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Daljit Singh, Sukhjeet Kaur Ranade / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1736-1741 Comparative Analysis of Transform based Lossy Image Compression Techniques Daljit Singh*, Sukhjeet Kaur Ranade** *(Department of Computer Science, Punjabi University, Patiala) ** (Asst.Prof. Department of Computer Science, Punjabi University, Patiala)ABSTRACT We undertake a study of the performance can be removed when it is not needed or can bedifference of the discrete cosine transform (DCT) reinserted to interpret the data when needed. Mostand the wavelet transform for gray scale images. often, the redundancy is reinserted in order toWide range of gray scale images were considered generate the original data in its original form. Aunder seven different types of images. Image types technique to reduce the redundancy of data isconsidered in this work are standard test images, defined as Data compression [1]. The redundancy insceneries, faces, misc, textures, aerials and data representation is reduced such a way that it cansequences. Performance analysis is carried out be subsequently reinserted to recover the originalafter implementing the techniques in Matlab. data, which is called decompression of the data.Reconstructed Image Quality values for everyimage type would be calculated over particular bit Data compression can be understood as arate and would be displayed in the end to detect method that takes an input data D and generates athe quality and compression in the resulting shorter representation of the data c(D) with lessimage and resulting performance parameter number of bits compared to that of D. The reversewould be indicated in terms of PSNR , i.e. Peak process is called decompression, which takes theSignal to Noise Ratio. Testing is performed on compressed data c(D) and generates or reconstructsseven types of images by evaluating average the data D’ as shown in Figure 1. Sometimes thePSNR values. Our studies reveal that, for gray compression (coding) and decompression (decoding)scale images, the wavelet transform outperforms systems together are called a “CODEC”the DCT at a very low bit rates and typically gavea average around 10% PSNR performanceimprovement over the DCT due to its betterenergy compaction properties. Where as DCTgave a average around 8% PSNR performanceimprovement over the Wavelets at high bit ratesnear about 1bpp and above it. So Waveletsprovides good results than DCT when morecompression is required.Keywords - JPEG standard, Design metrics, JPEG2000 with EZW, EZW coding, Comparison between Fig.1 Block Diagram of CODECDCT and Wavelets. The reconstructed data D’ could be1. INTRODUCTION identical to the original data D or it could be an Data compression is the technique to reduce approximation of the original data D, depending onthe redundancies in data representation in order to the reconstruction requirements. If the reconstructeddecrease data storage requirements and hence data D’ is an exact replica of the original data D, thecommunication costs. Reducing the storage algorithm applied to compress D and decompressrequirement is equivalent to increasing the capacity c(D) is lossless. On the other hand, the algorithmsof the storage medium and hence communication are lossy when D’ is not an exact replica of D.bandwidth. Thus the development of efficient Hence as far as the reversibility of the original datacompression techniques will continue to be a design is concerned, the data compression algorithms canchallenge for future communication systems and be broadly classified in two categories – lossless andadvanced multimedia applications. Data is lossy [2].represented as a combination of information andredundancy. Information is the portion of data that Transform coding has become the de factomust be preserved permanently in its original form standard paradigm in image (e.g., JPEG [3], [4])in order to correctly interpret the meaning or purpose where the discrete cosine transform (DCT) is usedof the data. Redundancy is that portion of data that because of its nice decorrelation and energy 1736 | P a g e
