Data compression techniques can be divided into lossless and lossy methods. Lossless compression preserves the integrity of the data by removing redundant data in compression and adding it back during decompression so that the original and reconstructed data are exactly the same. Lossy compression throws away perceptually insignificant information and cannot recover all bits, but this is acceptable for applications like video where small differences do not impact quality. Compression performance is measured by the compression ratio, bits per sample, and distortion between original and reconstructed data. Compression involves modeling data patterns and encoding the residual differences between the data and model.

1. Data Compression
Techniques
Module-1 (Modelling and types of compression))
Introduction to Compression Techniques- Lossy compression & Lossless
compression, Measures of Performance, Modeling and coding. Mathematical
modelling for Lossless and lossy compression - Physical models and probability
models.

3. Why compress data?
Storing, managing, and transferring data becomes essential in data communication
and other data-driven solutions. This is because no matter the degree of advancement
in computer hardware (RAM, ROM, GPU) and forms of communication (internet),
these resources are scarce.
To utilize these resources efficiently, the data is often required to be compressed, i.e.,
reduced to a smaller size without losing any or losing minimal information.

4. Compression Technique

5. • Data compression implies sending or storing a smaller number of bits.
Although many methods are used for this purpose, in general these
methods can be divided into two broad categories: lossless and lossy
methods.

6. Lossless Compression
In lossless data compression, the integrity of the data is preserved.
The original data and the data after compression and decompression are exactly the same because,
in these methods, the compression and decompression algorithms are exact inverses of each other:
no part of the data is lost in the process.
Redundant data is removed in compression and added during decompression. Lossless
compression methods are normally used when we cannot afford to lose any data.

7. Lossless Compression: Examples
• Text Compression
• It is very important that the reconstruction is identical to the text
original, as very small differences can result in statements with very
different meanings.
Consider the sentences “Do not send money” and
“Do now send money.”

8. Lossless Compression: Examples
 suppose we compressed a radiological image in a lossy fashion, and the
difference between the reconstruction and the original was visually
undetectable.
 If this image was later enhanced, the previously undetectable differences
may cause the appearance of artifacts that could seriously mislead the
radiologist

9. Lossless Compression: Examples
• Data obtained from satellites often are processed later to obtain
different numerical indicators of vegetation, deforestation, and so on.
• If the reconstructed data are not identical to the original data,
processing may result in “enhancement” of the differences.
• It may not be possible to go back and obtain the same data over
again

10. Lossy Compression
throw away perceptually insignificant information
cannot recover all bits
• In many applications, this lack of exact reconstruction is not a problem.
• For example, when storing or transmitting speech, the exact value of each
sample of speech is not necessary.
• Similarly, when viewing a reconstruction of a video sequence, the fact that
the reconstruction is different from the original is generally not important
as long as the differences do not result in annoying artifacts.
• Thus, video is generally compressed using lossy compression.

11. Measures of Performance
Factors affecting Performance
The relative complexity of the algorithm
 The memory required to implement the algorithm
 How fast the algorithm performs on a given machine
 The amount of compression
How closely the reconstruction resembles the original.

12. Compression Ratio
• The ratio of the number of bits required to represent the data before
compression to the number of bits required to represent the data after
compression. This ratio is called the compression ratio.
• Suppose storing an image made up of a square array of 256×256 pixels
requires 65,536 bytes. The image is compressed and the compressed
version requires 16,384 bytes. We would say that the compression ratio is
4:1.
• We can also represent the compression ratio by expressing the reduction in
the amount of data required as a percentage of the size of the original
data. In this particular example the compression ratio calculated in this
manner would be 75%.

