TUT logoSGN-2306  Signal Compression

Lectures

1.      Simple codes

1.1 Signal Representation versus Signal Compression

1.2 Prefix Codes

1.3 Trees associated with prefix codes

1.4 Kraft inequality

1.5 A lower bound on the average length of optimal prefix codes 

1.6 Shannon codes

1.7 Encoding a binary tree

2.  Huffman codes

2.1Huffman algorithm for binary coding alphabets

2.2 Canonical Huffman coding

2.3 Huffman algorithm for D-ary coding alphabets

2.4 Huffman codes for infinite alphabets

3. Lempel-Ziv Coding

3.1 Dictionary methods

3.2 The LZ77 family of adaptive dictionary coders (Ziv-Lempel 77)

3.3 The gzip variant of Ziv-Lempel 77

3.4 The  LZ78 family of adaptive dictionary coders (Ziv-Lempel 78)

3.5 The LZW variant of Ziv-Lempel 78

3.6 Statistical analysis of a simplified Ziv-Lempel algorithm

4. Shannon-Fano-Elias Codes and Arithmetic Coding

4.1 Shannon-Fano-Elias Coding

4.2 Arithmetic Coding

5. Adaptive Models for Arithmetic Coding

5.1 Adaptive arithmetic coding

5.2 Models for data compression

5.3 Prediction by partial matching

6. Coding: a bag of tricks?

6.1  Burrows-Wheeler coding

6.2  Run length codes

6.3  Elias code for integers

7. Image Compression. Lossless Techniques

7.1 JPEG-LS (also known as LOCO-I)

7.2 Other coders

8. Lossy image compression: Principle of embedding

9. Lossy image compression: SPIHT and S+P

            9.1  SPIHT embedded coder

9.2  The reversible multiresolution transform S+P

9.3 Error resilience in embedded coding

10. Lossy image compression: JPEG 2000

Baseline JPEG encoder and decoder 9-11

JPEG 2000 Compression Paradigm 12, 26

Preprocessing 27-29

Discrete wavelet Transform 50-54, 84

Quantization 86-92, 103-105

Entropy (Tier 1) Coding 107, 113-134

Entropy (Tier 2) Coding 136-145, 154-160

Rate allocation162-168

Region of Interest coding 172-181

 

11. Lossless audio coding

 

12. A short review and some exam questions

 

Slides for the chapters 1 to 9 (2 pages per sheet) or 1page per sheet

 

Additional slides comparing statistical and dictionary based methods :1 page per sheet

 

Slides for the chapter 8 (2 pages per sheet) or 1page per sheet

 

The reference for chapter 8 (including figures for Chapter 8)

 

Slides for the chapter 9 (2 pages per sheet) or 1page per sheet

 

Slides for the chapter 10 (Large file, approx. 10M) (do not print, too large file)

Another reference for chapter 10 (shorter document)

 

Slides for the chapter 11

Slides for chapter 12