Image denosing in underwater acoustic noise using discrete wavelet transform with different noise level estimation

Image denosing in underwater acoustic noise using discrete wavelet transform with different noise level estimation Yasin Yousif A l-Aboosi, Radhi Sehen I ssa, Ali k halid Jassim Faculty of En gineering, Univer sity of Mustansir iyah, Iraq ABSTRACT In many applications, Image de-noising and improvement represent essential processes in presence of colored noise such that in unde rwater. Power spec tral density of the noise is changeable within a definite frequency range, and autocorrelation noise function is does not like delta function. So, noise in underwater is characteriz ed as colored noise. In this paper, a novel image de-noising method is proposed using multi-level noise power estimation in discr ete wavelet transform with different basis functions. Peak si gnal to noise rat io (PSNR) and m ean squared error represented performance me asures that the results of this study depend on it. The results of various bases of wavelet such as: Daubechies (db), biorthogonal (bior.) and s ymlet (sym.), show that denois ing process that uses in this method produces extra prominent ima ges and improved values of PSNR than other methods. 1. INTRODUCTION Efficient underwater image denoising is a critical aspect for m any applications [ 1]. Underwater images present two main problems: light scattering that alters light path direction and color change. Th e basic processes in underwater light propa gation are scattering and absorption. Underwater noise generall y originates from man-made (e.g. shipping and machiner y sounds) and natural (e.g. wind, seism ic and rain) sources. Underwater noise reduces image qualit y [1, 2], and de noising has to be applied to improve it [3]. Underwater sound attenuation is dependent on frequenc y. Consequently, pow er spectral density (PS D) for ambient noise is defined as colored [4]. Many image denoising techniques are described in [5-9]. A method based on adaptive wavelet with adaptive thr eshold selection was su ggested i n [5] to overcome the underwater im age denoising problem. Assume that an underwater image has a small signal - to -noise ratio (SNR) and image qualit y is poor . The simulation results s how that the proposed m ethod successfull y eliminates noise, improves the p eak S NR (PSNR) output of the image and produces a high - quality im age. Light is repeatedly deflected and reflected by ex isting particles in the water due to the light scattering ph enomenon, which degrades the visibility and contrast of underwater images. Therefore, under water images exhibit poor quality . To process im ages further, w avelet transform and Weber’s law we re proposed in [8]. Firstly, seve ral pre -processing methodologies were conduc ted prior to wavelet denoising thresholdi ng. Then, Weber’s law was u sed for image enhancement along with wavelet transform. Consequentl y, the recovered images were enhanced and the noise level was reduced. In the current stud y, a novel image denoising method is proposed in the p resence of underwater noise using a pre-whitenin g filter and disc rete wavelet transform (DWT) with single-level estimation. 2. Ambient Noise Characteris tics The characteristics of underwater noise in seas h ave been dis cussed ex tensively [10]. Such noise has four components: turbulence, shipping, wind and thermal noises. Each component occupies a certain frequency band of spectrum. The PSD of each component is expressed as [11-13]. where f represents th e frequency in KHz. Therefore, the total PSD of underwater noise for a given frequency f (kHz) is Each noise source is dominant in certain frequency bands, as indicated in Table 1. 3. Image Mode l in Presence of Colored Noise Noise interference is a common problem in digital communication an d image processing. An underwater noise m odel f or ima ge denoisin g in an additive coloured noise channel is presen ted in this section. Numerous appli cations assume tha t a received im age can be expressed a s follows: where  󰇛 󰇜 is the original image and  󰇛󰇜 denotes underw ater noise. Hence, denoisi ng aims to eliminate the corruption degree of  󰇛  󰇜 caused by  󰇛  󰇜  The pow er spectrum and autocorrelation o f additive whi te Gaussian noise (A W GN) are expressed a s [ 14 ]: The PSD of A W GN remains constant across the entire frequency range, in which all ranges of frequencies hav e a magnitude o f    . The probability distribution function   󰇛󰇜 for A W GN is speci fied by [ 15 ] where   represents t he standard deviation. W ith regard to autocorrelation functions, the de lta function indicates that adjacent samples are independent. Therefore, observed samples are considered independent and identically distributed. Underw ater noise is dependent on frequency [ 16 , 17 ]; and it i s suitably modelled as col ored noise [ 1 , 2 , 18 ]. The P SD of colou red noise is defined a s [ 19 , 20 ] Howev er, the   󰇟󰇠 of coloured noise is not like a delta function, bu t, it is takes the formula o f a 󰇛󰇜 function [ 14 , 19 ] . In contrast to A W G N, noise sa mples are cor r elated [ 20 ]. 4. Image Deno ising Wavelets are used in image processin g for sample edge detection, watermarkin g, compression, denoisin g and coding of interesting f eatures f or subsequent classi fication [ 21 , 22 ]. The following subsections discuss image denoising by thresholding the DWT co efficients . 