| Analysis-synthesis filter banks have been used for a variety of applications since their introduction over two decades ago. Although initially used for one-dimensional signals such as speech, subband decompositions were eventually extended to the two-dimensional case and applied to image and video coding. By separating a signal into its various frequency components, filter banks allow each subband to be operated on independently, according to its relative importance to a given task. Currently, most still image coders use a subband decomposition in the compression scheme.; When selecting a filter bank for a particular application, there are many variables to take into account. Subband decompositions come in several varieties, as they can either have uniform-band splits, octave-band splits, or more generally, nonuniform-band splits. They can use filter sets that have finite-duration impulse responses (FIR) or infinite duration impulse responses (IIR). Furthermore, they can be perfectly reconstructing (PR), such as many biorthogonal filter sets or conjugate quadrature filter banks (CQFs), or near-perfectly reconstructing like the quadrature mirror filter bank (QMF). Traditionally, once the filters are chosen, however, they remain fixed and do not vary depending on the input type.; In our thesis we propose that for certain applications, such as image coding and denoising, these filter banks should be time varying. The filters used to perform the subband decomposition should adapt to the statistical nature of the current input. Our goal for this research is to further develop the body of knowledge surrounding time-varying filter banks and show that they can be applied in practical situations. |
