Loss Less Image firmness comparision by DPCM and DPCM with LMS Algorithm

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1 Lo Le Image firmne compariion by DPCM and DPCM with LMS Algorithm Pramod Kumar Rajput 1 and Brijendra Mihra 2 1,2 Department of Electronic & Communication, Nagaji Intitute of Technology and Management Datia, M.P , india Abtract In thi paper we compare the compreed image for 1 and 3, bit (2, 4 and 8 quantization level, repectively), etimation error and average quare ditortion uing DPCM with fixed coefficient and uing DPCM with LMS algorithm. The LMS algorithm may be ued to adapt the coefficient of an adaptive prediction filter for image ource encoding. Reult are preented which how LMS may provide more reduction in tranmitted image compare to DPCM when ditortion level are approximately the ame for both method. Alternatively, LMS can be ued in fixed bit-rate environment to decreae the recontructed image ditortion and prediction mean quare error. When compared DPCM and DPCM with LMS, recontructed image ditortion i reduced and the prediction mean quare error i reduced uing DPCM with LMS.The LMS algorithm i eay to implement and computationally inexpenive. Thi feature make the LMS algorithm attractive for image compreion compare to only DPCM. The LMS Filter length wa taken to be fixed tap. The parameter of LMS algorithm µ wa et to be.0006 and thi provide the good reult. Thi i preenting the performance of uing DPCM, uing DPCM with LMS algorithm for lo le image compreion. Keyword-Compreion; DPCM; LMS; Average quare ditortion. I. INTRODUCTION Compreing an image i ignificantly different than compreing raw binary data. Of coure, general purpoe compreion program can be ued to compre image, but the reult i le than optimal [1]. Thi i becaue image have certain tatitical propertie which can be exploited by encoder pecifically deigned for them. Alo, ome of the finer detail in the image can be acrificed for the ake of aving a little more bandwidth or torage pace. Thi alo mean that loy compreion technique can be ued in thi area. Lole compreion involve with compreing data which, when decompreed, will be an exact replica of the original data. Thi i the cae when binary data uch a executable, document etc. are compreed. They need to be exactly reproduced when decompreed. On the other hand, image (and muic too) need not be reproduced 'exactly'. An approximation of the original image i enough for mot purpoe, a long a the error between the original and the compreed image i tolerable. A two-layer image compreion device i dicloed with a halftone circuit, an invere halftone circuit and a quantization circuit. In thi circuit, the halftone circuit convert the input gray-cale image into a binary image and rearrange the binary image output equence to erve a a bae layer of the input gray-cale image. The invere halftone circuit recover a predicted image from the binary image uing the LMS algorithm. The quantization circuit then compare the input gray-cale image with the predicted image and encode the difference between them to obtain an enhancement layer of the input gray-cale image. In DPCM, a prediction of the next ample value i formed from pat value. Thi prediction can be through of a intruction for the quantizer to conduct it earch for the next ample value in a particular interval [2]. By uing the redundancy in the ignal to form a prediction, the region of uncertainty i reduced and the quantization can be performed with a reduced and the quantization can be All right Reerved 21

2 with a reduced number of deciion (or bit) for a given quantization level or with reduced quantization level for a given number of deciion(or bit). The reduction in redundancy i realized by ubtracting the prediction from the next ample value. Thi difference i called the prediction error. II. THE IMAGE COMPRESSION PRINCIPLE In a communication environment, the difference between adjacent time ample for image i mall, coding technique have involved baed on tranmitting ample-to-ample difference rather than actual ample value [3]. Succeive difference are in fact a pecial cae of a cla of non-intantaneou converter called N-tap linear predictive coder. Thee coder, ometime called predictor-corrector coder, predict the next input ample value baed on the previou input ample value. Thi tructure i hown in figure 1. In thi type of converter, the encoder form the prediction error (or the reidue) a the difference between the next meaured ample value and the predicted ample value. The equation for the prediction loop i.... (1) + Q Predict and compare loop LMS Predictor + Predict and correct loop + FIGURE : N-tap predictive differential pule code modulator (DPCM) for image compreion ytem Where Q=Quantizer, x i the nth input ample, y i the predicted value, and e i the aociated prediction error. Thi i performed in the predict-and-compare loop, the loop hown in figure 1. It prediction by forming the um of it prediction and the prediction error. (2).(3) Where quant (.) repreent the quantization operation, e q i the quantization verion of the prediction error, and x i the corrected and quantized verion of the input ample. Thi i performed in the predict-and-correct loop. The communication tak i that of tranmitting the difference (the error ignal) between the prediction and the actual data ample. For thi reaon, thi cla of coder i often called a differential pule code modulator (DPCM) [4], [5], [6], [7]. If the prediction model form prediction that are cloe to the actual ample value, the reidue variance (relative to the original ignal). The predictive converter mut have a hort term memory that upport the real-time operation required for prediction algorithm. In addition, they will often have a long-term memory that upport the low time, often data-dependent operation, uch a automatic gain control and filter All right Reerved 22

