CONVEX SET-THEORETIC IMAGE RECOVERY BY EXTRAPOLATED ITERATIONS OF PARALLEL SUBGRADIENT PROJECTIONS

Solving a convex set theoretic image recovery problem amounts to findi ng a point in the intersection of closed and convex sets in a Hilbert space, The projection onto convex sets (POCS) algorithm, in which an i nitial estimate is sequentially projected onto the individual sets acc ording to a periodic schedule, has been the most prevalent tool to sol ve such problems, Nonetheless, POCS has several shortcomings: It conve rges slowly, it is ill suited for implementation on parallel processor s, and it requires the computation of exact projections at each iterat ion, In this paper, we propose a general parallel projection method (E MOPSP) that overcomes these shortcomings, At each iteration of EMOPSP, a convex combination of subgradient projections onto some of the sets is formed and the update is obtained via relaxation, The relaxation p arameter may vary over an iteration-dependent, extrapolated range that extends beyond the interval ]0,2] used in conventional projection met hods, EMOPSP not only generalizes existing projection-based schemes, b ut it also converges very efficiently thanks to its extrapolated relax ations, Theoretical convergence results are presented as well as numer ical simulations.