ĐIỆN tử VIỄN THÔNG bài 4 lossy compression khotailieu

3  Lossless compression algorithms do not deliver compression ratios that are high enough..  In order to achieve higher rate of compression, we give up complete reconstruction and cons

Multimedia Engineering

Lecture 4: Lossy Compression

-Techniques

Lecturer: Dr Đỗ Văn Tuấn

Department of Electronics and

Telecommunications

Email: tuandv@epu.edu.vn

3

 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

Introduction

5

 Mean Square Error (MSE)

 Signal to Noise Ratio

 Peak Signal to Noise Ratio

Distortion Measures

6

 We trade-off rate (number of bits per symbol) versus distortion this is

represented by a rate-distortion function R(D)

Rate-Distortion Theory

8

 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

Quantization

10

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

12

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

13

 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

Discrete Cosine Transform

14

 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

Discrete Cosine Transform

15

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)

16

Discrete Cosine Transform

 1D discrete cosine transform (1D DCT)

 Where i , u = 1,2, ,7

 1D inverse discrete cosine transform (1D IDCT)

17

Basic functions of DCT

18

Basic functions of DCT

19

Example of 1D DCT

20

Example of 1D DCT

22

End of the lecture