Fixed Analysis Adaptive Synthesis

Filter Banks

ByClyde A. Lettsome, P.E.Mark J. T. Smith, Ph.D.

Russell M. Mersereau, Ph.D.

2 Outline

Introduction

Time-Varying FIR Filter Banks

Designing The Filters

Results And Conclusions

Future Work

3

Introduction

Analysis-synthesis filter banks have been employed pervasively in the signal processing community for more than three decades. They are:

Computationally efficient and exactly reconstructing

For image compression the subbands are quantized

4

Introduction

When bit rates are lowered, inevitably distortions occurChallenge: designing of subband image compression systems that can yield improved performance at these lower bit rates.

5

Time-varying Filter Banks

Prior Solution- Time-varying filter banks evolution

Nayebi explored a technique where analysis-synthesis filters are switched to reduce edge distortion.

Arrowood and Sodagar applied Nayebi’s work, investigated post-filtering restore PR.

Time-varying filter banks can reduce the magnitude of these distortions observed at edges in natural images.

6

Time-varying Filter Banks

A disadvantage is that the synthesis filters must be changed in lock step with the analysis filters

7

Time-varying Filter Banks

AnalysisSingle Set

AnalysisMultiple Set

SynthesisSingle Set

Numerous ResearchersConventional Filter bankWavelets

No known research done

SynthesisMultiple Set

Our Research Nayebi, Arrowood, Chung, Sodagar, and othersTime-Varying filter banksNewer

8

Time-varying Filter Banks

Our Solution- Adaptive FIR filter banks for image coding: have the analysis filters fixed, but

the synthesis filters change adaptively,

have no overhead associated with synchronization,

are compatible with existing subband/wavelet encoders.

9

Time-varying Filter Banks

10

Designing the Filters

11 Designing the Filters

•Nayebi introduced a time domain formulation that allowed even length FIR filters to be design at a pre-specified system delay.

12 Designing the Filters

An optimization equation is formed using:

• reconstruction error component

•component associated with the frequency domain characteristics

• and a weighting factor

13 Designing the Filters

where

14Result and Conclusion

Conventional SPIHT Coder

Bit Rate: 0.5 bpp

PSNR: 31.47 dB

Adaptive SPIHT Coder

Method applied: Last level of reconstruction

Filters used: 9/7 and complementary min and max phase filters

Bit Rate: 0.5 bpp

PSNR: 32.95 dB

15

Future Work

Applying technique on more levels Develop a more sophisticated phase selection

approach