SIGNAL AND IMAGE PROCESSING

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6 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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INFORMATION ENGINEERING IN
SIGNAL AND IMAGE PROCESSING

Aleš Procházka

Institute of Chemical Technology, Prague

Dept. of Computing and Control Engineering

The

science of physics does not only give us (mathematicians) an

opportunity to solve problems, but helps us also to discover the

means of solving them

Signal

processing combines the unique

ability of mathematics to
generalize with the prior

information gained from the underlying
physics of the problem at

hand

RELATION BETWEEN MATHEMATICS AND PHYSICS

(Henri Poincare)

POSITION OF SIGNAL
PROCESSING

(Simon Haykin)


1.
INTRODUCTION

INTEGRATION ROLE OF SIGNAL

AND IMAGE PROCESSING IN

THE FRAME OF INFORMATION

ENGINEERING




Interdisciplinary area connecting mathematics and engineering



Basis for control and measuring engineering, vision, robotics,


speech processing, biomedicine, environmental engineering …



Fundament for data acquisition, system and signal identification


and modelling, signal and image de
-
noising, feature extraction,


segmentation, classification, compression, prediction, …




Similar mathematical background based upon general methods


of time
-
frequency and time
-
scale analysis



Close information engineering tools: databases, mathematical


software, computer networks, remote data processing

BASIC PROBLEMS

2. SIGNAL AND IMAGE ANALYSIS


2.1 Discrete Fourier Transform


2.2 Discrete Wavelet Transform


3. SIGNAL AND IMAGE PROCESSING


3.1 Signal and Image De
-
Noising


3.2 Image Interpolation and Correlation


3.3 Signal Modelling and Prediction


4. INFORMATION ENGINEERING IN SIGNAL AND IMAGE
PROCESSING



2.
SIGNAL ANALYSIS


2.1
DISCRETE FOURIER TRANSFORM








1
0
1
,...,
1
,
0
),
/
2
exp(
)
(
)
(
N
n
N
k
N
jkn
n
x
k
X

IMAGE
ANALYSIS

TWO
-
DIMENSIONAL

DISCRETE FOURIER
TRANSFORM










1
0
1
0
)
/
2
exp(
)
/
2
ln
exp(
)
,
(
)
,
(
M
m
N
n
M
jkm
N
j
n
m
x
l
k
X


2.2 WAVELET
TRANSFORM

BASIC PROPERTIS



Initial wavelet defined either in


the analytical form or by a


dilation equation




Dilation and translation


coefficients: a=2^m, b=k 2^m



Initial wavelet represents a


pass
-
band filter



Wavelet dilation corresponds


to its pass
-
band compression



Scaling function represents


the final low
-
pass filter



The set of wavelet functions


and a scaling function defines


a filter bank

)
(
1
)
(
,
a
b
t
h
a
t
h
b
a


TIME
-
FREQUENCY
AND TIME
-
SCALE
ANALYSIS

COMPARISSON




Signal decomposition



Different resolution in the case of


Wavelet transform



Constant resolution in the case of


short time Fourier transform













1
0
1
2
/
0
2
0
)
2
(
)
(
1
n
m
m
N
k
k
k
n
h
a
a
n
x
m
m
3. SIGNAL AND
IMAGE
PROCESSING


3.1 DE
-
NOISING



Signal decomposition using a


chosen wavelet function



The choice of threshold limits


and coefficients modification



Signal or image reconstruction



Application of gradient method


for image enhancement

BASIC PROBLEMS:
Choice between hard and soft thresholding


Threshold limits estimation

3.2 IMAGE INTERPOLATION AND CORELATION

Evaluation of
correlation coefficient












m
n
m
n
n
m
n
m
n
n
m
n
m
m
B
B
A
A
B
B
A
A
R
2
,
2
,
,
,
)
(
)
(
)
)(
(
3.3 SIGNAL MODELLING AND PREDICTION

Reliability limits estimation

e
m
j
v
j
h
u
n
x
n
x






1
1
2
2
/
)
)
(
1
(
)
(
ˆ
)
(

)
(
)
(
)
(
...
)
1
(
)
1
(
)
(
n
e
na
n
x
na
a
n
x
a
n
x







LINEAR
Autoregressive

modelling

NON
-
LINEAR MODELLING

Artificial neural network

B2
B1
P
W1
W2
Y



)
*
(
1
*
F
Problems



Structure selection



Optimization

OPTIMIZATION

Problems: Initial coefficients selection


Optimization method choice

4. INFORMATION ENGINEERING
IN SIGNAL AND IMAGE
PROCESSING



Mathematical background of


signal and image processing is


similar for many applications



Information technologies form a


basis for signal processing



Information engineering


provides a basis for various


disciplines

EVOLUTION OF MODERN
STATISTICAL DIGITAL
PROCESSING METHODS IN
21
ST

CENTURY


(Simon Haykin)

Interdisciplinary basis of digital signal processing will bring
together mathematics and physics reconciling the ever
-
present
tension between them allowing to (i) test algorithms with real
-
life
data and (ii) learn from the data

INFORMATION LINKS

http://dsp.vscht.cz

Link to DSP group server:

Link to Wavelet discussion group:

http://www.wavelet.org

Link to extensive DSP group:

http://www.rice.edu