Data and Image Compression
S. Xambó
In this page (WiP) you can access the materials for the
Data and Image Compression class
of the Spring Semestrer 2014-2015 at the
FIB
of the UPC.
LECTURES
The dates in parenthesis correspond to the last update.
- Review of Basic Probability Theory (18.2.2015)
- Introduction (2.3.2015)
- Information and Entropy (2.3.2015)
- Probability Coding (2.3.2015)
- Arithmetic Coding (3.3.2015)
- Other lossless procedures (3.3.2015)
- 1D Haar wavelets (28.4.2015)
- 1D Daubechies wavelets (27.4.2015)
- The DCT (21.5.2015)
IN-CLASS LABS
-
L217: Installing pyzo and first steps in Python.
-
L219:
Extracting elements of list/tuple/set with assigned probabilities/weights.
-
L224:
Analyze the first problem on T0.2 (Chevalier de Meré's problem).
-
L303:
First experiments in source coding/decoding.
-
L305:
Computing various entropies.
-
L310:
Graphics related to entropy functions.
-
L312:
Working with prefix codes.
-
L317:
An exercise about Kraft's inequality.
-
L319:
Finding the average length of an encoding.
-
L324:
In class lab on arithmetic interval encoding.
-
L326:
In class lab on arithmetic bit encoding and decoding.
-
L407:
In class lab on scaled arithmetic encoding and decoding.
-
L409:
Haar wavelets algorithms: first steps.
-
L414:
Haar wavelets algorithms: High level Haar transforms.
-
L416:
Haar wavelets algorithms: High level trend and fluctuation functions.
Iterative form of the high level Haar transform.
-
L421:
Haar wavelets algorithms: Computing the arrays of
scaling and wavelet vectors.
-
L423:
Haar wavelets algorithms: work on several
aspects of multiresolution.
-
L428:
Checking the fundamental identities of the Daub4 coefficients.
Computing D4trend
and D4fluct.
-
L505:
Defining D4trend(f,r=1),
D4fluct(f,r=1) and
D4(f,r=1).
-
L507:
Define functions that compute the scaling and wavelet arrays for the Daub4 wavelets.
Adapt the pattern used in the case of the Haar wavelets.
-
L512:
Implementation of filters for computing the Daub4 multiresolution of a signal.
-
L514:
Work on Daub6 wavelets.
-
L519:
In class lab to consolidate theory and practice of wavelet theory.
-
L521:
Solving in detail L519.
-
L526:
Quantitative appendix to A519.
WEEKLY ASSIGNMENTS
-
A217:
Three exercises on lists.
-
A224:
Computations about Bayes' formula.
-
A303:
Reinforcing the experience L303
with a binary encoding of monogram English.
-
A310:
Generate two graphics related to entropy.
-
A317:
Construction of an optimal encoding and related questions.
-
A324:
Finding the average number of time units needed to transmit a character
using the Morse code.
-
A407:
Functions that implement residual/predictive coding and decoding.
(T05.9)
-
A414:
Work on Haar transforms of higher level.
-
A421:
Computation of the functions
Ar(f, r)
and Dr(f, r)
using scaling and wavelet vectors.
-
A428:
Graphics of D4(f).
-
A505:
Draw graphics of some Daub4 scaling and wavelet vectors
of different levels.
-
A512:
Work on Daub4 MRA.
-
A519:
Work on compression/decompression using D2, D4 and D6.
-
A526:
Work on the DCT.
PAPER PROJECTS
Resources
PYTHON
Main programming environment: pyzo.
Why python?
© SXD