Avoiding phase-retrieval algorithm stagnation using the zeros of the Fourier magnitude

Summary form only given. The phase retrieval problem is the problem of reconstructing a two-dimensional signal f(x,y) from measurements of its Fourier magnitude |F(u,ν)|. The iterative algorithm of Fienup, a modification of the Gerchberg-Saton alternating projections algorithm, works reasonably well for real signals f(x, y)<0 that have compact support. However, the algorithm tends to stagnate, since the projections are not onto convex sets. The most difficult stagnations to escape have stripes running through the image. These stripes are more than just an artifact of the algorithm; they seem to be a fundamental difficulty, and a considerable amount of work has gone into studying ways of avoiding the stripes stagnation (other stagnations are much easier to escape). An approach that has successfully avoided stripes stagnations in numerical testing is reported