Method and apparatus for processing or compressing n-dimensional signals by foveal filtering along trajectories

Abstract

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.