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Fixed Analysis Adaptive Synthesis Filter Banks for Image Compression and Image Interpolation
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Fixed-Analysis Adaptive-Synthesis (FAAS)
Filter Banks
ByClyde A. Lettsome, P.E.
Ph.D. Dissertation AdvisorsDr. Mark J. T. Smith
Dr. Russell M. Mersereau
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What is a Filter Bank?
Uniform M-Channel Filter BankA S
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Time-Varying Combinations for Filter Banks
Fixed Analysis Adaptive Analysis
Fixed Synthesis
Numerous ResearchersConventional Filter bankWavelets
No known research done
Adaptive Synthesis
Our Research Nayebi, Arrowood, Chung, Sodagar, and othersTime-Varying filter banksNewer
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Purpose of this Dissertation
In this thesis we introduce the new FAAS class of filter banks.
This thesis is devoted to defining, designing, exploring, and evaluating this new class.
We demonstrate this new class on image compression and image resizing.
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Outline
1. Background of AAAS Filter Banks2. Introduction of FAAS Filter Banks3. FAAS Filter Design Methodology for Image
Compression4. FAAS Distortion Suppression for Image
Compression5. Application of FAAS Filter Banks to Image Coding6. Applications of FAAS Filter Banks to Interpolation7. Conclusions8. Contributions9. Future Work
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The First AAAS Filter Bank
Nayebi et al. introduced AAAS filter banks. Nayebi wanted to see if it was possible to switch filters
and still achieve exact reconstruction (ER). This system achieved exact reconstruction.
A single switch requires 2L synthesis filters.
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AAAS Filter Banks Postfilters
Sodagar et al. simplified the AAAS filter banks with postfilters. When switching occurs
To restore ER, a postfilter is added making
This allows for the switching of the analysis filters and then directly switching the synthesis filters in lockstep.
8 AAAS Filter Bank Structure with a Postfilter
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AAAS Filter Banks for Image Coding
Arrowood et al. explored the use of AAAS filter banks for image coding. They used them to reduce perceived distortion. They switched between filters with asymmetric impulse
responses and varying group delays.
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Disadvantages of the AAAS
Disadvantages of the AAAS filter bank: Synchronization information must be communicated to
keep the filters in synchrony Postfiltering becomes more complex when
Interval between switching decreases and The number of switches increases.
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Motivation for the FAAS Filter Bank
Motivation for Asymmetric Filter Banks: Eliminate the need for synchronization information to be transmitted, Reduce complexity related to postfiltering, Increase quantitative and perceptual quality over conventional filter
banks, Make compatibility with conventional systems.
Why FAAS over AAFS? FAAS can remove ringing artifacts after the quantization. FAAS can compensate for distortion after the quantization. FAAS can exploit diversity after quantization in image coding
applications. FAAS can be used for image enlargement.
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FAAS Filter Banks Block Diagram
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Application of Image compression
One common use of filter banks is in image compression
To use FAAS filter banks for image compression we must redesign some components.
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FAAS Filter Design
Recall our design goals. We want our system to be compatible with existing standard coders. We want to exploit phase diversity to enhance images.
Odd-length filters are used pervasively in image coders. We need an odd-length time-domain algorithm to develop
filters for this compatible system. We introduce an new time domain method for designing
these odd-length method which has not been done before. With this method, we are able to design odd-length filters and
control the filter ripple, transition bandwidth, reconstruction fidelity, and system group delay.
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FAAS Filter Banks Filter Design
Where
A is a block Toeplitz matrix of analysis coefficients.
S is a matrix of synthesis filter coefficients.
B is a reconstruction matrix where the system delay can be adjusted.
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FAAS Filter Banks Filter Design
1. Insert initial analysis filter coefficients for A.
2. Choose a desired delay by sliding the exchange matrix in B.
3. Solve for S.
Note: S contains the synthesis filter coefficients given by Q ……
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FAAS Filter Banks Filter Design
4. Use A, S, and B to form reconstruction error component.
5. Form a frequency domain component.
6. Find the total system weighted error.
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Implementation Protocols
The implementation protocol for the FAAS synthesis section:
1. The starting point is an existing encoding system. 2. Design filter set to exploit phase diversity. 3. Design via the new design methodology (step 3-6).
System characteristics notes: For this thesis:1. Only the linear-linear phase pair deliver ER.2. All other filter pairings have significantly higher reconstruction
errors. The low-delay and high-delay synthesis filters are designed strictly for distortion suppression.
