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We discuss in this paper a new subject, ridgelet analysis, which can e®ectively deal with linelike phenomena in dimension 2, planelike phenomena in dimension 3 and so on. It encompasses a colle...
In dimensions two and higher, wavelets can efficiently represent only a small range of the full diversity of interesting behavior. In effect, wavelets are welladapted for pointlike phenomena, whereas ...
In a previous paper [1], the author introduced a new system for representing multivariate functions, namely, the ridgelets. In a following article [3], ridgelets were shown to be optimal for represent...
We show that ridgelets, a system introduced in [4], are optimal to represent smooth multivariate functions that may exhibit linear singularities. For instance, let {u · x − b > 0} be an arbitrar...
Feedforward neural networks, projection pursuit regression, and more generally, estimation via ridge functions have been proposed as an approach to bypass the curse of dimensionality and are now becom...
This paper reviews the development of several recent tools from computational harmonic analysis. These new systems are presented under a coherent perspective, namely, the representation of bivariate f...

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