Showing papers by "Emmanuel J. Candès published in 1910"

Monoscale Ridgelets for the Representation of Images with Edges

Abstract: In a previous paper [1], the author introduced a new system for representing multivariate functions, namely, the ridgelets. In a following article [3], ridgelets were shown to be optimal for representing functions that are smooth away from hyperplanes, e.g. in two dimensions ridgelets provide optimally sparse representations of smooth functions that are discontinuous along lines, i.e. straight edges. This is unlike Fourier or wavelet methods. This paper applies the localization principle for constructing local ridgelet frames, the monoscale ridgelets. This simple refinement allows efficient representations of smooth images with smooth edges. A model of such images is introduced and the present work shows that naive thresholding of the monoscale ridgelet expansion gives optimal nonlinear approximation bounds. The method is constructive and computationally attractive. Potential applications of these results include image compression and statistical estimation.