Ridgelet Transform on the Sphere

 

 

Algorithm: we extract first the 12 faces of the Healpix image representation, we decompose each face into blocs (partitionning), and we apply sequentially the 2D ridgelet transform on each individual block. The 2D ridgelet transform is obtained by i) computing the 2D Fourier transform, ii) extracting lines going through the origin, iii) computing the 1D inverse transform if the line, and iv) computing 1D wavelet transform if the line.

Examples of backprojection of a few ridgelet coefficients.