Data that represent complex and multivariate processes are well known to be multiscale due
to the variety of changes that could occur in a process with different localizations in time and …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

The word 'multiscale'can mean many things. However, in this book we are generally
concerned with the representation of objects at a set of scales and then manipulating these …

This paper defines and studies a new class of non‐stationary random processes constructed
from discrete non‐decimated wavelets which generalizes the Cramér (Fourier) …

We derive minimax rates for estimation in anisotropic smoothness classes. These rates are
attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis …

For gears and roller bearings, periodic impulses indicate that there are faults in the
components. However, it is difficult to detect the impulses at the early stage of fault because …

Nonlinear thresholding of wavelet coefficients is an efficient method for denoising signals
with isolated singularities. The quasi-optimal value of the threshold depends on the sample …

Various aspects of the wavelet approach to nonparametric regression are considered, with
the overall aim of extending the scope of wavelet techniques to irregularly spaced data, to …

Johnstone and Silverman (1997) described a level-dependent thresholding method for
extracting signals from correlated noise. The thresholds were chosen to minimize a data …

Data Rectification by univariate filtering is popular for processes lacking an accurate model.
Linear filters are most popular for online filtering; however, they are single‐scale best suited …