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 110 different 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. [Copyright &y& Elsevier]