Data%20Compression%20%20Systematisation%20of%20Techniques%20and%20Methods

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Data Compression Systematisation of Techniques
and Methods
Dr.-Ing.habil. Tilo Strutz University of
Rostock based on Strutz Datenkompression -
Grundlagen, Verfahren und deren Anwendung in der
Verarbeitung von Graustufen- und Farbbildern,
2002, thesis for doctor-habilitatus degree,
University of Rostock, also ISBN 3-89825-575-1
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Basics

• Objective of data compression
• transfer of information of digital data into
  such a description format (embodiment), which
  requires as less expense of storage/transmission
  as possible
• Application

storage or transmission of digital data
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Basics (2)

• What are primal characteristics of digital data?

Digital Data
Origin
Format
Resolution

• digitisation of analogue data
• (photography, microphone
• recordings)
• digital generation (ASCII text,
• computer graphics, machine-
• code)

• one-dimensional (audio signals,
• ultrasonic echos, text)
• two-dimensional (image signals)
• three-dimensional
• (image sequences)
• ...

• binary (e.g. black/ white)
• multivalued (e.g. grey values
• with 8 bit)
• multi-channel (e.g. colour
• images with 3 x 8 bit)

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Systematisation

• Motivation
• rapid development at the field of data
  compression
• urgent needs for systematised overview
• Goals of this study
• uniform classification of techniques and methods
  ? clear overview over this area
• support for understanding of compression
• guidance to the design of new compression
  systems (reasonable combination of function
  blocks)

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Systematisation (2)
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Data Reduction
Sub-sampling
Quantisation
Quantisation
- reduction of temporal resolution
- resolution reduction of signal values
Vector Quantisation
Scalar Quantisation
- mapping of similar vectors to a common
representative vector
- mapping of similar values to a common
representative value
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Quantisation

• goal removal of irrelevant matters
• partition into two steps
• Quantisation (encoder)
• Reconstruction (decoder)

x .. signal value, q ... quantisation symbol, yq
... reconstruction value
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Coding

• reversible, removal of redundancy
• information content of one symbol si
• entropy (average information content)

• theoretical limit of minimum bitrate

• ! refers to independent symbols !
• What happens if symbols depend on each other?

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Coding
Entropy Coding
Precoding
considers symbols as dependent of each
other mapping of symbols to symbols of
another alphabet or seeking after
correlationen goal (H x N)new lt (H x
N)old
considers symbols as independent of each
other mapping of symbols to code words
goal convergence of storage expense to signal
entropy H
H ... Entropy of alphabet, N ... Number of
symbols to be transmitted
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Entropy Coding
Code-word based
Arithmetic
substitution of symbol srings by a
bitstream algorithms common arithmetic
coding, binary arithmetic coding,
range coder, ...
substitution of symbols by bit strings
algorithms Shannon-Fano, Huffman,
Golomb-Rice, ...

• Optimum transmitted bits per symbol
  information content bit

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Precoding
Block Sorting
Phrase Coding
- substitution of strings of arbitrary symbols
by symbols of another alphabet (dictionary-
based coding)
- increase of correlation between adjacent
symbols by sorting
Run Length Coding
Miscellaneous
- substitution of strings of identical symbols
by symbols of another alphabet
- techniques for provision of supplemental
information improving the subsequent
processing (e.g. quad-tree coding, bit-
mapping, etc.) - application also
multidimensional or hierarchical
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Decorrelation

• goal concentration of signal energy / information

Decorrelation
Prediction
Filterbanks
Transformation

• forecast of signal values

• decomposition of signals in
• (overlapping) frequency domains

• decomposition of signals
• in basis functions

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Prediction
Sender
Receiver
Recursive !
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Prediction (2)
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Transformation

• common discrete signal transformation
• inverse transformation
• matrix notation

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Transformation (2)

• matrix for inverse transformation B
• columns are basis vectors

B
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Transformation (3)

• columns are basis vectors
• signal reconstruction by sum of weighted basis
  functions
• transform coefficients Xk are the weights

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Filterbanks

• Two-Channel Filterbank

g1n
?2
?2
h1n
xn
xn

?2
?2
g0n
h0n
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Filterbanks (2)

• cascade of 2-channel filterbanks
• frequency decomposition

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Filterbanks (3)

• Wavelet Filterbank ? Wavelet Transformation

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Filterbanks (3)

• Wavelet Filterbank ? Wavelet Transformation

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Systematisation
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Flow Chart

• e.g. chrominances of Yxx-colour space

• prediction, transformation, filterbank

• feedback at prediction with quantisation

• scalar quantisation or vector quantisation

• maybe combination of different methods

• prefixcode, arithmetic code

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Characteristic Properties

• Decorrelation
• signal information will be concentrated to few
  values / symbols
• number of symbols / samples remains the same
• is reversible dependent on accuracy of
  calculations
• result of decorrelation is tolerant against
  quantisation (concerning signal reconstruction)

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Characteristic Properties (2)

• Entropy Coding
• mapping of symbols to a bitstream
• presumption symbols are independent on each
  other
• operation is invertible
• Precoding
• mapping of one symbol alphabet to another
• uses statistical relations between symbols
• number of symbols / samples can change
• operation is invertible

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Characteristic Properties (3)

• Data Reduction
• decrease of irrelevancy
• precondition relevant and irrelevant
  constituents are separated to the greatest
  possible extent
• quantisation number of samples remains the same
• subsampling number of samples decreases

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Characteristic Properties (4)

• Adaptation
• fixed signal model
• updating of model parameter
• switching between parameter sets
• different signal models
• context-based ? finite-state-machine