We study a notion of ridgelet transform for arrays of digital
data in which the analysis operator uses true ridge functions, as does the
synthesis operator. There are fast algorithms for analysis, for synthesis,
and for partial reconstruction. Associated with this is a transform which is
a digital analog of the orthonormal ridgelet transform (but not orthonor-
mal for finite n). In either approach, we get an overcomplete frame; the
result of ridgelet transforming an n x n array is a 2n x 2n array. The
analysis operator is invertible on its range; the appropriately precondi-
tioned operator has a tightly controlled spread of singular values. There
is a near-parseval relationship.