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X-ray fluorescence computed tomography(XFCT)is a stimulate emission tomography that allows nondestructive reconstruction of elements distribution in the sample and has been applied in many fields.The XFCT system was established at the X-ray imaging(BL13W1)and hard X-ray micro-focusing beamline(BL15U1)of Shanghai Synchrotron Radiation Facility(SSRF)[1-2].To obtain accurate distributions of trace elements in soft tissues nondestructively,the problems on absorption correction and radiation dose are confronted in XFCT.Ordered subsets expectation maximization(OSEM)[4] and absorption-corrected ordered subsets expectation maximization(AC-OSEM)[5]algorithms are developed to solve these problems.Ongoing studies of our group are being carried out on the possibility to accelerate XFCT.A method of fast scanning X-ray fluorescence imaging,on-the–fly,will be used to collect the fluorescence photons [6].The OSEM algorithm for XFCT reconstruction and the experimental results obtained in BL13W1 and BL15U1 beamline will be reported.The nondestructive XFCT for rare-earth elements(REEs)in fish teeth from deep-sea sediments wis carried out[7}.The virtual cross-sectional distribution of Ce、Sm、Pm、Pr、Nd and La were obtained,which provides a feasible approach for analyzing the enrichment mechanism of rare-earth elements.