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Wavelets in Image Compression. Bhushan D Patil PhD Research Scholar Department of Electrical Engineering Indian Institute of Technology, Bombay Powai, Mumbai 40076. What are the principles behind compression?.

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wavelets in image compression

Wavelets in Image Compression

Bhushan D Patil

PhD Research Scholar

Department of Electrical Engineering

Indian Institute of Technology, Bombay

Powai, Mumbai 40076

what are the principles behind compression
What are the principles behind compression?
  • Two fundamental components of compression are redundancy and irrelevancy reduction.
  • Redundancy reduction aims at removing duplication from the signal source (image/video).
  • Irrelevancy reduction omits parts of the signal that will not be noticed by the signal receiver, namely the Human Visual System (HVS).
image compression steps

Original image

Source encoder

linear transform to decorrelate the image data (lossless)


(inverse T)


Compressed image

Entropy Coding

of the resulting quantized values(lossless)


Image compression steps:


of basis functions coefficients (lossy)

basic ideas of linear transformation
Basic ideas of linear transformation
  • We change the coordinate system in which we represent a signal in order to make it much better suited for processing (compression).
  • We should be able to represent all the useful signal features and important phenomena in as compact manner as possible.
  • Important to compact the bulk of the signal energy into the fewest number of transform coefficients.
which options do we have for linear transformation
Which options do we have for linear transformation?

A possible choice for the linear transformation are:

  • DFT
  • or, avoiding complex coefficients, the DCT
  • JPEG (decomposition into smaller subimages of size 8x8 or 16x16, followed by DCT as the compression algorithm)
why wavelet based compression
Why Wavelet-based Compression?
  • No need to block the input image and its basis functions have variable length to avoid blocking artifacts.
  • More robust under transmission and decoding errors.
  • Better matched to the HVS characteristics
  • Good frequency resolution at lower frequencies, good time resolution at higher frequencies – good for natural images.
energy compactness
Energy Compactness

No compression yet

ezw zerotree coding
EZW: ZeroTree Coding
  • Uses “parent-child” dependencies between
  • subband coefficients at same spatial location
  • ‘Bit-plane’ coding: enables an embedded

bitstream wrt distortion

significance pass
Significance Pass
  • Significant Coefficient y w.r.t. Threshold T: |y|≥T
  • 􀁺 In a significance pass, all as yet insiginfant

coefficients are examined and declared either:

􀁺 Significant positive

􀁺 Significant negative

􀁺 Root of a zerotree (All children and root insigificant)

􀁺 Isolated insisignificant

  • 􀁺 At each pass, T ←T/2
refinement pass
Refinement Pass
  • All coefficient previously declared significant are refined by one bit:
  • 􀁺 y-estimate quantized to + or – T/4
  • 􀁺 Coefficients are visited by decreasing magnitude, then in raster order
set partitioning in hierarchical trees spiht
Set Partitioning in Hierarchical Trees(SPIHT)
  • Same sort of idea as EZW
  • More efficient
  • Based on two types of zerotrees (not including


  • 􀁺 All descendants of a node are insignificant (Type A)
  • All descendants of a node starting with the

grandchildren are insignificant (Type B)

  • Coefficients and trees are stored in lists

processed in sequence

  • 􀁺 List of Significant Coefficients (LSC)
  • 􀁺 List of Insignificant Coefficients (LIC)
  • 􀁺 List of Insignificant Sets (LIS)
  • 􀁺 The lists enable a more efficient scan order of the different trees and coefficients
coding passes
Coding passes
  • All nodes from low-res LL in LIC, all those with

descendants in LIS

  • Examine nodes in LIC. If become significant, “1” and

their sign, move to LSC; otherwise “0”

  • 􀁺 Examine sets in LIS.

􀁺 If remains insignificant, “0”.

􀁺 Else “1” and:

􀁺 If Type A:

􀂃 Encode all children’s current bit (and sign), move them to end of LIC

or LSC

Change Type to B, move to end of LIS

􀁺 If Type B: delete tree from LIS. Add each child at end of LIS

as Type A.

  • 􀁺 Refinement: refine all coefficients in LSC
matlab implementation
MATLAB Implementation
  • Analysis at various Compression rate.
  • PSNR