Sparse+Image+Reconstruction+for+Molecular+Imagi....pdf

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1、Thisarticlehasbeenacceptedforinclusioninafutureissueofthisjournal.Contentisfinalaspresented,withtheexceptionofpagination.IEEETRANSACTIONSONIMAGEPROCESSING1SparseImageReconstructionforMolecularImagingMichaelTing,Member,IEEE,RavivRaich,Member,IEEE,andAl

2、fredO.Hero,III,Fellow,IEEEAbstract—Theapplicationthatmotivatesthispaperismolec-of3-Dimaging.Recently,imagingofabiologicalsamplewithularimagingattheatomiclevel.Whendiscretizedatsubatomicnanometerresolutionwasdemonstrated[5].GiventhatMRFMdistances,thevo

3、lumeisinherentlysparse.NoiselessmeasurementsandindeedevenAFM[6]measurestheconvolutionofthefromanimagingtechnologycanbemodeledbyconvolutionoftheimagewithapointspreadfunction(psf),adeconvolutionmustimagewiththesystempointspreadfunction(psf).Suchisthecas

4、ewithmagneticresonanceforcemicroscopy(MRFM),anemergingbeperformedinordertoobtainthemolecularimage.Thistechnologywhereimagingofanindividualtobaccomosaicviruspaperconsidersthefollowingproblem:supposeoneobservesawasrecentlydemonstratedwithnanometerresolu

5、tion.WealsolineartransformationofasparseimagecorruptedbyAWGN.consideradditivewhiteGaussiannoise(AWGN)inthemeasure-Withonlyknowledgeofthelineartransformationandnoisements.Manypriorworksofsparseestimatorshavefocusedonthevariance,thegoalistoreconstructth

6、eunknownsparseimage.casewhenhaslowcoherence;however,thesystemmatrixinourapplicationistheconvolutionmatrixforthesystempsf.AThesystemmatrixisthelineartransformationthat,intypicalconvolutionmatrixhashighcoherence.Thispaper,there-thecaseofMRFM,represent

7、sconvolutionwiththeMRFMfore,doesnotassumealowcoherence.Adiscrete-continuouspsf.SeveralpriorworksareonlyapplicablewhenthesystemformoftheLaplacianandatomatzero(LAZE)p.d.f.usedbymatrixhassmallpairwisecorrelation,i.e.,lowcoherenceorJohnstoneandSilvermani

8、sformulated,andtwosparseestimatorslowcollinearity[7]–[10].Othersassumethatthecolumnsofderivedbymaximizingthejointp.d.f.oftheobservationandimageconditionedonthehyperparameters.Athresholdingrulecomefromaspecificrandomdistribution,e.g.,theuniformt