Thismonographisintendedasasimpleintrodu…-calledLULU-theory and the practical use of
LULU-smoothers leading up to a full Multiresolution Analysis of any? nite sequence. The …

The LULU operators for sequences, that is Ln, Un and their compositions, are extended to
multidimensional arrays in a way which preserves their essential properties, eg, consistent …

We investigate a recent algorithm, here called a discrete pulse transform (DPT), for the
multiresolution analysis of a sequence. A DPT represents a sequence as a sum of pulses …

The smoothing of time series plays a very important role in various practical applications.
Estimating the signal and removing the noise is the main goal of smoothing. Traditionally …

Publisher Summary To many interested observers from fields near to image processing, the
need for mathematics of vision, as articulated by Meyer (1993), is convincing. This is …

This paper considers a class of non-linear smoothers, called LULU smoothers, introduced
by Rohwer in the late eighties in the mathematics literature, and since then investigated …

The concept of fully trend preserving (ftp) operators on sequences was introduced to prove
variation preservation on the outputs of LULU-separators. It turns out that this property is …

Viewing the elements of RS as images f with pixels i∈ S of grey-scale value f (i) motivates
the study of certain nonlinear operators Φ: RS→ R S. For translation invariant Φ (called …

Abstract The Discrete Pulse Transform (DPT) of images is defined by using a new class of
LULU operators on multidimensional arrays. This transform generalizes the DPT of …

Data analysis frequently involves the extraction (ie recognition) of parts that are important at
the expense of parts that are deemed unimportant. Many mathematical perspectives exist for …