The next two
important contributors to the field of wavelets were Yves Meyer and Stephane
Mallat. Although Meyer is a mathematics professor from France and
Mallat was a former student of Ecole Polytechnique (where Meyer used to
teach), the two first met in the United States in 1986. Mallat
was very intrigued by a paper Meyer had written about his orthogonal wavelets.
They spent three days researching work being done on wavelets in many different
applied fields. At the end of their research, Multiresolution Analysis
for wavelets was born.
This idea of multiresolution
analysis was a big step in the research of wavelets. It was where
the scaling function of wavelets was first mentioned, and it allowed researchers
and mathematicians to construct their own family of wavelets using its
criteria.