1. Sangeun Han and Yi Liang
Comparison Study on the Performance of Critically Sampled Pyramid vs. Over-Complete Pyramid
Notation of the notes:
C: critically sampled pyramid
O: oversampled
Sangeun Han and Yi Liang
Dec. 4, 2000

2. Overview Introduction of multiresolution and pyramid coding
Critically sampled and overcomplete pyramids
Bit allocation and quantization
Comparison and results

3. Multiresolution and Pyramid Coding
Multiresolution offers excellent coding efficiency.
Multiresolution supports scalability.
Note: animation showing scalability
Introduction and background.
Compression efficiency: obtained by removing the statistical correlation of the signal, and redundancy.
Scalability: decoding using different layers and different number of bits. This feature is desired for streaming multimedia applications when the channel characteristics not known. Also useful for receivers with difference decoding speed and complexity.
r=0.09, 0.23, 0.60, 1.00 bpp

4. Critically Sampled PyramidH1 2 Q 2 G1 H1 2 Q 2 G1 +
Input H0 2
Recon. 2 G0 + H0 2 Q 2 G0
Octave subband coding
Channel
Spectrum in each subband is pretty much flat due to the decomposition.
Correlation is thus removed. Can achieve coding efficiency in this way.
Octave subband is even more efficient since at low frequency spectrum delays more rapid.
Original Image Decomp. Subbands

5. Oversampled Pyramid
Briefly explain the difference between open-loop and close loop from block diagram.
Emphasize scalability and multiresolution from different layers.

6. Choosing the Filters
I am not sure if we need this slide to go into such detail of choosing filters for O.
Mention one of the advantages of O is more freedom in choosing interp/decim filters, and what filter to use is important.

7. Bit Allocation Analytical form The “greedy” algorithm
Critically sampled, open-loop oversampled
The “greedy” algorithm
Close-loop oversampled
where
No need to talk about maths in detail for the analytical form.
But explain about how the “greedy” alg is implemented in practice in more detail. Give one more bit to the subband or layer which needs it more. Thus to make the slope of dD/dR the same of all subbands.
Mention the reason why greedy alg. is not opt.
Mention what quantizer we use. The performance quantizer is nearly as good as Loyd quantizer. Since entropy coding is used after quantization.
(According to Vetterli’s book, VQ is usually not worthwhile for its complexity.)

8. Comparison of Rate-distortion Performance
This is the most important slide. Spend some time explaining the plot in quantity.
Explain the reason why C performs better than O. Mention O is more suitable for low bit-rate.
Mention the close-loop is slightly better than open-loop, especially for high bit rate.
Mention the two bit allocation schemes don’t make big difference, though greedy alg. is sub-optimal.
In general, critically sampled outperforms oversampled in terms of rate-distortion. Reason: oversampling.

9. Scalability Critically sampled Overcomplete PSNR = 28.4 dB
For almost the same full res psnr, O gives better subjective quality in full res layer and 1st layer.
Ripples in C go away due to the filter used (?) in O.
Note O has to use more bits.
PSNR = 23.8 dB
PSNR = 20.9 dB
PSNR = 25.8 dB
PSNR = 22.8 dB

10. Number of Layers Critically sampled Overcomplete
Different trend of performance as number of layers increases in two schemes.
For C, L>=3, difference is small. For O, use L=4 to have same # of multiresolution pictures.
We use L=3, L=4 for the two cases.
Critically sampled Overcomplete

11. Conclusions
Critically sampled pyramid outperforms the over-complete pyramid in terms of rate-distortion.
Coarse images from overcomplete pyramids show better subjective quality.
Other features of overcomplete pyramid: lower complexity, freedom in choosing filters, control of quantization noise.