3 Predictor that incorporate the lower, data-dependent adjutment algorithm are called adaptive predictor. Simply, the adaptive filter i elf adjuting hence the name adaptive. In an image compreion, a model of predict and correct loop may vary continuouly hence the model to be updated continuouly. Thi i done by adaptive filtering algorithm. III. PSYCHONALYSIS OF DPCM In DPCM we tranmit not the preent ample x, but e (the difference between x and it predicted value y). At the receiver, we generate y from the pat ample value to which the received x i added to generate x. There i, however, one difficulty aociated with thi cheme. At the receiver, intead of the pat ample x(n-1),x(n-2),.., a well a e,we have their quantized verion x ( n 1), x ( n 2),... Thi will increae the error in recontruction. In uch a cae, a better trategy i to determine y, the etimate of x (intead of x), at the tranmitter alo from the quantized ample x ( n 1), x ( n 2),... The difference e=x-y i now tranmitted via PCM [10]. At the receiver, we can generate y, and from the received e, we can recontruct x. Figure 2. N-tap predictive differential pule code modulator (DPCM) The difference of the original image data, x and y prediction image data e i called etimation reidual, e. So e = x y (4) i quantized to yield (5) Where q i the quantization error, e q quantized ignal. And (6) The prediction output y i fed back to it input o that the predictor input i x (7) IV. LMS ALGORITHM FOR FIRMNESS It i een that the image prediction y i formed in a linear manner at the output of the LMS filter: (8) All right Reerved 23

4 In equation (8) the w k are N adaptive predictor coefficient, the x are the recontructed image data, and k i 1, 2.N integer value which elect the previou image pixel on which bae the current prediction. The quantized reidual i alo ued to update the predictor coefficient for the next iteration by the well known leat mean quare (LMS)[8], [9], [11] algorithm (10) The parameter µ i known a the tep ize parameter and i a mall poitive contant, which control teady-tate and convergent mean-quare reidual characteritic of the predictor. The LMS algorithm i an approximation to the gradient earch method for iteratively computing the N optimal w coefficient which minimize the mean quare prediction reidual. V. SIMULATION PARAMETERS In thi thei ha ued the fixed weight coefficient DPCM [13] and adaptive tap weight coefficient LMS parameter. Thi parameter ha been hown in bellow table. Thee parameter are the reulted parameter of our imulation for DPCM and LMS algorithm [12]. TABLE1:PARAMETER VALUE /CONFIGURATION AND RESULTS OF DPCM AND USING DPCM WITH LMS ALGORITHM Parameter 1bit/pixel recontructed Image ize 3bit/pixel recontructed Image ize 1bit/pixel ditortion level 3bit/pixel ditortion level DPCM DPCM with LMS 34.4 kb 29.3 kb 38.9 kb 34.7 kb -24 db -26 Db -27 db Db Tap Weight coefficient W=[.395 W=[one(1,t value.570] ap )] No of Bit 1, 2, 3 bit 1, 2, 3 bit Quantization level 2, 4, 8 level 2, 4, 8 level LMS Parameter ( µ) VI. REPRODUCTION AND EXAMINATION OF RESULT The LMS algorithm wa imulated uing Matlab with repected to the application of image compreion comparion uing DPCM with LMS algorithm depicted in figure 1. LMS algorithm i eay to implement and computationally inexpenive. Thi feature make the LMS algorithm attractive for image All right Reerved 24

