DATA COMPRESSION

1
DATA COMPRESSION

• By ARCHANA MEKA

2
Outline

• Introduction
• Lossless Compression techniques
• Lossy Image coding

3
Outline

• Introduction
• Lossless Compression techniques
• Lossy Image coding

4
Introduction

• Why Compression ???
• To reduce redundancy in stored or communicated
  data
• Applications in file storage and Distributed
  Systems
• Reduces storage and transmission costs

5
Introduction

• Prime Target
• Redundant and Irrelevant Information
• Compression techniques exploit inherent
  redundancy and irrelevancy by transforming a data
  file into a smaller file

6
Introduction

• Performance Efficiency
• Compression efficiency
• Complexity
• Distortion Measurement ( lossy algorithm)

7
Introduction

• Classification
• Lossless compression
• lossless compression for legal and medical
  documents, computer programs
• exploit only data redundancy
• Lossy compression
• digital audio, image, video where some errors or
  loss can be tolerated
• exploit both data redundancy and irrelevant data

8
Outline

• Introduction
• Lossless Compression techniques
• Lossy Image coding

9
Lossless Compression Techniques

• Image can be recovered exactly upon decompression
• These algorithms fall into two broad categories
• Dictionary-based techniques
• Statistical methods

10
Lossless Compression Techniques

• DictionaryBased Techniques
• Generates a compressed file containing
  fixed-length codes, representing a particular
  sequence of bytes in the original file
• Run-Length Encoding
• Simplest consecutive elements, or runs, are
  replaced by just one element showing how many are
  in the run
• "aaaabbaaa" -gt "4a2b3a"
• 9 characters have become 6

11
Lossless Compression Techniques

• Run length encoding cont
• Code can be stored specifying the value followed
  by length of the run, rather than simply storing
  the value many times over
• WWWWWWWWWWWWBWWWWWWWWWWWWBBB
• 12WB12W3B

12
Lossless Compression Techniques

• LZW (Lemple Ziv Welch) Encoding
• Like RLE, it effects compression by encoding
  strings of characters
• Unlike RLE, it builds up a table of strings and
  their corresponding codes as it encodes the file

13
Lossless Compression Techniques

• LZW Encoding cont..
• Dictionary is maintained to catalog pieces of
  data
• Ask not what your country can do for you - ask
  what you can do for your country
• 1 not 2 3 4 5 6 7 8 - 1 2 8 5 6 7 3 4

14
Lossless Compression Techniques

• LZW Encoding cont..
• Ask not what your country can do for you --
  ask what you can do for your country
• Quotation has 17 words- 61 letters, 16 spaces,
  1 dash, 1 period. If each letter, space or
  punctuation mark takes up one unit of memory,
  total file size -79 units
• The redundancies that can be noticed are
• "ask" appears two times ,"what" appears two times
  
• "your" appears two times, "country" appears two
  times
• "can" appears two times, "do" appears two times
• "for" appears two times , "you" appears two times
  

15
Lossless Compression Techniques

• LZW Encoding cont..
• Compressing program doesnt have concept of
  separate wordslooks for patterns
• Ask not what your country can do for you -- ask
  what you can do for your country

16
Lossless Compression Techniques

• LZW adaptive based Encoding eg
• Here Underscore represents space

"1not__2345__-__12354"
17
Lossless Compression Techniques

• Statistical Encoding Methods
• They implement data compression by representing
  frequently occurring characters in the file with
  fewer bits than they do less commonly occurring
  ones
• Huffman Coding
• It uses Binary encoding tree representing
  commonly occurring values in few bits and less
  commonly occurring values in more bits

18
Lossless Compression Techniques

• Algorithm to generate Huffman codes
• Find the probability of each data and sort them
• Generate new node by combination the two smallest
  probability together then sort the probability of
  new node with the remainder probabilities
• Define 1 for a brach of new node and 0 for
  another
• Repeat (2) and (3) until the final probability is
  1.0

19
Lossless Compression Techniques

• Huffman encoding eg

20
Lossless Compression Technique

• Huffman encoding eg

Courtesy www.cs.utexas.edu/scottm/cs307/handouts
/Slides
21
Outline

• Introduction
• Lossless Compression techniques
• Lossy Image coding

22
Lossy Compression algorithm

• Eliminates redundant as well as irrelevant
  information
• only an approximate reconstruction of the
  original image is possible
• Achieves higher compression ratios

23
Lossy Compression Techniques

• Vector Quantization
• Composed of two operations
• Encoder
• takes an input vector and outputs the index of
  the codeword that offers the lowest distortion
• Once the closest codeword is found, the index of
  that codeword is sent
• Decoder
• The decoder receives the index of the codeword,
  and outputs the codeword

24
Lossy Compression Technique Vector Quantization
cont..
Courtesy http//www.geocities.com/mohamedqasem/ve
ctorquantization/vq.html
25
Lossy Compression Techniques

• The algorithm
• Determine the number of code words, N,  or the
  size of the codebook
• Select N code words at random, and let that be
  the initial codebook (randomly chosen from the
  set of input vectors)
• Using the Euclidean distance measure, cluster the
  vectors around each codeword ( by finding the
  Euclidean distance between it and each
  codeword, The input vector belongs to the cluster
  of the codeword that yields the minimum distance

26
Lossy Compression Technique

• Algorithm cont..
• Compute the new set of code words.  This is done
  by obtaining the average of each cluster.  Add
  the component of each vector and divide by the
  number of vectors in the cluster
• Repeat steps 3 and 4 until either the code words
  don't change or the change in the code words is
  small

27
Questions?