SGN-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.
An introduction to lossless audio compression
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)