2264 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 58, NO. 5, OCTOBER 2011 Properties and Mitigation of Edge Artifacts in PSF-Based PET Reconstruction Shan Tong, Member, IEEE, Adam M. Alessio, Member, IEEE, Kris Thielemans, Senior Member, IEEE, Charles Stearns, Senior Member, IEEE, Steve Ross, Senior Member, IEEE, and Paul E. Kinahan, Fellow, IEEE Abstract—PSF (point spread function) based image reconstruc- tion causes an overshoot at sharp intensity transitions (edges) of the object. This edge artifact, or ringing, has not been fully studied. In this work, we analyze the properties of edge artifacts in PSF-based reconstruction in an effort to develop mitigation methods. Our study is based on 1D and 2D simulation experi- ments. Two approaches are adopted to analyze the artifacts. In the system theory approach, we relate the presence of edge artifacts to the null space and conditioning of the imaging operator. We show that edges cannot be accurately recovered with a practical number of image updates when the imaging matrices are poorly conditioned. In the frequency-domain analysis approach, we calculate the object-specific modulation transfer function (OMTF) of the system, defined as spectrum of the reconstruction divided by spectrum of the object. We observe an amplified frequency band in the OMTF of PSF-based reconstruction and that the band is directly related to the presence of ringing. Further analysis shows the amplified band is linearly related to kernel frequency support (the reciprocal of the reconstruction kernel FWHM), and the relation holds for different objects. Based on these properties, we develop a band-suppression filter to mitigate edge artifacts. We apply the filter to simulation and patient data, and compare its performance with other mitigation methods. Analysis shows the band-suppression filter provides better tradeoff of resolution and ringing suppression than a low-pass filter. Index Terms—Image reconstruction, positron emission tomography. I. INTRODUCTION I TERATIVE reconstruction methods can offer improved contrast to noise performance over analytical reconstruc- tion methods for positron emission tomography (PET) image reconstruction [1], [2], and are widely used in clinical prac- tice. Performance of iterative reconstruction could be further improved when the full physics of the imaging process is accu- rately and precisely modeled. One important component of the physics modeling is the detector point spread function (PSF), which could be obtained through analytical derivations [3], Manuscript received January 26, 2011; revised June 20, 2011; accepted Au- gust 05, 2011. Date of publication September 29, 2011; date of current version October 12, 2011. This work was supported by a grant from GE Healthcare and NIH Grants CA74135, HL086713, and CA115870. S. Tong, A. M. Alessio, and P. E. Kinahan are with the Department of Radiology, University of Washington, Seattle, WA 98195 USA (e-mail: sara.stong@gmail.com; kinahan@u.washington.edu). K. Thielemans was with Hammersmith Imanet, GE Healthcare, London W12 0NN, U.K. C. Stearns and S. Ross are with GE Healthcare, Waukesha, WI 53188 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNS.2011.2164579 Monte Carlo simulations [4], [5] or experimental measurements [6], [7]. Modeling of the detector PSF during fully 3D iterative reconstruction has been shown to improve the spatial resolution and contrast [4]–[8], and to generate images with distinct noise properties and improved SNR measures and lesion detectability [9]–[11]. However, PSF-based reconstruction can cause edge artifacts, which appear as overshoot or ringing at sharp intensity tran- sitions (edges) of the object. Edge artifacts are acknowledged throughout the literature of tomographic reconstruction of PET [4], [7], SPECT [12]–[14], and CT [15], [16] images. They are observed in PET reconstruction with resolution modeling in ei- ther image space [17], [18] or projection space [4], [6], [7], [19], and lead to unpredictable image quantitation. However, the im- pact of edge artifacts has largely been neglected, partially due to the difficulty in identifying these artifacts under high noise levels. Recently, Bai and Esser [20] studied how PSF edge ar- tifacts affect PET quantitation using measured phantom scans. It is shown that edge artifacts could result in up to 70% over- estimate in the center of a cylinder phantom and about 25% overestimate for a Hoffman brain phantom. With increasing use of PSF-based iterative reconstruction methods in clinical PET imaging, the causes and the properties of PSF edge artifacts should be better understood, and proper mitigation methods are needed for more accurate PET quantitation. The causes of edge artifacts have been detailed in only a few studies. In the work of Snyder et al. [21], edge artifacts are ex- plained with two possible reasons. The first one is the mismatch between reconstruction kernel and actual system PSF, and small mismatch can be amplified due to the instability of deconvo- lution. Second, high frequency information corresponding to the image edges may be lost through image acquisition and cannot be accurately recovered. PSF reconstruction attempts to recover the object at a finer resolution than the data can support, and leads to ringing artifacts at the edges. One recent study [22] analyzed edge artifacts using spectral analysis of the Hessian of the log-likelihood function. It is shown that edges with ringing are preserved at late iterations of reconstruction algorithms. Another study [23] analyzed ringing artifacts in rotator-based reconstruction with Monte Carlo-based PSF models, and attributed the artifacts to the rotator model which blurs the system response. These studies provide useful insights into the edge artifact problem. However, the root cause of the artifacts is still not clear. Typical mitigation methods for edge artifacts include post- reconstruction smoothing with a low-pass filter. Alternatively, Snyder et al. proposed to estimate a blurred version of the true object, which does not contain the high frequencies unavailable 0018-9499/$26.00 © 2011 IEEE