ĐIỆN tử VIỄN THÔNG bài 4 lossy compression khotailieu

Multimedia Engineering
--------Lecture 4: Lossy Compression
Techniques
Lecturer: Dr. Đỗ Văn Tuấn
Department of Electronics and
Telecommunications
Email:


Lecture contents

1.
2.
3.
4.

Introduction
Distortion measures
Quantization
Transform coding

2


Introduction
 Lossless compression algorithms do not deliver compression ratios that are
high enough. Hence, most multimedia compression algorithms are lossy.
 In order to achieve higher rate of compression, we give up complete
reconstruction and consider lossy compression technique
 So we need a way to measure how good the compression technique is meaning
that how close to the original data the reconstructed data is.

3


Lecture contents

1.
2.
3.
4.

Introduction
Distortion measures
Quantization
Transform coding

4


Distortion Measures
 Mean Square Error (MSE)

 Signal to Noise Ratio

 Peak Signal to Noise Ratio

5


Rate-Distortion Theory

 We trade-off rate (number of bits per symbol) versus distortion this is
represented by a rate-distortion function R(D)

6


Lecture contents

1.
2.
3.
4.

Introduction
Distortion measures
Quantization
Transform coding

7


Quantization
 Quantization is a heart of any scheme
 The source we are compressing contains a large number of distinct output
values (infinite for analog)
 We compress the source output by reducing the distinct values to a
smaller set via quantization
 Each quantizer can be uniquely described by its partition of the input
range (encoder side) and set of output values (decoder side).
 Two types of quantization: Uniform quantization and non-uniform

quantization

8


Uniform Quantization

Uniform Scalar Quantizers: (a) Midrise, (b) Midtread

9


Non-uniform Quantization
 Typical one is companded quantization

 Companded quantization is nonlinear
 As shown above, a compander consists of a compressor function G, a uniform
quantizer, and an expander function G−1.
 The two commonly used companders are the μ-law and A-law companders.

10


Lecture contents

1.
2.
3.
4.

Introduction
Distortion measures
Quantization
Transform coding

11


Transform coding
 Reason for transform coding
 Coding vectors is more efficient than coding scalars so we need to group
blocks of consecutive samples from the source into vectors
 If Y is the results of a linear transformation T of an input X such that the
elements of Y are much less correlated than X, then Y can be coded more
efficiently than X
 With vectors of high dimensions, if most of the information in the vectors is
carried in the first few components we can roughly quantize the remaining
elements
 The more decorrelated the elements are, the more we can compress the less
important elements without affecting the important ones.
12


Discrete Cosine Transform
 The DCT is a wildly used transform technique
 Spatial frequency: indicates how many times pixel values change across
an image block
 The DCT formalizes this notion in terms of how much the image contents
change in correspondence to the number of cycles of a cosine wave per
block

 The DCT decomposes the original signal into its DC and AC components
 The inverse DCT (Called IDCT) reconstructs the original signal.

13


Discrete Cosine Transform
 Given an input function f(i,j) over two integer variables i and j (a piece of
an image), the 2D DCT transforms it into a new function F(u, v), with integer
u and v running over the same range as i and j . The general definition of
the transform is:

 Where i , u = 0, 1, . . . ,M − 1; j , v = 0, 1, . . . ,N − 1 and the constants
C(u), C(v) are determined by

14


Discrete Cosine Transform
 2D discrete cosine transform (2D DCT) – In JPEG

 Where i , j, u , v = 1,2,..,7.
 2D inverse discrete cosine transform (2D IDCT)

15


Discrete Cosine Transform
 1D discrete cosine transform (1D DCT)

 Where i , u = 1,2,..,7.
 1D inverse discrete cosine transform (1D IDCT)

16


Basic functions of DCT

17


Basic functions of DCT

18


Example of 1D DCT

19


Example of 1D DCT

20


 More things to read
 Karhunen-Loeve Transform
 Wavelet-based coding
 JPEG

21


End of the lecture
--------------

22