Name
ridgelet Ridgelet transform of an image
Command Synopsis
ridgelet [-I in_im] np in_re out_re out_im
-I in_im : imaginary input (Fimage N*N)
np : resolution np
in_re : real input (Fimage N*N)
out_re : real ridgelets coefficients (Fimage 2N*2N)
out_im : imaginary ridgelets coefficients (Fimage 2N*2N)
Function Summary
void ridgelet (in_re , in_im , np , out_re , out_im )
int np ;
Fimage in_re , in_im ;
Fimage out_re , out_im ;
Description
The module ridgelet computes the np level discrete ridgelet transform of a Fimage according to the algorithm of J.L. Starck, E. Candès et D.Donoho [SCD02].
It transforms a
N×N image into a
2N×2N image where, from left to right, we have from thinner details to approximation.
In continuous, the 2D-ridgelet transform in I R^{2} can be defined as follows:
Let's consider : I R I R a smooth univariate function with sufficient decay and satisfying the condition:
Let's suppose that is normalized so that
This function is constant along lines
x_{1}cos + x_{2}sin = k, for k constant in
I R. Tranverse to these ridges, it is a wavelet.
Given an integrable bivariate function f (x), we define its ridgelet coefficients by
f (x) = R_{f}(a, b,)(x)db | (12) |
Let's go back to the coefficients R_{f}(a, b,) calculus. We can view ridgelet analysis as a form of wavelet analysis in the Radon domain. We recall that the Radon transform of an object f is the collection of line integrals indexed by (, t) [0, 2]× given by
Our algorithm starts calculating the Radon transform Rf (t,), and then applies the one-dimensional wavelet transform to the slices Rf (.,). In order to calculate the Radon transform, we use the projection-slice formula:
See Also
fft2d, fline_extract, ridgrecpol, stkwave1.
Version 1.0
Last Modification date : Thu Apr 15 08:03:52 2004
Author
Claire Jonchery, Amandine Robin