Analysis and Comparison of Various Lossless Compression Techniques

Transcription

1 Analysis and Comparison of Various Lossless Compression Techniques Ritu Antil, Sandeep Gupta CSE, Deenbandhu Chotu Ram University, Murthal, Sonipat , India Abstract-Compression is very much needed in today s network for efficient transmission and efficient storage of data. In this paper we review and discuss about the image compression, need of compression, its principles, and classes of compression and various algorithm of image compression and showing how one technique is better than other. All the techniques with examples are discussed in this paper. Keywords- Data Compression; Lossless data compression; Data Redundancy; Advantages of Compression: Run Length coding, Huffman coding, Arithmetic coding, Lempel Ziv Welch coding (BIT REDUCTION METHOD) I.INTRODUCTION Today data transmission and storage is very expensive. So data compression is very much needed. Compression is useful because it helps us to reduce the resources usage, such as data storage space or transmission capacity. [1]Data compression is one of many technologies that enables today s information revolution. The term data compression refers to the process of reducing the amount of data required to represent a given quantity of information. Today the data transmission and storage is very expensive. Generally, as we all know that for presentation of digital data, we use encoding. By the encoding process also, we have very large amount of data (in comparison to original data).thus the overall consideration is: 1. To save the transmission bandwidth for transmission of data/image. 2. To save the space for storage of data/image. For that purpose, we use compression techniques, By compression we mean to compress the data for easy transmission and easy storage of data. Image compression is a part of data compression. IMAGE COMPRESSION: IMAGE COMPRESSION is the application of data compression on digital images. In effect, the objective is to reduce redundancy of the image data in order to be able to store or transmit data in an efficient form. Image compression addresses the problem of reducing the amount of information required to represent a digital image. It is a process intended to yield a compact representation of an image, thereby reducing the image storage transmission requirements. Every image will have redundant data. Data redundancy is the center issue in digital image compression. II. PRINCIPAL OF DATA COMPRESSION A data that is not relevant to represent any information is called data redundancy. Data redundancy is the center issue in digital image compression. In most of the images the neighboring pixels are correlated and contain redundant information. So the main task is to Page 251

2 find less correlated representation of the image. The two main component of compression are redundancy and irrelevancy reduction [2]. Reduction of Redundancy aims at removing duplication from the signal source (image/video). Irrelevancy reduction omits parts of the signal that will not be noticed by the signal receiver, namely the Human Visual System (HVS). In general, three types of redundancy can be identified: In digital image processing, we have three basic types of redundancies: (A)Coding redundancy (B) Inter pixel redundancy (C)Psycho visual redundancy A.CODING REDUNDANCY If the gray level of an image is coded in a way that uses more code symbol than absolutely necessary to represent each gray level, the resulting image is said to be code redundancy. Generally, the code redundancy is present when the codes assigned to set of events have not been selected to take full advantage of the probabilities. By natural coding, we assign the equal number of bits for symbols of high probability and less probability results in code redundancy. It is better to assign less bits for more probable grey level. That will provide image compression. This method is called variable length coding. Examples of image coding schemes that explore coding redundancy are the Huffman codes and the arithmetic coding technique. B.INTERPIXEL REDUNDANCY The only disadvantage of coding redundancy is that it would not provide the correlation between the pixels. For correlation of pixels, we need to analysis the structural or geometrical analysis of codes as shown in fig: 1) In Figure1 (a) and (b) show two identical histogram having three denominating range of gray levels. 2) Now, if we apply the variable length coding, we get code redundancy and for both images, we get similar code pattern. 3) Now, if we draw the autocorrelation function. FIGURE 1: INTERPIXEL REDUNDANCY. III. IMAGE COMPRESSION MODEL We see that there is dramatic difference between the shapes of functions for image d we have very high correlation between pixels of image. Because the value of any given pixel can be reasonably predicted from the value of its neighbors, the information carried by individual pixels is relatively small. That is called interpixel redundancy. In order to reduce the interpixel redundancy in an image, the 2-D pixel arrays are normally used for human viewing and interpretation must be transformed into more efficient format [3]. e.g., an array of differences between adjacent pixels. If the original image pixels can be reconstructed from the transformed data set the mapping is said to be reversible. C.PSYCHOVISUAL REDUNDANCY The brightness of a region does not depend upon only the reflection made by region. It also depends upon eye. Certain information simply has less relative importance that other information in normal visual processing. This information is said to be pyschovisual redundant. It can be eliminated without significantly impairing the quality of image perception. Unlike coding and interpixel redundancy, pyschovisual redundancy is associated with real or quantifiable visual information. Its elimination is only possible because the information itself is not essential for normal visual processing.[4] Most of the image coding algorithms in use today exploit this type of redundancy, such as the Discrete Cosine Transform (DCT) based algorithm at the heart of the JPEG encoding standard. Figure 2 shows the block diagram for image compression system FIGURE2: IMAGE COMPRESSION MODEL Page 252

