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

Fixed-Analysis Adaptive-Synthesis (FAAS)Filter Banks

ByClyde A. Lettsome, P.E.

Ph.D. Dissertation AdvisorsDr. Mark J. T. SmithDr. Russell M. Mersereau

What is a Filter Bank? Uniform M-Channel Filter BankAS

Time-Varying Combinations for Filter Banks

Fixed AnalysisAdaptive AnalysisFixed SynthesisNumerous ResearchersConventional Filter bankWaveletsNo known research done

Adaptive SynthesisOur ResearchNayebi, Arrowood, Chung, Sodagar, and othersTime-Varying filter banksNewer

Purpose of this DissertationIn 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.

Outline Background of AAAS Filter BanksIntroduction of FAAS Filter BanksFAAS Filter Design Methodology for Image CompressionFAAS Distortion Suppression for Image CompressionApplication of FAAS Filter Banks to Image CodingApplications of FAAS Filter Banks to InterpolationConclusionsContributionsFuture Work

The First AAAS Filter BankNayebi 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.

AAAS Filter Banks PostfiltersSodagar 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.

AAAS Filter Bank Structure with a Postfilter

AAAS Filter Banks for Image CodingArrowood 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.

Disadvantages of the AAASDisadvantages of the AAAS filter bank:Synchronization information must be communicated to keep the filters in synchronyPostfiltering becomes more complex whenInterval between switching decreases and The number of switches increases.

Motivation for the FAAS Filter BankMotivation 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.

FAAS Filter Banks Block Diagram

Application of Image compressionOne common use of filter banks is in image compression

To use FAAS filter banks for image compression we must redesign some components.

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.

FAAS Filter Banks Filter DesignWhere 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.

FAAS Filter Banks Filter Design1. 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

FAAS Filter Banks Filter Design4. Use A, S, and B to form reconstruction error component.5. Form a frequency domain component.6. Find the total system weighted error.

Implementation ProtocolsThe implementation protocol for the FAAS synthesis section:The starting point is an existing encoding system. Design filter set to exploit phase diversity. Design via the new design methodology (step 3-6). System characteristics notes:For this thesis:Only the linear-linear phase pair deliver ER.All other filter pairings have significantly higher reconstruction errors. The low-delay and high-delay synthesis filters are designed strictly for distortion suppression.Reconstruction errors can be optimized as desired using additional equations found in the dissertation document.

Distortion at Low Bit RateRinging distortion occurs at low bit rates.

Original ImageImage at 0.25 bpp

Cause of Distortion in Coding ApplicationsThis occurs because highpass information is discarded.

Low Delay Step ResponseLow delay step response

Linear Phase Step ResponseLinear Phase Step Response

High Delay Step ResponseHigh Delay Step Response

Distortion SuppressionLinear phase =greenLow delay =blueHigh delay =redAll step responses

Distortion Suppression Protocol Distortion suppression protocol Let LD=low delay, HD=high delay, and LP=linear phase IfIfandandthenthenOn a pixel by pixel basis.

Distortion Suppression MaskRow filtered maskOriginal imageLinear phase =greenLow delay =blueHigh delay =red

Convolution and Boundary DistortionThe 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 imageOriginal Image

Symmetric ExtensionSymmetric extension has become a common method used to address boundary distortion in subband/wavelet coding.Symmetrically extended and convolved low bit rate coded imageSymmetric extension does not accommodate nonlinear phase filters within the filter bank structure.

ConsiderAfter

FAAS Filter Bank Application to Symmetric ExtensionResults 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 lowpassResults

FAAS Filter Bank Application to Symmetric Extension(g) Results after post filtering

(h) Results after windowingResults from a filter bank system with half-point nonlinear symmetric extension

Image Coding ResultsConventional SPIHT coder at 0.5bppFAAS SPIHT coder using optimal selection at 0.5bpp

Image Interpolation

Interpolation Results Bicubic InterpolatedOptimal Adaptive InterpolatedAreas of interest

Summary of ResultsWe 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.

ContributionsThe 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.

Publications and Planned Publications

PublicationsYing 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).

Future WorkInvestigate 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.

This allows for the switching of the analysis filters based on the input characteristics and then directly switching the synthesis filters in lockstep.

Efficient and low complexityThis is an equation that represents convolution and the extension can be implemented within the matrix construct