4 research outputs found
Bell-shaped nonstationary refinable ripplets
We study the approximation properties of the class of nonstationary refinable
ripplets introduced in \cite{GP08}. These functions are solution of an infinite
set of nonstationary refinable equations and are defined through sequences of
scaling masks that have an explicit expression. Moreover, they are
variation-diminishing and highly localized in the scale-time plane, properties
that make them particularly attractive in applications. Here, we prove that
they enjoy Strang-Fix conditions and convolution and differentiation rules and
that they are bell-shaped. Then, we construct the corresponding minimally
supported nonstationary prewavelets and give an iterative algorithm to evaluate
the prewavelet masks. Finally, we give a procedure to construct the associated
nonstationary biorthogonal bases and filters to be used in efficient
decomposition and reconstruction algorithms. As an example, we calculate the
prewavelet masks and the nonstationary biorthogonal filter pairs corresponding
to the nonstationary scaling functions in the class and construct the
corresponding prewavelets and biorthogonal bases. A simple test showing their
good performances in the analysis of a spike-like signal is also presented.
Keywords: total positivity, variation-dimishing, refinable ripplet, bell-shaped
function, nonstationary prewavelet, nonstationary biorthogonal basisComment: 30 pages, 10 figure
Convergence of nonstationary cascade algorithms
SIGLEAvailable from British Library Document Supply Centre-DSC:1571.430(974) / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Convergence of nonstationary cascade algorithms
10.1007/s002119900095Numerische Mathematik8411-3