3 Source encoder is responsible for reducing or eliminating any coding, interpixel or physchovisual redundancy in the input image. Mapper transforms the input data into a format designed to reduce interpixel redundancies in the input image. Quantizer will reduce the efficiency of map per. Encoder and decoder are designed to reduce the impact of channel noise by inserting a controlled form of redundancy into source encoded data. [5] IV. ADVANTAGES OF COMPRESSION A. Provides a believable cost savings involved with sending less data over the switched telephone network where the cost of the call is really usually based upon its duration. B. Not only reduces storage requirements but also overall execution time. C. Reduces the probability of transmission errors since fewer bits are transferred. D. Provides a level of security against unlawful monitoring. V.COMPARISION BETWEEN COMPRESSION TECHNIQUES Two types of compression strategies are there named as lossless and lossy. Lossless technique means that the restored data file is identical to the original.e.g.executable code, word processing file, tabulated numbers etc. In lossless techniques there is no loss of data [6]. In comparison, data files that represent images and other acquired signals do not have to be kept in perfect condition for storage or transmission. If the changes made to these signals resemble a small amount of additional noise, no harm is done. The technique that allows this type of degradation is called lossy. Lossless technique provide very low compression ratio than lossy technique [16]. In this paper only lossless techniques are discussed. VI. LOSSLESS COMPRESSION TECHNIQUES A. Run length coding B. Variable length coding C. Arithmetic coding D.Lempel ziv Welch coding (lzw) A.RUN LENGTH CODING TECHNIQUE The first step in this technique is read file then it scans the file and find the repeating string of characters.when repeating characters found it will store those characters with the help of escape character followed by that character and count the binary number of items it is repeated. This method is useful for image having solid black pixels. This algorithm is also effective for repeating of characters. But it is not effective if data file has less repeating of characters. Run length encoding can be used with one of the character, several of the characters, or all of the characters. We can compress the run-length symbols using Huffman coding, arithmetic coding, or dictionary based methods [7]. e.g.: Page 253

4 ORIGINAL DATA STREAM: RUN LENGTH ENCODED: In this example each time a zero is encountered two values are written to the output file. The first value is zero, a flag to indicate that run length compression is begning.the second value is the number of zero in the run. But if the average runs length is longer than two compressions will take place. And many single zero in the data make the encoded file larger than the original. B.VARIABLE LENGTH CODING OR HUFFMAN CODING It is named after D.A Huffman, who developed this technique in 1950s.it is also known as huffman encoding technique.[8] The main feature of huffman encoding is how the variable length codes are packed together. Imagine receiving a serial data stream of ones and zeros [13].If each character is represented by eight bits, you can directly separate one character from the next by breaking off 8 bit chunks. Consider a Huffman encoded data stream, where each character can have a variable number of bits[9].now the question arise how do you separate one character from the next? Answer lies in the proper selection of the Huffman codes that allow the correct separation. This will be clear by this example: TABLE 1 ENCODING TABLE LETTER PROBABLITY HUFFMAN E A.152 CODE 00 F B G C D Original data stream: C E A G B F E D A Huffman encoded: Grouped into bytes: Page 254