5 Average Square Ditortion[dB] International Journal of Modern Trend in Engineering and Reearch (IJMTER) Simulation involving real image input ignal conited of ample point. Filter length wa taken to be 420 tap. The parameter of LMS algorithm µ wa et to be.0006 and.001. The original image i hown in figure 6.1. Thi image ize i 83.6 kb. Thi original image paed with the reidual quantizer coniting of b=1, 2 and 3 bit(2, 4 and 8 quantization level, repectively) uing DPCM with LMS algorithm adaptive coefficient w. The characteritic of the quantizer follow the Laplacian denity model [6]. The coefficient of the fixed DPCM predictor were choen in accordance with the globally optimum model [7] and fixed coefficient value taken by w=[ ] The dynamic range of the data wa eight bit from grey level 0 to 399. The imulation reult hown in bellow figure. Figure 3 plot the average quare ditortion veru tranmitted bit rate for the Rt image. All value of average quared error in db referenced to the performanced of the 1bit/pixel fixed coefficient predictor. The bit rate i in bit/ pixel and i controlled by the number of level in the quantizer. The top graph i for the fixed DPCM predictor and the lower i for LMS with µ=.0006-value. The LMS filter wa initialized at the beginning of the picture reception. In fact, the DPCM at 3bit/pixel ha approximately the ame ditortion than LMS 1 bit/pixel. The rabt image more compre 1bit/pixel LMS compare to 3bit/pixel DPCM with approximately ame ditortion level. The difference of 1bit/pixel LMS to 3bit/pixel DPCM i 9.6 kb more in 1bit/pixel LMS. Latly, the viual characteritic of LMS ditortion are preented in figure 3, diplaying the reult for 3 bit/pixel and 1 bit/pixel tranmiion. At 3 bit/pixel, comparing the LMS predictor figure 4(a) and the DPCM prediction figure 4(b) how there i no ignificant viual different between either method or original Rt image. How ever, a the bit rate i decreaed to 1 bit/pixel, there i ignificance difference between the LMS proceing and that uing DPCM. Figure 4(c) diplay the recontruction uing LMS, which provide a ignificantly harper image than that hown in figure 4(d) which reult of uing 1 bit/pixel DPCM. Figure 5.Thee figure how le PMSE of LMS compare to DPCM Average quare ditortion veru tranmitted bit rate DPCM LMS bit/pixel Figure 3. Average Square ditortion veru tranmiion bit All right Reerved 25

6 Original image compreed image compreed image (a)3 bit/pixellms (b)3 compreed image compreed image ( c)1 bit/pixellms (d)1 Figure 4. Viual reult for proceing rabt image with LMS and All right Reerved 26

7 PMSE [db] International Journal of Modern Trend in Engineering and Reearch (IJMTER) Compariion of PMSE 3bit/pixelLMS 1bit/pixelDPCM ample number Figure 5. Comparion of PMSE uing 1bit/pixel DPCM and 3bit/pixel LMS. VII. CONCLUSION A comparion on uing DPCM and uing DPCM with LMS algorithm with repect to image compreion ha been carried out baed on their coefficient and the number of bit. The reult how that the LMS algorithm ha the leat computational complexity. Reult are preented which how LMS may provide almot 2 bit/pixel reduction in tranmitted bit rate compared to DPCM when ditortion level are approximately the ame for both method. The LMS can be ued in fixed bit rate environment to decreae the recontructed image ditortion. If the ame ditortion level for 3bit/pixel DPCM and 1bit/pixel LMS then LMS provide 9.6kB more reduction compare to DPCM. REFERENCES [1] S. ANNADURAI and R. SHANMUGALAKSHMI Fundamental of digital image proceing Publihed by Dorling Kinderley (India) 7. [2] E. A. Rikin, "Optimum bit allocation via the generalized BFOS algorithm,'' IEEE Tranaction on Information Theory, vol. 37, pp. -402, Mar [3] Digital Image Proceing - A Remote Sening Perpective, Jhon R. Jenon, 3rd Edition, Prentice Hall, 3. [4] A. Habbi, Comparion of Nth-order DPCM encoder with linear tranformation and block quantization technique, IEEE Tran. Commun., vol. COM-19, pp , Dec [5] S.Haykin and T.Kailath Adaptive Filter Theory Fourth Edition. Prentice Hall, Pearon Eduaction 2. [6] S. T. Alexander and S. A. Rajala, Analyi and imulation of an adaptive image coding ytem uing the LMS algorithm, in Proc IEEE Int. Conf. Acout., Speech Signal Proceing, Pari, France, May [7] KMM et al., Deign and Fabrication of Color Scanner, Indian Journal of Technology, Vol 15, Apr [8] Fundamental Of Digital Image Proceing - Anil K. Jain, Prentice-Hall, [9] Digital Image Proceing - R.C. Gonzalez Wood, Addion Weley, 1992 [10] B. P. Lathi and Zhi ding Modern Digital and Analog Communication Sytem International Fourth Edition. New York Oxford Univerity Pre-2010, pp.292. [11] J. E. Modetino, and D. G. Daut, Source-channel coding of image, IEEE Tran. Commun., vol. COM-27, pp , Nov [12] Ranbeer Tyagi, Rohit yadav and Shekhar Sharma, Image Compreion Uing DPCM with LMS Algorithm Journal of Communication and Computer (2011) [13] Rime Raj Singh Tomar and Kapil Jain, Lole Image Compreion Uing Differential Pule Code Modulation and It Application International Journal of Signal Proceing, Image Proceing and Pattern Recognition Vol.9, No.1 (2016), All right Reerved 27