| This thesis introduces a number of new subband decompositions constructed from nonlinear filters, and applies these subband decompositions to several signal and image processing applications. The subband decompositions are constructed using filters from the order statistics, morphological, and M-estimator families. Additional possibilities for different subband decompositions, including decision-based and fuzzy filters, are also considered. Transform-domain sparsity is introduced, and some nonlinear subband decompositions are shown to have equivalent, or better, transform-domain sparsity for certain classes of signals and images than wavelet transforms. Next, nonlinear subband decompositions are used in a multiresolution peak detection algorithm on two different types of signals: balloonsonde temperature measurements and electrocardiogram signals. Then, nonlinear subband decompositions are used within the JPEG-2000 image compression codec, and are shown to produce high-quality images at very high compression ratios. Finally, a new image-oriented data embedding algorithm using nonlinear subband decompositions is presented, and decomposition sparsity is shown to govern the capacity of the cover image. |
