Methods and apparatus for processing n-dimensional digitized signals with a
foveal processing which constructs a sparse representation by taking
advantage of the geometrical regularity of the signal structures. This
invention can compress, restore, match and classify signals. Foveal
coefficients are computed with one-dimensional inner products along
trajectories of an n-directional trajectory list. The invention includes a
trajectory finder which computes an n-directional trajectory list from the
input n-dimensional signal, in order to choose optimal locations to
compute the foveal coefficients. From foveal coefficients, a foveal
reconstruction processor recovers a signal approximation which has the
same geometrical structures as the input signal along the trajectories and
which is regular away from these trajectories. A foveal residue can be
calculated as a difference with the input signal. A bandelet processor
decorrelates the foveal coefficients by applying invertible linear
operators along each trajectory. Bandelet coefficients are inner products
between the signal and n-dimensional bandelet vectors elongated along the
trajectories. A geometric processor computes geometric coefficients by
decorrelating the coordinates of these trajectories with linear operators,
to take advantage of their geometrical regularity. Setting to zero small
bandelet coefficients and small geometric coefficients yields a sparse
signal representation.