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Daljit Singh, Sukhjeet Kaur Ranade / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1736-1741compaction properties [5]. In recent years, much of As summarized in the figure 2, JPEG Compressionthe research activities in image coding have been separates the image into the parts containing 8x8focused on the discrete wavelet transform. While the gray values. Discrete cosine transformation isgood results obtained by wavelet coders (e.g., the applied on each part to pass the frequency base onembedded zerotree wavelet (EZW) coder) are partly each. The reason why this transformation is chosenattributable to the wavelet transform. is coefficients are not complex but real numbers. The numbers obtained are quantized by utilizing a In this paper, we will study the table due to the ratio of the quality. QUANTIZERTransform based lossy image compression table determines how many of the high frequencytechniques and basic concepts to keep in mind for numbers will be abandoned. Some of the 64 pairs ofthe transform based image coding. the frequency coefficient obtained by discrete cosine transformation after QUANTIZING process will get The rest of the paper is organized as the zero value. The fact that these coefficients arefollows. In section 2 we discuss the design metrics. compressed by Huffman coding provides more placeThen we discuss JPEG Standard Image Compression seriously. When the image is intended to be obtainedin section 3. Then in section 4, we describe JPEG again, the reverse of this process will be applied2000 with EZW coding in detail. The comparison again. At first, Huffman code is encoded and thebetween DCT and Wavelets is explained in section block including 64 coefficients with the zeros are5. Finally conclusions are made in section 6. obtained. This block is multiplied by quantizing table. Most of the coefficients will get the value2. DESIGN METRICS closer to its initial value but the ones multiplied by Digital image compression techniques are zero will be zero again. This process determines theexamined with various metrics. Among those the losses that exist after discrete cosine process. So ifmost important one is Peak Signal to Noise Ratio we pay more attention, the losses occur in the(PSNR) which will express the quality. There exists quantizing process.another property which expresses the quality, that is,Mean Square Error (MSE). PSNR is inverselyproportional to MSE. The other important metric isCompression Ratio, which express the amount ofcompression embedded in the technique. The givenbelow are equations for PSNR and MSE: PSNR = 10 log10 (MSE) = ∑j,k(f[j,k]-g[j,k])2The higher the compression ratio reduces the imagequality. The given below is the formula to find thecompression ratio: Comp ratio = Original_size/compressed_size3. JPEG STANDARD All the compression algorithms dependon the human eye filtering. Human eye can notperceive from a proper level. Therefore, the graylevel values in the original image can be moved tothe frequency base. Some kind of coefficients willappear in the transformation that we use in thefrequency base. It’s possible to obtain the original Fig.2 JPEG compressionimage by using these coefficients again. However, Quantization is the main factor ofit’s unnecessary to benefit from infinite frequency compression. JPEG process uses varying levels ofcomponent. High frequency coefficients can be image compression and quality are obtainableabandoned by taking the risk of some losses. The through selection of specific quantization matricesnumber of the frequency abandoned shows the [6]. This enables the user to decide on quality levelsquality of the image obtained later. In the ranging from 1 to 100, where 1 gives the poorestapplications done, despite very little quality losses, quality and highest compression, while 100 gives theit’s possible to make the image smaller in 1:100 best quality and lowest compression.ratio. JPEG used commonly in the compression For a quality level greater than 50 (lessalgorithms works as shown in figure 2. compression, Higher image quality), the standard quantization matrix is multiplied by (100- qualitylevel)/50. For a quality level less than 50 1737 | P a g e
