Kivanc Ozonat
 ozonat@stanford.edu

 Project Topic: Distributed Source Coding Schemes for Correlated Still Images

 Project Description:


 This project aims to transmit a still image efficiently, given that a
noisy version of the image is present at the decoder end, and that the
original and the noisy versions do not communicate at th encoder. The
efficient bit rate in coding the original image is targeted to be as close
as possible to the conditional entropy rate of the original image given
the noisy image, as established by Slepian and Wolf ([1]).

 It should be noted that the major strategy is to use cosets as suggested
by Pradhan and Ramchandran ([2]), paying attention to two objectives: One
is that the members of the same coset should be as distant from each other
as possible, and the other is that members with similar probabilities of
occurence should be placed in each coset.

 One method to achieve these two objectives is to use bit-plane encoding
and to use the Asymptotic Equipartition Property (AEP) to form a uniformly
distributed set of strings. However, this approach is not succesful at
high noise levels, as the lowest three or four bit-planes, which are
responsible for most of the total bit rate, remain completely below the
noise level.

  The method proposed here is to first transform the image using DCT,
followed by quantization. The distribution of each of the coefficents,
after zonal coding, can be approximated by a Laplacian, Markov model.
However, the Laplacian model is far from being uniform and given the large
number of qunatization levels, it is not efficient to use the Shannon-
McMillan-Breiman Theorem to get a uniform distribution from this Laplacian
distribution. However, through dividing each coeffient sequence into
bit-planes as in bit-plane encoding, the distribution of each bit-plane is
a 2-state Markov model (in approximation), whose entropy rate can be
computed, and which can be turned into a string of 0's and 1's with
each distant string (to be placed in the same coset) having a similar
probability of occurence.

 The general scheme is as below:

 (i) Production of a correlated image by adding an i.i.d. zero
 mean, Gaussian noise. The noisy image at the decoder is aimed to have
 a PSNR of around 28-30 dB; hence, a variance of 100 is to be used for the
 initial stages.

 (ii) Using transform coding for the original image at the encoder. This
 stage will include discrete cosine transforming the image, bit allocation
 based on the coefficent variances, and quantization. The quantization is
 to be performed initially by a uniform quantizer, but Lloyd-Max quantizer
 is also going to be tried as it ends up giving a more uniform (although
 not much for the Laplacian distribution of the coefficients) quantized
 output. The coefficients are to be coded by zonal coding.

 (iii) Bit-plane encoding of the quantized coefficent levels, and using
 the 2-state Markov model to approximate the behavior of each of the bit-
 planes. This is to be followed by the application of the Shannon-McMillan
 Breiman Theorem to compute the entropy rate and the probability
 distribution of the typical sets.

 (iv) A careful distribution of the strings of 0's and 1's of the
 bit-planes into cosets, paying particular attention to combining
 strings with similar probability values and as distant from each other
 as possible.



  References:

 [1] D. Slepian and J.K. Wolf, "Noiseless Coding of Correlated
     Information Sources," IEEE Trans. Information Theory, July 1973

 [2] S. Pradhan and K. Ramchandran, "Distributed Source Coding Using
     Syndromes Design and Construction," Proc. IEEE Data Compression
     Conf., Snowbird, UT, March 1999

 [3] S. Pradhan and K. Ramchandran, "Efficient Image Denoising using Side
     Information," Proc. SPIE Conference on Electronic Imaging: Image and
     Video Communications and Processing, January 2000

 [4] T.M Cover and J.A. Thomas, Elements of Information Theory, Wiley,
     New York, 1991

 [5] S.L. Lin and D.J. Costello, Error Control Coding, Prentice Hall,
     New Jersey, 1983

 [6] R.C. Gonzalez and R.E. Woods, Digital Image Processing, Addison
     Wesley, Massachusetts, 1992