Design and Application of Quincunx Filter Banks

Quincunx filter banks are two-dimensional, two-channel, nonseparable filter banks. They are widely used in many signal processing applications. In this thesis, we study the design and applications of quincunx filter banks in the processing of two-dimensional digital signals. Symmetric extension algorithms for quincunx filter banks are proposed. In the one-dimensional case, symmetric extension is a commonly used technique to build nonexpansive transforms of finite-length sequences. We show how this technique can be extended to the nonseparable quincunx case. We consider three types of quadrantally-symmetric linear-phase quincunx filter banks, and for each of these types we show how nonexpansive transforms of two-dimensional sequences defined on arbitrary rectangular regions can be constructed. New optimization-based techniques are proposed for the design of high-performance quincunx filter banks for the application of image coding. The new methods yield linear-phase perfect-reconstruction systems with high coding gain, good analysis/synthesis filter frequency responses, and certain prescribed vanishing moment properties. We present examples of filter banks designed with these techniques and demonstrate their efficiency for image coding relative to existing filter banks. The best filter banks in our design examples outperform other previously proposed quincunx filter banks in approximately 80% cases and sometimes even outperform the well-known 9/7 filter bank from the JPEG-2000 standard.