Scampi: a robust approximate message-passing framework for compressive imaging

摘要

Reconstructionofimagesfromnoisylinearmeasurementsisacoreprobleminimageprocessing,forwhichconvexoptimizationmethodsbasedontotalvariation(TV)minimizationhavebeenthelong-standingstate-of-the-art.Wepresentanalternativeprobabilisticreconstructionprocedurebasedonapproximatemessage-passing,Scampi,whichoperatesinthecompressiveregime,wheretheinverseimagingproblemisunderdetermined.WhiletheproposedmethodisrelatedtotherecentlyproposedGrAMPAalgorithmofBorgerding,Schniter,andRangan,wefurtherdeveloptheprobabilisticapproachtocompressiveimagingbyintroducinganexpectation-maximizationlearningofmodelparameters,makingtheScampirobusttomodeluncertainties.Additionally,ournumericalexperimentsindicatethatScampicanprovidereconstructionperformancesuperiortobothGrAMPAaswellasconvexapproachestoTVreconstruction.Finally,throughexhaustivebest-caseexperiments,weshowthatinmanycasesthemaximalperformanceofbothScampiandconvexTVcanbequiteclose,eventhoughtheapproachesareaproridistinct.Thetheoreticalreasonsforthiscorrespondenceremainanopenquestion.Nevertheless,theproposedalgorithmremainsmorepractical,asitrequiresfarlessparametertuningtoperformoptimally...