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Daljit Singh, Sukhjeet Kaur Ranade / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1736-1741(more compression, lower image quality), thestandard quantization matrix is multiplied by Table1. DCT Results50/quality level. Img No. Q=10 Q=30 Q=50 The given below is the original image and Type of img Av. Av. Av. Av. Av. Av.reconstructed images after applying 2D – DCT at s PSN Co PSN Co PSN Covarying levels of quantization matrices Q1, Q10, Q30 R mp R mp R mpand Q50 with PSNR values. The test is performed on (db) (db)standard image cameraman to explain this concept.The Q1 level gives more compression but lower Stand 7 29.49 17. 33.6 9.5 35.4 7.2quality but the Q50 level gives less compression but ard 23 5 1 6 1higher quality. imgs Scen 20 26.70 15. 29.8 7.6 31.9 5.8 eries 18 5 2 7 4 Faces 21 29.25 19. 31.9 10. 33.0 7.1 48 2 24 2 6 Sequ 23 26.38 11. 29.8 5.7 31.3 4.4 ences 65 3 5 2 9 Textu 20 22.09 7.9 25.6 4.1 27.7 3.3 res 5 9 4 2 8Original image Q=1, PSNR=16.89 Misc 15 28.75 16. 32.8 9.6 34.6 7.9 43 5 5 4 5 Aeria 20 27.71 16. 30.9 7.8 32.4 5.9 ls 56 6 9 5 1 4. JPEG 2000 WITH EZW CODING The JPEG committee has released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEGQ=10, PSNR=27.81 Q=30, PSNR=31.91 standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based on the wavelet transform, in contrast to the discrete cosine transform (DCT) used in the original JPEG standard. The state of wavelet-based coding has improved significantly since the introduction of the original JPEG standard. A notable breakthrough wasQ=50, PSNR=33.87 the introduction of embedded zero-tree waveletThe table 1 given below shows the average (EZW) coding by Shapiro [7]. The EZW algorithmcompression ratio and average PSNR of 7 different was able to exploit the multi resolutional propertiestypes of images, each type having a different number of the wavelet transform to give a computationallyof images. The Q1 level have higher compression simple algorithm with outstanding performance.but poor image quality i.e. lower PSNR value and Improvements and enhancements to the EZWQ50 level have the lower compression but higher algorithm have resulted in modern wavelet codersPSNR value. which have improved performance relative to block transform coders. As a result, wavelet-based coding has been adopted as the underlying method to implement the JPEG 2000 standard [8]. 4.1 EZW Coding Algorithm The EZW coding algorithm can now be summarized as follows. 1) Initialization: Place all wavelet coefficients on the dominant list. Set the initial threshold to T0=2floor( log2 xmax). 1738 | P a g e
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Daljit Singh, Sukhjeet Kaur Ranade / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1736-1741 Table2. EZW pseudocode 2) Dominant Pass: Scan the coefficients in mortan scan order using the current Initialization threshold Ti . Assign each coefficient one T0=2floor(log2(max(coefficients))) of four symbols: k=0 positive significant (ps): meaning Dominant List=All coefficients that the coefficient is significant Subordinate List=[] relative to the current threshold Ti and positive. Significant Map negative significant (ns): meaning for each coefficients in the Dominant List that the coefficient is significant if |x| ≥ Tk relative to the current threshold Ti if x> 0 and negative. set symbol POS isolated zero (iz): meaning the else coefficient is insignificant relative set symbol NEG to the threshold Ti and one or else if x is non-root part of a zerotree more of its descendants are set symbol ZTD(ZeroTree Descendant) significant. if x is zerotree root zero-tree root (ztr): meaning the set symbol ZTR current coefficient and all of its otherwise descendant are insignificant set symbol IZ relative to the current threshold Ti. . Dominant Pass Any coefficient that is the descendant of a if symbol(x) is POS or NEG(it is significant)coefficient that has already