The second homework Huang only

1, reference book "Introduction to Data Compression (4th edition)" Page 66

3-2 Use the program Huff_enc to do the following (in each case, using the codebook generated by the compressed image).

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

Answer: (a) Sena: Before compression: 64.0 KB (65,536 bytes)--After compression: 56.1 KB (57,503 bytes) Compression ratio: 88%

Sensin: Before compression: 64.0 KB (65,536 bytes)--After compression: 60.2 KB (61,649 bytes) Compression ratio: 94%

Omaha: Before compression: 64.0 KB (65,536 bytes)--After compression: 56.1 KB (57,503 bytes) Compression ratio: 89%

3-4 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) The entropy of this source is:

H=-P (A1) log2p (A1)-P (A2) log2p (A2)-P (A3) log2p (A3)-P (A4) log2p (A4)-P (A5) log2p (A5)

=-0.15 * LOG2 (0.15)-0.04 * LOG2 (0.04)-0.26 * LOG2 (0.26)-0.05 * LOG2 (0.05)-0.5 * LOG2 (0.5)

=0.411+0.1856+0.5044+0.216+0.5

=1.817 (BITS)

(b)

Answer: Hoffman code: A1 001

A2 0000

A3 01

A4 0001

A5 1

                      

(c)

L=p (A1) *l (A1) +p (A2) *l (A2) +p (A3) *l (A3) +p (A4) *l (A4) +p (A5) *l (A5)

=0.15*3+0.04*4+0.26*2+0.05*4+0.5*1

=1.83 (BITS)

Redundancy of h-l=2.368-1.83=0.538

2-6. 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:

(a):

Filename	First-order entropy	Second order entropy	Differential entropy
SENA. Img	6.834299	3.625204	3.856899
Sensin. Img	7.317944	4.301673	4.541547
OMAHA. Img	6.942426	4.488626	6.286834
EARTH. Img	4.770801	2.568358	3.962697
GABE. RAW	7.116338	6.654578	8.978236
BERK. RAW	7.151537	6.705169	8.976150

(b). Second-order entropy is smaller than first-degree entropy

(c). The entropy of the pixel difference is greater than the first order entropy and the second entropy.

The second homework Huang only