Image Compression using Discrete Wavelet Transform

Preston Dye

Social Media and Image Compression

Source: https://www.quora.com/How-does-Facebook-compress-pictures-and-what-is-the-JPEG-compression-quality-value

Fourier Transform

Original Image

Wavelet Transform Quantization Compressed

ImageEntropy

Encoding

Image Compression

Thresholding

Original Image

Original Image

Restored

RestoredCompressed

Compressed

Lossless

Lossy

13

5 8

42

F = 1 D = 1 A =4C = 2 E = 2B = 3

0

0

0

1

11

1

0

0

Source Code“abfabcaecedba”

Huffman CodeA 4 11B 3 101C 2 100D 1 1E 2 1F 1 0

Huffman Coding

Discrete Fourier Transform Compression

Discrete Cosine Transform Compression

FBI and Finger Print Problem

Discrete Wavelet Transform

Source: https://archive.cnx.org/contents/476181d8-9096-43b1-ae7c-2e3e1885cb28@4/a-multiresolution-formulation-of-wavelet-systems#uid37

Discrete Wavelet TransfromHaar Scaling Function

Haar Wavelet Function

HAAR WAVELET TRANSFORM

Resolution ApproximationsDetail

Coefficients

4 [8 5 3 4]

2 [6.5 3.5] [1.5 .5]

1 [5] [.5]

Discrete Wavelet Transform

Source: https://archive.cnx.org/contents/476181d8-9096-43b1-ae7c-2e3e1885cb28@4/a-multiresolution-formulation-of-wavelet-systems#uid37

L

H

LL

LH

HL

HH

2

2

2

2

2

2

A1

DH

DV

DD

2D Image Decomposition

2D Image Decomposition

Energy and Thresholding

Wavelet Families

Symlets and Coiflets

Sym2 at level 4 and 18.74 threshold Db4 at level 4 and 18.74 global threshold

Questions?