Feng Juan's second assignment

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2, using the program Huff_enc and Huff_dec to do the following (in each case, the use of compressed images generated by the codebook).

(a) Encode Sena, Sensin, and Omaha images.

(b) Write a procedure to get the difference between adjacent, and then encode the difference image using Huffman.

Give the file size of each experiment and explain the difference.

Solution: (a)

Filename	Before compression	After compression	Compression ratio
Sena	34.	57K	1.14
Sensin	34.	31.	1.06
Omaha	34.	58K	1.12

4. A source selects letters from the symbol set A={A1,A2,A3,A4,A5} with a probability of P (A1) =0.15,p (A2) =0.04,p (A3) =0.26,p (A4) =0.05,p (A5) = 0.50.

(a) Calculate the entropy of the source.

(b) To seek the Huffman code of this source.

(c) Ask for the average length and redundancy of the code in (b).

Solution:

(a) H (a) = -0.15*log20.15-0.04*log20.04-0.26*log20.26-0.05*log20.05-0.50*log20.50

=0.15* 2.737+0.04*4.644+0.26*1.943+0.05*4.322+0.5*1

=0.411+0.186+0.505+0.216+0.5

=1.818 (Bits/symbol)

(b) a1:001

a2:0000

A3:01

a4:0001

A5:1

(c) Average length: l=0.15*3+0.04*4+0.26*2+0.05*4+0.5*1

=0.45+0.16+0.52+0.2+0.5

=1.83 (Bits/symbol)

Redundancy: l-h (A) =1.83-1.818=0.012 (Bits/symbol)

5. A symbol set A={A1,A2,A3,A4}, with a probability of P (A1) =0.1,p (A2) =0.3,p (A3) =0.25,p (A4) = 0.35, use the following procedure to find a Huffman code:

(a) The first process outlined in this chapter;

(b) The minimum variance process.

Explain the differences between the two Huffman codes.

Solution:

(a) The first Huffman code

Symbol	Probability	Code
A1	0.1	000
A2	0.3	01
A3	0.25	001
A4	0.35	1

The second type of Huffman code

Symbol	Code
A1	11
A2	01
A3	10
A4	00

(b) Average code length:

First Huffman code: l=3*0.1+2*0.3+3*0.25+1*0.35=2

The second Huffman code: l=2*0.1+2*0.3+2*0.25+2*0.35=2

Variance:

First type: s2=0.1 (3-2) 2+0.3 (2-2) 2+0.25 (3-2) 2+0.35 (1-2) 2=0.70

Second type: s2=0.1 (2-2) 2+0.3 (2-2) 2+0.25 (2-2) 2+0.35 (2-2) 2 =0

The second type of Huffman code is superior

6, reference book "Introduction to Data Compression (4th edition)" Page 30

6. There are several images and voice files in the accompanying data set in this book.

(a) Write a procedure to calculate the first-order entropy of some of the images and voice files.

(b) Select an image file and calculate its second-order entropy. Try to explain the difference between the first order entropy and the second entropy.

(c) For the image file used in (b), calculate the entropy of the difference of its neighboring pixels. Try to explain your findings.

For:

                 

(b) The first order entropy of the image file is earth.img: 4.770801, the second entropy is: 2.568358

It is known that the first-order entropy of the image is much larger than the second entropy. The second-order compression of files can increase the compression and reduce storage space.

(c) The first order entropy of the image file is earth.img: 4.770801, the second entropy is: 2.568358, the difference entropy is 3.962699

By comparison , the difference entropy is between the first order entropy and the second entropy. For the first order entropy, the difference entropy is an ideal compression algorithm.

Feng Juan's second assignment