Title : Comparison Study on the Performace of Critically Sampled Pyramid
vs. Over-Complete Pyramid

Yi Liang     <yiliang@leland>  
Sang-Eun Han <sehan@leland>

A pyramid structure of an image is frequently used in computer vision and 
image coding since the scheme can inherently achieve a successive 
approximation or multiresolution. 

In this project, we will implement two different pyramid coders for still
images; a critically sampled subband pyramid coder and an over-complete 
pyramid coder. We will also design and implement scalar quantizers 
(or maybe vector quantizers) followed by a few different encoding methods.

For the critically sampled subband pyramid coder, we are making a choice 
among memoryless encoding, run-length encoding or Shapiro's zero-tree  
encoding of the subband coefficients. For the over-complete pyramid 
structure, we may use memoryless encoding of the error images or we can 
apply a transform coding, e.g. DCT, and then optimize entropy codes for
the transform coefficients. 

We will use Lagrangian cost function to optimize bit allocation for each
band(or each layer). The rate-distortion performance and computational
complexity for each scheme will be compared. 

References:

[1] EE368B Lecture Notes: Multiresolution & Subband
[2] M. Vetterli and J. Kovacevic, "Wavelets and Subband Coding,"  
[3] U. Horn, T. Wiegand, and B. Girod, "Bit allocation methods for 
    closed-loop coding of oversampled pyramid decompositions," ICIP'97