13. • Another way of reporting compression performance is to provide the
average number of bits required to represent a single sample. This is
generally referred to as the rate.
• For example, in the case of the compressed image, if we assume 8
bits per byte (or pixel), the average number of bits per pixel in the
compressed representation is 2. Thus,
• we would say that the rate is 2 bits per pixel

14. • In lossy compression, the reconstruction differs from the original
data. Therefore, in order to determine the efficiency of a compression
algorithm, there have to be some way of quantifying the difference.
• The difference between the original and the reconstruction is often
called the distortion.
• fidelity and quality. When the fidelity or quality of a reconstruction is
high, it mean that the difference between the reconstruction and the
original is small

15. Modeling and Coding
• Data compression algorithms can be divided into two phases.
The first phase is modeling.
In this phase, try to extract information about any
redundancy that exists in the data and describe the redundancy in the form
of a model.
The second phase is called coding.
A description of the model and a “description” of how the data
differ from the model are encoded, generally using a binary alphabet.
The difference between the data and the model is often referred to as the
residual.

16. If we were to transmit or store the binary representations of these numbers, we would need to use 5 bits per
sample. The structure in the data can be characterized by an equation
CASE 1

17. The difference between the data and the model. The difference (or residual) is given
by the
010 −1 1 −101 −1 −111 The residual sequence consists of only three numbers −1 0 1.
Assign a code of 00 to −1, a code of 01 to 0, and a code of 10 to 1, so need to use 2
bits to represent each element of the residual sequence.
Therefore, compression can be obtainedby transmitting or storing the parameters of
the model and the residual sequence

18. • The sequence does not seem to follow a simple law as in the previous case.
• Each value is close to the previous value.
• Suppose we send the first value, then in place of subsequent values we send
the difference between it and the previous value.
CASE 2

19. The sequence of transmitted values would be
• The number of distinct values has been reduced.
• Fewer bits are required to represent each number and compression is achieved.
• The decoder adds each received value to the previous decoded value to obtain the
reconstruction corresponding to the received value.
• Techniques that use the past values of a sequence to predict the current value and then encode
the error in prediction, or residual, are called predictive coding schemes

20. • A very different type of redundancy is statistical in nature.
• There are sources that generate some symbols more often than
others. In these situations, it will be advantageous to assign binary
codes of different lengths to different symbols.
CASE 3

21. The sequence is made up of eight different symbols. In order to represent eight symbols, we need to
use 3 bits per symbol. Suppose instead the code shown in Table below is used

22. The sequence is made up of eight different symbols.
In order to represent eight symbols, we need to use 3 bits per symbol.
Suppose instead we used the code shown in Table 1.1. A codeword with only a
single bit to the symbol that occurs most often, and correspondingly longer
codewords to symbols that occur less often. After substituting the codes for each
symbol, 106 bits are required to encode the entire sequence.
As there are 41 symbols in the sequence, this works out to approximately 2.58 bits
per symbol. This means we have obtained a compression ratio of 1.16:1.

23.  When dealing with text, along with statistical redundancy, redundancy in the
form of words that repeat often can be considered.
 This form of redundancy can be taken by constructing a list of these words and
then represent them by their position in the list.
 This type of compression scheme is called a dictionary compression scheme

24. Mathematical preliminaries

27. iid identically distributed

30. • Module – 2 (Basic Compression Methods)
• Basic Compression Technique- Run length encoding, RLE Text compression. Statistical Methods- Prefix Codes,
Binary Huffman coding, non-binary Huffman Algorithms, Arithmetic Coding.
• Module - 3 (Text & Image Compression)
• Dictionary based Coding- LZ77, LZ78 and LZW compression.Image Compression- Image standards, JPEG image
Compression- Baseline JPEG, JPEG-LS.
• Module - 4 (Video Compression)
• Video Compression- Analog video, Digital Video, Motion Compensation. MPEG standards- MPEG 1, MPEG 4
• Module - 5 (Audio Compression)
• Audio Compression- Basics of Digital Audio, Basic Audio Compression Techniques, MPEG Audio Compression-
Layer 1 coding, Layer 2 coding and Layer 3 coding.
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