5 Byte 1 byte 2 byte 3 Figure 3: HUFFMAN ENCODING. The encoding table assigns each of the seven letters used in the example of variable length binary codes, based on the probability of occurrence. This example shows simple Huffman coding scheme. The character A through G occur in the original data stream with the probabilities shown in the TABLE1.Since the character A is most common, we represent it with two bits, the code: 00 the next character B receives two bits, the code 01.This continues to the least frequent character G, being assigned 4 bits,1111.and the variable length codes are restored into eight bit groups, the standard for computer use(process of coding has been discussed in this example). When uncompress ion occurs, all the eight bits group are placed end to end to form a long serial string of ones and zeros. In the encoding table each code consist of two parts number of zero before a one, and an optional binary code after the one[8].uncompress ion program looks at the stream of ones and zeros until a valid code is formed, and starting overlooking at the next character. The way that the codes are formed ensures that no ambiguity exists in the separation. STEPS FOR CALCULATING HUFFMAN CODING: 1. ARRANGE THE LETTERS ACCORDING TO DESCENDING ORDER OF PROBABLITY OF OCCURANCE. 2. ADD LOWEST TWO PROBABLITY AND GET NEW PROBABILITY AND PLACE NEW PROBABLITY AT EXACT PLACE ACC. TO DESCENDING ORDER 3.AT LAST WE WILL LEFT WITH ONLY TWO PROBABLITY A S WE NEED BINARY CODING WITH ONLY TWO SYMBOLS 1 AND NOW START CODING: (a) FOR LAST TWO PROBABLITIES ASSIGN 0 AND 1. (b)probablity OF PREVIOUS STEP ALWAYS RELATED TO THE PROBABLITY IF NEXT STEP. (c)again FOR LAST TWO: PUT 0 AND 1 AT PREFIX. (d)proceed TILL LAST (1 ST REDUCTION) STAGE JUST LIKE THAT. 5. WE GET MORE BINARY DIGITS FOR LESS PROBABLE DATA AND LESS BINARY DIGITS FOR HIGH PROBABLE DATA. 6. REPEAT THIS STEP UNTIL TWO PROBABLITY ARE LEFT. E.g. Letters with probability of occurrence is given and we have to find the Huffman encoding. B=0.110, A=0.154,G=0.011,D=0.063,E=0.059,C=0.072,F=0.015 Page 255

6 Letters are arranged in descending order of probability of occurrence. A=0.154, B=0.110, C=0.072, D=0.063, E=0.059, F=0.015, G=0.011 Last two probabilities are added:i.e (0.015)+(0.011)=0.026 and place them in descending order. Repeat this step until last two probabilities are left. TABLE 2 HUFFMAN ENCODING TABLE Letter 1 st reduction 11nd reduction 3 rd reduction 4 reduction 5threduction 6 th reduction A B C D E F G TABLE 3 1 st reduction 2 nd reduction 3 rd reduction 4 th reduction 5 th reduction 6 th reduction A B C D E F G Page 256

