The document introduces Fixed-Analysis Adaptive-Synthesis (FAAS) filter banks, a new class of filter banks that uses fixed analysis filters and adaptive synthesis filters. It discusses the motivation for developing FAAS filter banks and outlines how they can be designed and applied to tasks like image compression and image resizing. Experimental results demonstrate the potential benefits of FAAS filter banks for compression and interpolation compared to conventional filter banks.

1. 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

2. What is a Filter Bank? Uniform M-Channel Filter Bank A S

3. Time-Varying Combinations for Filter Banks Nayebi, Arrowood, Chung, Sodagar, and others Time-Varying filter banks Newer Our Research Adaptive Synthesis No known research done Numerous Researchers Conventional Filter bank Wavelets Fixed Synthesis Adaptive Analysis Fixed Analysis

8. AAAS Filter Bank Structure with a Postfilter

12. FAAS Filter Banks Block Diagram

15. 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.

16. 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 ……

17. 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.

21. Low Delay Step Response Low delay step response

22. Linear Phase Step Response Linear Phase Step Response

23. High Delay Step Response High Delay Step Response

24. Distortion Suppression Linear phase =green Low delay =blue High delay =red All step responses

26. Distortion Suppression Mask Row filtered mask Original image Linear phase =green Low delay =blue High delay =red

29. Consider After

32. Image Coding Results Conventional SPIHT coder at 0.5bpp FAAS SPIHT coder using optimal selection at 0.5bpp

33. Image Interpolation

34. Interpolation Results Bicubic Interpolated Optimal Adaptive Interpolated Areas of interest