Recovery of a class of Binary Images from Fourier Samples

In this paper, we study the recovery of a certain type of shape images modeled as binary-valued images from few Fourier samples. In particular, the boundary of the shapes is assumed to be the zero level-set of a trigonometric curve. This problem was previously considered in [1], and it was shown that such images can be studied withing the framework of signals with finite rate of innovation. In particular, an annihilation filter is introduced to recover the trigonometric boundary curve. It is proved in [1] that 3Λ Fourier samples are sufficient to exactly recover the edges of a binary shape, where Λ is the bandwith of the trigonometric boundary curve. In this paper, we introduce a class of shapes (that include convex shapes as special cases) for which |2Λ + 1| Fourier samples are sufficient for exact recovery using the same annihilation filter. Simulation results support our theoretical results.