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Fixed-Analysis Adaptive- Synthesis (FAAS) Filter Banks By Clyde A. Lettsome, P.E. Ph.D. Dissertation Advisors Dr. Mark J. T. Smith Dr. Russell M. Mersereau

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Fixed Analysis Adaptive Synthesis Filter Banks for Image Compression and Image Interpolation

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Page 1: My Dissertation Presentation Slides

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.

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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

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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.

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29 Consider

After

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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

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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.

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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.

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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).

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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.