An examination of decomposition sparsity
Sparsity of transform domain coefficients is a critical requirement for algorithms employing wavelet transforms to pre-process signals or images. This paper examines a measure of transform domain sparsity which provides a means of comparing wavelet and subband decomposition performance. The transforms of one-dimensional signals and two-dimensional images are considered using 110different wavelets and nonlinear subband decomposition filters, including weighted order statistics and functions of weighted order statistics. These measurements indicate that nonlinear subband decompositions employing median filters or central order statistics can produce sparser decompositions than wavelets for certain classes of signals and images.
sparsity wavelets nonlinear subband decomposition