significantly improves signal to noise ratio. Results methods for image processing”, Elsevier, 1997. are far better than in case of median filtration. Moreover, the [8] L. Kurz, M. H. Benteftifa: “Analysis of Variqance in algorithm compromises details less than Gaussian filtration. Statistical Image Processing”, Cambridge University Proposed method can be particularly useful in case of noisy Press, 1997. images presenting different details. However, it can be also [9] V. Madisetti, D. B. Williams (ed): “The digital signal successfully used in all digital image processing and analysis processing handbook”, CRC Press, 1998. applications as a part of image enhancement process.
______ European Social Fund and Polish State have supported this work in the frame of “Mechanizm WIDDOK” programme (contract number Z/2.10/II/2.6/04/05/U/2/06) .
CADSM’2007, February 20-24, 2007, Polyana, UKRAINE