# Jean Morlet

**Jean Morlet** is a geophysicist whose work in field of windowed Fourier Transforms actually led to a
new transform, called the *wavelet transform,* which has found usage in many areas of geophysics and
signal processing.

## Biography Citation for the Reginald Fessenden Award

*Contributed by Pierre Goupillaud*

I consider it a great honor and privilege to introduce to you my dear friend and fellow geophysicist, Jean Morlet, the recipient of the Fessenden Award for his discovery of the wavelet transform.

A product of the renown Ecole Polytechnique, Morlet performed the exceptional feat of discovering a novel mathematical tool which has made the Fourier transform obsolete after 200 years of uses and abuses, particularly in its fast version.

After several years of field work for Elf Aquitaine, Morlet transferred to Oric, an Elf research subsidiary, and beginning in 1972 devoted all his efforts to enhancing the resolution of seismic events while processing field data. By the mid-'70s, he had developed a technique he called "cycle-octave transform," which is now the universally accepted "wavelet transform."

Following in the footsteps of Denis Gabor (father of holography), Morlet was disconcerted by the poor results he obtained; but, being inquisitive and persistent, he asked himself, "Why?" and immediately provided the answer. Gabor paved the time-frequency plane in uniform cells and associated each cell with a wave shape of invariant envelope with a carrier of variable frequency. Morlet kept the constraint resulting from the uncertainty principle applied to time and frequency, but he perceived that it was the wave shape that must be invariant to give uniform resolution in the entire plane. For this he adapted the sampling rate to the frequency, thereby creating, in effect, a changing time scale producing a stretching of the wave shape. Today the wavelet transform is also called the "time-scale analysis" approach, which is comparable to the conventional time-frequency analysis.

By 1975 Jean Morlet had proof that his novel scheme worked. I had the luck to be given the opportunity of introducing this important discovery to the geophysical community when I approved it for publication in Geophysics (Vol. 47, 1982). However, due to the magnitude of the step, it remained overlooked by explorationists until just recently. It has been rediscovered as a very useful tool, particularly in data compression where it can produce significant savings in storage and transmission costs but also in mathematics, data processing, communications, image analysis, and many other engineering problems. It is clear that this is not a fad but a "great step for mankind."

Important contributions to the practical application of wavelet transform theory include the work of Alexandre Grossman, Yves Mayer, Ingrid Daubechies, and Stephane Mallat. Grossman, an expert in group theory and professor of mathematical physics at the

University of Marseilles, developed the rigorous basis of the wavelet transform based on the affine transformation. Mayer et al. helped develop wavelet technology by finding families of orthogonal wavelets and establishing a hierarchical structure of representations producing a zooming effect in which an image can be observed in sequence more and more locally with increasing detail.

Geophysicists young and old can still be proud of having among themselves major contributors to the advancement of science and to the progress of humanity, such as Reginald Fessenden did in his own time. Today Jean Morlet's friends and fellow geophysicists have the opportunity to grant him well-deserved recognition for his important contribution. Until now, his only reward for years of perseverance and creativity in producing this extraordinary tool was an early retirement from Elf. The old adage, "Better late than never," certainly applies in this case. The 1997 SEG Honors and Awards Committee is to be commended for its wisdom in recognizing Jean Morlet with the Reginald Fessenden Award.