been coded as a put symbol(x) on the Subordinate Listzero-tree root is not coded, since the decoder Remove x from the Dominant Listcan deduce that it has a zero value. Coefficientsfound to be significant are moved to the subordinate Subordinate Passlist and their values in the original wavelet map are for each entry symbol(x) in Subordinate Listset to zero. The resulting symbol sequence is entropy if value(x) ϵ Bottom Half of [Tk , 2Tk]coded. output ”0” 3) Subordinate Pass: Output a 1 or a 0 for all else coefficients on the subordinate list output ”1” depending on whether the coefficient is in the upper or lower half of the quantization Update interval. Tk+1 = Tk/2 4) Loop: Reduce the current threshold by two, K = K+1 Ti = Ti/2. Repeat the Steps 2) through 4) until the target fidelity or bit rate is Go to Significance Map achieved.The pseudocode for the embedded zerotree codingis shown in the table 2 given below: The compression ratio and quality of the image depends on the quantization level, entropy coding and also on the wavelet filters used[9]. In this section, different types of wavelets are considered for image compression. Here the major concentration is to verify the comparison between Hand designed wavelets. Hand designed wavelets considered in this work are Haar wavelet, Daubechie wavelet, Biorthognal wavelet, Demeyer wavelet, Coiflet wavelet and Symlet wavelet. Except Coiflet and Symlet wavelet, all the Hand designed wavelets produced less PSNR around 28dB and compression ratio around 1bpp. Coiflet and Symlet wavelet produced high PSNR around 29 dB, at same compression ratio. The Cameraman images experimental results are shown in figure3 to 8. A 1739 | P a g e
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Daljit Singh, Sukhjeet Kaur Ranade / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1736-1741Number of test images are considered and the results compression. The wavelet transform achieves betteron cameraman image are presented in the table 3. energy compaction than the DCT [10] and hence can help in providing better compression for the same Peak Signal to Noise Ratio (PSNR).A comparative study of DCT and wavelet based image coding can be found in [11]. This section describes the comparison between DCT and Wavelets. Testing is performed on seven types of images at a bit rate of 0.25 bpp and 1.00 bpp. The results are shown in the tables 4 and 5 : Table4. Comparison between DCT and WaveletsFig3: Original image Fig4: Haar wavelets at a Bit rate of 0.25 bpp Image No. DCT Wavelets Types of imgs Av. PSNR Av. PSNR (db) (db) Stand imgs 7 25.46 28.01 Sceneries 20 23.76 25.16 Faces 21 28.62 29.82 Sequences 23 23.08 25.01 Textures 20 17.15 18.62Fig5: Daubechie Fig6: Coiflets Misc 15 21.07 27.36 Aerials 20 24.39 25.01 Table5. Comparison between DCT and Wavelets at Bit rate of 1.00 bpp Image No. DCT Wavelets types of imgs Av. PSNR Av. PSNR (db) (db) Stand imgs 7 33.87 31.12 Sceneries 20 29.59 26.20Fig7: Symlet Fig8: Dymer Faces 21 32.52 30.34 Table3. Comparison between Filters Sequences 23 28.14 27.13 Fil Ha Dau Bior Dy Coifl Syml Textures 20 21.39 20.05 ters ar bech thog mer et et Misc 15 33.06 30.17 ie nal Aerials 20 30.07 28.59 Org 5242 5242 5242 5242 5242 5242 size 88 88 88 88 88 88 6. CONCLUSION In this paper, we studied the two common Co 9136 1218 8736 9328 9083 9165 schemes used in JPEG. We considered the modular mp 8 72 0 8 2 6 design of the scheme and considered various size possible cases. The non-block schemes gave better performance but they were less computationally Co 5.77 4.30 6.00 5.62 5.77 5.73 efficient. The performance of algorithm with two mp 38 20 15 01 21 82 common transforms used was considered. It was rati observed that the wavelet transform gave a average o around 10% PSNR performance improvement over the DCT due to its better energy compaction PS 25.1 27.8 27.5 27.5 28.8 28.9 properties at very low bit rates near about 0.25 bpp. NR 1 9 5 9 2 3 While DCT transform gave a average around 8% PSNR performance over wavelets at high bit rates of 1 bpp. So Wavelets provides good results than DCT5. COMPARISON BETWEEN DCT AND when more compression is required. The methods ofWAVELETS encoding such as Embedded Zero tree and our Wavelet based techniques for image implementation of JPEG 2000 were considered. Acompression have been increasingly used for image comparative study based on transform filters, 1740 | P a g e