3. Reconstruction errors can be optimized as desired using additional equations found in the dissertation document.
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Distortion at Low Bit Rate
Ringing distortion occurs at low bit rates.
Original Image Image at 0.25 bpp
20 Cause of Distortion in Coding Applications
This occurs because highpass information is discarded.
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Low Delay Step Response
Low delay step response
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Linear Phase Step Response
Linear Phase Step Response
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High Delay Step Response
High Delay Step Response
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Distortion Suppression
Linear phase =green
Low delay =blue
High delay =red
All step responses
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Distortion Suppression Protocol
Distortion suppression protocol
Let LD=low delay, HD=high delay, and LP=linear phase
If
If
and
and
then
then
On a pixel by pixel basis.
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Distortion Suppression Mask
Row filtered mask
Original image
Linear phase =green
Low delay =blue
High delay =red
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Convolution and Boundary Distortion The data expansion is an undesirable affect caused by linear convolution. Circular convolution eliminates data expansion but causes boundary distortion.
Circularly convolved low bit rate coded image
Original Image
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Symmetric Extension
Symmetric extension has become a common method used to address boundary distortion in subband/wavelet coding.
Symmetrically extended and convolved low bit rate coded image
Symmetric extension does not accommodate nonlinear phase filters within the filter bank structure.
29 Consider
After
30 FAAS Filter Bank Application to Symmetric Extension
Results from a filter bank system with whole-point nonlinear symmetric extension
(a) Original signal(b) Analysis lowpass filter (c ) Vo(n)
(d) Yo(n) after window function
(e) Yo(n) after symmetric extension and upsampling
(f) Results after filtering with the synthesis lowpass
•Results
31 FAAS Filter Bank Application to Symmetric Extension
(g) Results after post filtering
(h) Results after windowing
Results from a filter bank system with half-point nonlinear symmetric extension
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Image Coding Results
Conventional SPIHT coder at 0.5bpp
FAAS SPIHT coder using optimal selection at 0.5bpp
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Image Interpolation
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Interpolation Results
Bicubic Interpolated Optimal Adaptive Interpolated
Areas of interest
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Summary of Results
We were successful in demonstrating the proof of this concept.
FAAS filter banks are compatible with existing subband/wavelet coders.
Experimental results support the potential utilization of FAAS systems in areas of compression and interpolation.
36
Contributions
The FAAS filter bank was evaluated and compared against conventional FAFS systems for image compression.
The FAAS filter bank was applied to symmetric extension. The FAAS filter bank was examined as part of a video
compression algorithm. The FAAS filter bank was examined for image enlargement
and resizing. Performed a proof of concept for even-length adaptive
boundary symmetric extension. Developed the method for odd-length adaptive boundary
symmetric extension.
37 Publications and Planned Publications
Publications Ying Chen, Clyde Lettsome, Mark Smith and Edward Delp, "A Low Bit-rate
Video Coding Approach Using Modified Adaptive Warping and Long-Term Spatial Memory" in Visual Communications and Image Processing. (VCIP'2007), San Jose, California, Jan. 2007.
Clyde Lettsome, Mark Smith, and Russell Mersereau, “Fixed Analysis Adaptive Synthesis Filter Banks" in SPIE Defense + Security . (SPIE D+S’ 2008), Orlando, Florida, March 2008.
Clyde A. Lettsome and Mark J.T. Smith, "Image Interpolation Exploiting Phase Diversity" in IEEE DSP Workshop., Marco Island, Florida, Jan. 2009.
Planned Publications: Jienyu lIn, Clyde Lettsome and Mark Smith, "Optimized Non-linear phase
Filters for Subband/Wavlet Coding," in Transactions on Image Processing (In Preparation).
Clyde A. Lettsome, Mark J.T. Smith, and Russell Mersereau "Fixed-Analysis Adaptive - Synthesis Filter Banks: Theory and Applications," in Transactions on Image Processing (In Preparation).
38
Future Work
Investigate the use of the adaptive synthesis filters on the subsequent levels in the subband tree.
Determine the compression rate at which FAAS systems achieve significant gain is a topic worth examining.
Investigate alternative selection algorithms for exploiting phase diversity.
Consider the use of a rich set of synthesis filters such as 6, 9, or 12 and investigate the extent to which performance can be improved.
Investigate and analyze the results of using FAAS high delay filters for image interpolation.