7 Final codes Advantage of this technique is that letters/symbols occurring again and again will now take fewer bits for representation so automatically total required bits will be decreased. But a more sophisticated version of Huffman technique is Arithmetic encoding. C.ARITHMETIC TECHNIQUE In arithmetic coding, an entire sequence of source symbols is assigned a single code word. The code word itself defines an interval of real numbers between 0 and1.this technique is effective in wide range of situations and compression ratio.[10] It simplifies automatic modeling of complex sources, yielding near optimal or significantly improved compression for sources that are not independent and identically distributed[10]. This technique is better than Huffman and run length technique. ALGORITHM OVERVIEW: An alphabet with symbol A0,A1..An where each symbol has a probability of occurrence of P0,P1,.Pn such that Pi=1.since Pi=1,we can represent each probability, I, as unique non overlapping range of values between 0 and 1. Now assume that we have an alphabet a, b,c,d,e with probability of occurrence of 30%,15%,25%10%,20%.then we choose the following ranges assignment to each symbol based on its probability: SYMBOL A B C D E TABLE4 ARITHMETIC ENCODING TABLE PROBALITY RANGE 0.30 [ 0.00,0.30) [0.30,0.45) [0.45,0.70) [0.70,0.80) [0.80,1.00) Where square brackets [ Means the adjacent number is included and parenthesis ) means adjacent number is excluded. To assign the particular range, put the maximum limit of previous range as current minimum limit and for current maximum limit of a particular range, just add all previous probabilities. For e.g.: range of alphabet c Maximum unit=0.45(max limit of b) Maximum limit= =0.70 Formula for Arithmetic encoding: Lower bound =0 Upper bound=1 Formula for encoding: Current range=upper bound-lower bound,upper bound= lower bound+(current range *upper bound of new symbol),lower bound=lower bound +(current range*lower bound of new symbol) Eg: of Arithmetic encoding: Encode ace ENCODE A Current range=1-0=1, Upper bound= 0+(1*0.30)=0.30,Lower bound=0+(1*0.00)=0.00 ENCODE C CR= =0.30,Ub=0.00+(0.30*0.70)=0.210,Lb=0.00+( )=0.135 ENCODE E Cr= =0.75,Ub=0.135+(0.075*1.00)=0.210,Lb= (0.075*0.80)=0.195 SO ACE WORD MAY BE ENCODED BY ANY ONE VALUES WITHIN PROBABILITY RANGE[0.195,0.210]. D.LEMPEL ZIV WELCH TECHNIQUE Lempel Ziv Welch (LZW) is a universal lossless data compression algorithm created by Abraham Lempel, Jacob Ziv, and Terry Welch. It was published by Welch in 1984 as an improved implementation of the LZ78algorithm published by Lempel and Ziv in The algorithm is simple to implement, and has the potential for very high throughput in hardware implementations. [11] It was the algorithm of the widely used Unix file compression utility compress, and is used in the GIF image format. This coding technique compress almost any kind of data.it work well with almost any kind of data like executable code text and similar data files to half of their original size.lzw also work well when presented with extremely redundant data files such as tabulated numbers, computers source codes and acquired signals. Compression ratio of 5:1 are common for there cases. The scenario described in Welch's 1984 paper encodes sequences of 8-bit data as fixed-length 12- bit codes. The codes from 0 to 255 represent 1-character sequences consisting of the corresponding 8-bit character, Page 257