4.1 DWT of an image data An image is p resented as a 2D array of coefficients. Each coe fficient represents the brightness de gree atthat point. Most he rbal photographs exhi bit smooth col ouration variation swith ex cellent details represented as sharp ed ges among easy versions. Clean varia tions in colouration can be strictly labell ed as low-frequency v ersions, whereas pointy variations can be labelled as ex cessive- fre quency versions. The low- frequency component s (i.e. smooth v ersions) establish the base of a photograph , whereas the excessiv e-frequency components (i.e. the edges that prov ide t he details) are uploaded upon the low-frequency component s to refine the image, thereby producing an in- depth image. There fore, the easy versio ns are more importan t than the details. Numerous methods can be used to distin g uish be tween easy variati ons and photograph information . One example of these methods is picture decomposi tion via DWT remod elling. The di fferent decomposition lev els of D W T are shown in Figur e 1. Figure.1 D W T Deco mposition lev els 4.2 The Inverse DWT of an image Different classes of data are collected into a r econstructed image by using reverse wavelet transform. A pair of hig h- and low-pass f ilters is also used during the reconstruction process. This pai r o f filters is referred to as t he synthesis filter pa ir. The filtering p r ocedure is simply the opposite of transformatio n; that is, the procedure start s from the highest level. The filters are firstly applied column-wise and then row-wise lev el by level until the low est level is reached . 5. Proposed Method In this paper, t he D W T is used for th e transformation o f i mage in the process of denoisi ng. The advantages o f used multi level threshold estimation in denoising process to reduce the required of the use of the prewhiteni ng sta ge in case of usi ng single level threshold estimation [ 23 ]. The follow ing steps describe the image den oising procedure . 1. The D W T of a noisy image is computed. The W T is (t ime-frequency distribution) that used to de compose signal i nto family o f function s localiz e in frequency and time. The C W T can be described as: (11) where  is shifting in time and a is scale factor or dilation factor and h(t) is represent basis function. Debauchies, Coiflet, Symlet , an d Biorthogonal represent examples of functions used in C W T as show n in Figure 2. Figure.2 Some basis f unctions used in WT are: (a) Haar (b ) Symlet 6 (c) Debauchies 6 (d) Biorthogonal 1 .5 [ 24 ] 2. After the D W T representation done, de -noising is done using soft - threshol ding by m odified universal threshold esti mation (MUTE). Providing ambient noise is a colored, a threshold dependent on level applied to each level of frequency was proposed in [ 25 ]. The value of threshold applied to the coefficients of es timated time – frequency using MUTE [ 25 ] is expressed as (12) where N is len gth of signal,   is noise es timated s tandard deviatio n for level k, and c is the (modified universal threshold f actor)      . The standard deviation for noise at each level is:     󰇛 󰇛   󰇜 󰇜   (13) where 󰇛   󰇜 represents all the coe f ficients for fre quency lev el k [ 26 ]. The value of threshold   is used t o removing the noise and also for effici ent recover original signal. The threshold factor c is used to improve f urther perfor mance of denoising [ 27 ] . The value of c is calculaed g radually by increment it of 0.1 for each level to obtain the best results at highest PSNR. 3. after value s of threshold   is determine d f or all componen ts, the components representations of time – frequency after hard - thresh olding are   󰇛 󰇜   󰇛   󰇜   󰇛   󰇜        󰇛   󰇜     (14) and the components after soft - threshol ding are ((15) where   denotes the thres hold value in level k. 4. The image is r econstr ucted by applying inverse D W T to obtain the denoised image. The IWT is expressed a s:  󰇛  󰇜     󰇛   󰇜                   (16) Figure 3 shows the data flow diag ram of the ima ge denoising process. Figure.3 Data flow diagram of i mage denoisin g using Level-Dependent Estima tion Discrete W avel et Transform . 6. Performance Measures Common measurement para m eters for ima ge reliability i nclude mean absolute error, normalized MSE (NMS E), PSNR and M SE [ 28 ]. An SNR over 40 dB provi des excel lent i m age quality tha t is cl ose to tha t of the ori ginal image ; an SNR o f 30 – 40 dB typical ly produces good image q uality with accept able distortion; an SN R o f 20 – 30 dB presents poor ima ge quality; an SNR below 20 dB generates an unacceptable image [ 29 ]. T he calculation m ethods of PSNR and NMSE [ 30 ] are presented as follow s: where MSE is the MSE between the original image (  ) and the denoised image (   ) with size M × N: 7. Results and Discussion MATLAB is used as the experimental tool for simulation, and simulatio n experi ments a re performed on a diver image to confirm the validity of the al gorithm. The simulations are achieved at PSNR ranging from 30 dB to 60 dB by changing noi se power fr om 0 dB to 15 dB. The applied order of t he whitening filter is 10. Diff erent denoisin g wavelet biases (i.e. Debauchies, biorthogona l 1.5 and symlet) are tested on an image with underwater noise v ia numerical simulation. As shown in Figure 4, soft thresholding and four decomposition levels are used. Biaes type Noisy image De -noise image PSNR (dB) Sym4 45.7 dB Sym4 29.01dB   45.77 dB   28.96 dB Biort hogonal 1.3 45.27 dB Biort hogonal 1.3 28.97dB Figure.4 Simula tion results on div er image using d ifferent wav elet biases. Tables 2, 3 and 4 show the performance of the proposed method on vario us noise power based on the Debauchies, symlet and biorthogonal wav elet biases, respectively. The PSN R and MSE values are calculated based on each no ise power val ue. Table 2 Perfor mance results of PSNR and MSE on div er image based on D ebauchies wavel et bias Noise power (db) PSNR MSE 0 59.35 0.0756 3 55.57 0.2161 5 52.3 0.5226 10 42.9653 0.5062 15 33.2530 0.8279 Table 3 Perfor mance results o f PSNR and MSE on diver image based on sy m let wavelet bias Noise power (db) PSNR MSE 0 61.066 0.0759 3 55.48 0.2948 5 52.032 0.5509 10 43.33 0.4420 15 35.0591 0.392 Table 4 Perfor mance results o f PSNR and MSE on diver image based on bi orthogonal wavel et bias Noise power (db) PSNR MSE 0 59.7560 0.0773 3 55.76 0.321 5 52.867 0.5240 10 43.7970 0.767 15 35.125 0.8604 8. Conclusion Underwater noise is mainly characterised as non -white and non-Gaussian noise. Therefore, traditional methods used for image denoi sing using wav elet transform underw ater are inefficient because these methods use multi - level estimation discrete wavelet transform for noise variance . 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