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Daljit Singh, Sukhjeet Kaur Ranade / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1736-1741computational complexity and rate-distortion Geoscience and Remote Sensing, Vol. 49,tradeoff is also presented. Some terms related to No. 1, January 2011, PP. 236-240.Transform based lossy image compression are [14] Independent JPEG Group, versionexplained in very simple language to help the 6a:http://www.ijg.org.beginners to have clear understanding of the topic. [15] Jianyu Lin, Member, IEEE, and Mark J. T. Smith, Fellow, IEEE,” New PerspectivesREFERENCES and Improvements on the Symmetric [1] Cebrail Taskin, Serdar Kursat Sarikoz, ”An Extension Filter Bank for Subband/Wavelet Overview of Image Compression Image Compression”, IEEE Transactions Approaches”, the Third International on Image Processing, Vol. 17, No. 2, Conference on Digital February 2008, PP.177-189. Telecommunications, 2008. [16] JPEG2000, [2] Abhishek Kaushik, Maneesha Gupta http://www.jpeg.org/JPEG2000.html. “Analysis of Image Compression [17] Rafeal C. Gonzalez, Richard E. Woods, Algorithms”, International Journal of “Digital Image Processing”, Third Edition, Engineering Research and Applications Pearson Education, 2010. Vol. 2, Issue 2,Mar-Apr 2012, pp.773-779. [18] Rohini S. Asamwar, Kishor M. Bhurchandi, [3] G. K.Wallace, “The JPEG still-picture and Abhay S. Gandhi, “Piecewise Lifting compression standard,” Commun.ACM, Scheme Based DWT to Model Human Vol. 34, pp. 30–44, Apr. 1991. Vision Interpolation Phenomenon”, [4] W. B. Pennebaker and J. L. Mitchell, JPEG Proceedings of the World Congress on Still Image Data Compression Standard. Engineering 2009 Vol I WCE 2009, July 1 - New York: Van Nostrand Reinhold, 1992. 3, 2009, London, U.K, PP. 978-983. [5] K. R. Rao and P. Yip, “Discrete Cosine [19] Yu Liu, Student Member, IEEE, and King Transform”, New York: Academic, 1990. NgiNgan, “Weighted Adaptive Lifting- [6] Ken Cabeen and Peter Gent, “Image Based Wavelet Transform for Image Compression and DCT”, Math 45, College Coding”, IEEE Transactions on Image of Red Woods. Processing, Vol. 17, No. 4, April 2008, PP. [7] J. M. Shapiro, “Embedded image coding 500-511. using zerotrees of wavelet coefficients,” [20] Zhigang Gao, Member, IEEE, and Yuan F. IEEE Trans. Signal Processing, vol. 41, pp. Zheng, Fellow, IEEE,” Quality Constrained 3445–3463, Dec. 1993. Compression Using DWT-Based Image [8] Bryan E. Usevitch, ”A Tutorial on Modern Quality Metric”, IEEE Transactions on Lossy Wavelet Image Compression: Circuits and Systems for Video Technology, Foundations of JPEG 2000”, IEEE Signal Vol. 18, No. 7, July 2008. Processing Magazine, 2001. [21] Zhijun Fang, NaixueXiong, Laurence T. [9] Dr.B Eswara Reddy and K Venkata Yang, “Interpolation-Based Direction- Narayana “A Lossless Image compression Adaptive Lifting DWT and Modified using Traditional and Lifting Based SPIHT for Image Compression in scheme”, Signal & Image Processing : An Multimedia Communications”, IEEE International Journal (SIPIJ) Vol.3, No.2, Systems Journals, Vol. 5, No. 4, December April 2012, PP. 213-222. 2011, PP. 583-593 [10] Sonja Grgic, MislavGrgic and BrankanZovko-Cihlar, ”Performance Analysis of Image Compression Using Wavelets”, IEEE Transactions on Industrial Electronics, Vol.48, No.3, June 2001, PP. 682-695. [11] ZixiangXiong, KannanRamchandran, Michael T.Orchard, Ya-Qin Zhang, ”A Comparative Study of DCT-and Wavelet- Based Image Coding”, IEEE, 1999. [12] Armando Manduca, “Compressing Images with Wavelet/subband Coding”, IEEE Engeneering Medicine and Biology, 1995. [13] Bo Li, Rui Yang, and Hongxu Jiang ” Remote-Sensing Image Compression Using Two-Dimensional Oriented Wavelet Transform”, IEEE Transactions on 1741 | P a g e
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