8 and the codes 256 through 4095 are created in a dictionary for sequences encountered in the data as it is encoded. At each stage in compression, input bytes are gathered into a sequence until the next character would make a sequence for which there is no code yet in the dictionary. The code for the sequence (without that character) is emitted, and a new code (for the sequence with that character) is added to the dictionary. The scenario described in Welch's 1984 paper encodes sequences of 8-bit data as fixed-length 12-bit codes. The codes from 0 to 255 represent 1-character sequences consisting of the corresponding 8-bit character, and the codes 256 through 4095 are created in a dictionary for sequences encountered in the data as it is encoded. At each stage in compression, input bytes are gathered into a sequence until the next character would make a sequence for which there is no code yet in the dictionary. The code for the sequence (without that character) is emitted, and a new code (for the sequence with that character) is added to the dictionary ENCODING PROCESS A dictionary is initialized that contain the single-character strings corresponding to all the possible input characters (and nothing else except the clear and stop codes if they're being used). The algorithm works by scanning through the input string for successively longer substrings until it finds one that is not in the dictionary. When such a string is found, the index for the string less the last character (i.e., the longest substring that is in the dictionary) is retrieved from the dictionary and sent to output, and the new string (including the last character) is added to the dictionary with the next available code. The last input character is then used as the next starting point to scan for substrings. In this way, successively longer strings are registered in the dictionary and made available for subsequent encoding as single output values. The algorithm works best on data with repeated patterns, so the initial parts of a message will see little compression. As the message grows, however, the compression ratio tends asymptotically to the maximum.[12][13] DECODING PROCESS: The decoding algorithm works by reading a value from the encoded input and outputting the corresponding string from the initialized dictionary. At the same time it obtains the next value from the input, and adds to the dictionary the concatenation of the string just output and the first character of the string obtained by decoding the next input value. The decoder then proceeds to the next input value (which was already read in as the "next value" in the previous pass) and repeats the process until there is no more input, at which point the final input value is decoded without any more additions to the dictionary. e.g. Text to be encoded is: TOBEORNOTTOBEORTOBEORNOT# # Marker shows end of the message. Now we use the decimal symbols for representing the symbols like A =1, Z=26, # IS REPRESENTED BY 0.It would be more clear by this. There are thus 26 symbols in the plaintext alphabet (the 26 capital letters A through Z), plus the stop code #. We arbitrarily assign these the values 1 through 26 for the letters, and 0 for '#'. (Most flavors of LZW would put the stop code after the data alphabet, but nothing in the basic algorithm requires that. The encoder and decoder only have to agree what value it has.) A computer will render these as strings of bits. Five-bit codes are needed to give sufficient combinations to encompass this set of 27 values. The dictionary is initialized with these 27 values. As the dictionary grows, the codes will need to grow in width to accommodate the additional entries. A 5-bit code gives 2 5 = 32 possible combinations of bits, so when the 33rd dictionary word is created, the algorithm will have to switch at that point from 5-bit strings to 6-bit strings (for all code values, including those which were previously output with only five bits). Note that since the all-zero code is used, and is labeled "0", the 33rd dictionary entry will be labeled 32. (Previously generated output is not affected by the codewidth change, but once a 6-bit value is generated in the dictionary, it could conceivably be the next code emitted, so the width for subsequent output shifts to 6 bits to accommodate that.) TABLE 5 Page 258

9 SYMBOL S DECIMAL NUMBER ARE ASSIGNED TO ALPHABETS BINARY DECIMAL # A B C D E F G H I J K L M N O P Q R S T U Page 259

10 V W X Y Z TABLE 6 ENCODING PROCESS Current Sequence Next Char Output Code Bits NULL T Extended Dictionary Comments T O : TO 27 = first available code after 0 through 26 O B : OB B E : BE E O : EO O R : OR R N : RN 32 requires 6 bits, so for next output use 6 bits N O : NO O T : OT T T : TT TO B : TOB BE O : BEO OR T : ORT TOB E : TOBE EO R : EOR RN O : RNO OT # # stops the algorithm; send the cur seq and the stop code Un encoded length=25 symbols*5 Bits*symbols=125 bits Encoded length=(6 codes*5 bits/codes)+(11codes *6bits/code)=96bits Using LZW has saved 29 bits out of 125 reducing the message almost 22% VII. MEASURING COMPRESSION PERFORMANCES There are various criteria to measure the performance of a compression algorithm. However, the main concern has always been the space efficiency and time efficiency. Following are some measurements used to evaluate the performances of lossless algorithm. Page 260

