# SIGNAL AND IMAGE PROCESSING

Τεχνίτη Νοημοσύνη και Ρομποτική

6 Νοε 2013 (πριν από 4 χρόνια και 6 μήνες)

68 εμφανίσεις

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

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