The ridgelet transform (Candµ es and Donoho,

1999) was introduced as a sparse expansion for functions on continuous spaces that are smooth away discontinuities along lines. Our construction uses the ¯ finite Radon transform

(FRAT) as a building block. Taking the one-dimensional wavelet transform

on the projections of the FRAT in a special way results in the ¯ finite ridgelet transform (FRIT), which is invertible,non-redundant, and computed via fast algorithms. -The ridgelet transform (Candµ es and Donoho,

1999) was introduced as a sparse expansion for functions on continuous spaces that are smooth away　discontinuities along lines.　Our construction uses the ¯ finite Radon transform

(FRAT) as a building block.　Taking the one-dimensional wavelet transform

on the projections of the FRAT in a special way results in the ¯ finite ridgelet transform (FRIT), which is invertible,non-redundant, and computed via fast algorithms.