11 1. Compression Ratio: It is the ratio between the size of the compressed file and the size of the source file. 2. Compression factor: It is the inverse of the compression ratio. 3. Saving percentage: it calculates the shrinkage of the source file. VIII. COMPARING THE TECHNIQUES A. Run Length Encoding Run length encoding is used only when sequence of characters are repeated many times. In the worst case RLE generates the output data which is 2 times more than the size of input data. This is due to the fewer amount of runs in the source file. And the files that are compressed have very high values of compression ratio. This algorithm does not provide significant improvement over the original file. B. Huffman Coding vs. Arithmetic Coding Huffman Coding Algorithm uses a static table for the whole coding process, so it is faster. However it does not produce efficient compression ratio. On the contrary, Arithmetic algorithm can generate a high compression ratio, but its compression speed is slow. C. LEMPEL ZIV WELCH (BIT REDUCTION METHOD) It is most efficient technique among all other technique. It provides better compression ratio. Its compression speed is fast. It work well with string and character. It compresses the data to half of their original size. It is always used in GIF image file and also in TIFF and Post Script. This method also works well with extremely redundant data files. TABLE 4 PRESENTS A SIMPLE COMPARISION BETWEEN THESE COMPRESSION METHODS COMPRESSION METHOD HUFFMAN CODING ARITHMETIC CODING LEMPEL ZIV WELCH(BIT REDUCTION METHOD) Compression ratio Poor Very good Very good Compression speed Fast Slow fast Decompression speed Fast Slow fast IX.CONCLUSIONS Page 261

12 Each technique has its own importance. in this paper different lossless technique are explained but the Lempel ziv Welch technique is better than all other techniques explained above this is the only technique that provide better memory space better compression speed better compression ratio and this technique uses the bit reduction method. Bit Reduction algorithm-which is more efficient and less complex than Huffman coding algorithm and also from that algorithm which is defined in base paper. So the overall conclusion is that this technique is better in all aspect than all other lossless techniques. REFERENCES [1]S.Gavaskar,Dr.E.Ramaraj,R.Surendiran, A Compressed Anti IP Spoofing Mechanism Using Cryptography, IJCSNS International Journal of Computer Science and Network Security, VOL.12 No.11, November [2]Ming Yang and Nikolaos Bourbakis, An Overview of Lossless Digital Image Compression Techniques, IEEE, pp ,2005. [3] Wei-Yi Wei, An Introduction to Image Compression, pp1-29. [4] Manjeet Gupta Brijesh Kumar, Web Page Compression using Huffman Coding Technique, International Conference on Recent Advances and Future Trends in Information Technology (irafit2012) Proceedings published in International Journal of Computer Applications (IJCA),2012. [5] Rafael C. Gonzalez, Richard Eugene; Digital image processing, Edition 3, 2008, page 466.Alan Conrad Bovik; Handbook of image and video processing, Edition , page 673 [6] Rajinder Kaur,Mrs. Monica Goyal, A Survey on the different text data compression techniques, International Journal of Advanced Research in Computer Engineering & Technology (IJARCET), Volume 2, Issue 2, February [7] Majid Rabbani, Paul W.Jones; Digital Image Compression Techniques. Edition-4, [8] Jagadish H. Pujar and Lohit M. Kadlaskar, A New Lossless Method Of Image Compression and Decompression Using Huffman Coding Techniques, JATIT, pp , 2012 [9] Ronald G. Driggers; Encylopedia of optical engineering, Volume 2, Edition 1,2003. [10] Ioannis Pitas; Digital image processing algorithms and applications., ISBN [11] David Salomon, Data Compression The complete reference, 4th ed., page 212. [12] Jacob Ziv and Abraham Lempel; Compression of Individual Sequences Via Variable-Rate Coding, IEEE Transactions on Information Theory, September [13] Manjeet Gupta Brijesh Kumar, Web Page Compression using Huffman Coding Technique, International Conference on Recent Advances and Future Trends in Information Technology (irafit2012) Proceedings published in International Journal of Computer Applications (IJCA),2012. [14] Ziv, J.; Lempel, A. (1978). "Compression of individual sequences via variable-rate coding". IEEE Transactions on Information Theory 24 (5): 530. [15] Mark Daniel Ward, Exploring Data Compression via Binary Trees1, International Journal of Advanced Computer Science and Applications (IJACSA), Vol. 3, No.8, [16] Tzong Jer Chen and Keh-Shih Chuang, A Pseudo Lossless Image Compression Method, IEEE, pp , Page 262