ADVAI\CES in communication, sensing, and computational power have
Jed to an cxplosion of data. The size and varied formats for these
datasets challenge existing techniqucs for transmission, storage,
querying, display, and numerical manipula tion. This Ieads to the
paradoxical situation where experiments or numerical com pulations
produce rich, detailed inforrnation, for which, at this point, no
adequate analysis tools exist. -Conference annow cement, Joint
IDR-1/v A Workshop on Ideal Data Nepresentaticm, Minneapolis, R.
De\'ore and A. Ron, cJ/gani ers Wavelct theory stands on the
interface betwccn signal processing and harmonic analy sis, the
rnathematical tools involved in digitizing continuous data with a
vicw to storage, and thc synthesis proccss, recreating, for
cxample, a picturc or time signal from stored data. The algorithms
involved go under the name of tilter banks, and their spectacular
efticiency derivcs in patt from the use of hidden self-similarity,
relati\ c to somc scaling operation, in the daLJ. being analyzed.
Observations or time signals are functions, and classes of
functions make up linear spaces. Numcrical correlations add
structure to thc spaccs at hand, Hilbcrt spaces. There are
opcrators in the spaces deriving lrom the dis crcte data and others
from the spaces of continuous signals. The first type arc good for
computations, whilc the sccond retlect the real world. The
operators between thc two are the focus of the prescnt monograph.
Relations between operations in thc discrete xn Preface and
continuous domains are studied as symbols."
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