Regularization parameter selection for penalized-likelihood list-mode image reconstruction in PET.

Penalized likelihood (PL) reconstruction has demonstrated potential to improve image quality of positron emission tomography (PET) over unregularized ordered-subsets expectation-maximization (OSEM) algorithm. However, selecting proper regularization parameters in PL reconstruction has been challenging due to the lack of ground truth and variation of penalty functions. Here we present a method to choose regularization parameters using a cross-validation log-likelihood (CVLL) function. This new method does not require any knowledge of the true image and is directly applicable to list-mode PET data. We performed statistical analysis of the mean and variance of the CVLL. The results show that the CVLL provides an unbiased estimate of the log-likelihood function calculated using the noise free data. The predicted variance can be used to verify the statistical significance of the difference between CVLL values. The proposed method was validated using simulation studies and also applied to real patient data. The reconstructed images using optimum parameters selected by the proposed method show good image quality visually.

[1]  Jian Zhou,et al.  Monte Carlo SURE-based regularization parameter selection for penalized-likelihood image reconstruction , 2014, 2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI).

[2]  Richard M. Leahy,et al.  Resolution and noise properties of MAP reconstruction for fully 3-D PET , 2000, IEEE Transactions on Medical Imaging.

[3]  M. Bertero,et al.  Efficient gradient projection methods for edge-preserving removal of Poisson noise , 2009 .

[4]  Laure Blanc-Féraud,et al.  Sparse Poisson Noisy Image Deblurring , 2012, IEEE Transactions on Image Processing.

[5]  Dianne P. O'Leary,et al.  The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems , 1993, SIAM J. Sci. Comput..

[6]  Alan C. Bovik,et al.  Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures , 2009, IEEE Signal Processing Magazine.

[7]  D. M. Titterington,et al.  A Study of Methods of Choosing the Smoothing Parameter in Image Restoration by Regularization , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  J. Bardsley,et al.  Tikhonov regularized Poisson likelihood estimation: theoretical justification and a computational method , 2008 .

[9]  Roger Lecomte,et al.  Cross-validation stopping rule for ML-EM reconstruction of dynamic PET series: effect on image quality and quantitative accuracy , 1999 .

[10]  Finbarr O'Sullivan,et al.  Data-dependent bandwidth selection for emission computed tomography reconstruction , 1993, IEEE Trans. Medical Imaging.

[11]  H. Malcolm Hudson,et al.  Accelerated image reconstruction using ordered subsets of projection data , 1994, IEEE Trans. Medical Imaging.

[12]  J. Fessler,et al.  Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs , 1996, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[13]  M. Bentourkia,et al.  Cross-validation stopping rule for ML-EM reconstruction of dynamic PET series: effect on image quality and quantitative accuracy , 1999, 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 Nuclear Science Symposium and Medical Imaging Conference (Cat. No.99CH37019).

[14]  Kuang Gong,et al.  On the assessment of spatial resolution of PET systems with iterative image reconstruction , 2016, Physics in medicine and biology.

[15]  Jinyi Qi,et al.  Iterative reconstruction techniques in emission computed tomography , 2006, Physics in medicine and biology.

[16]  Richard M. Leahy,et al.  Accurate estimation of the fisher information matrix for the PET image reconstruction problem , 2004, IEEE Transactions on Medical Imaging.

[17]  C. Stein.  Estimation of the Mean of a Multivariate Normal Distribution , 1981 .

[18]  H. Malcolm Hudson,et al.  Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to Poisson noise , 1998 .

[19]  Jeffrey A. Fessler,et al.  Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs , 1996, IEEE Trans. Image Process..

[20]  Jorge Núñez de Murga,et al.  Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies , 1993, IEEE Trans. Medical Imaging.

[21]  Li Yang,et al.  Regularization design in penalized maximum-likelihood image reconstruction for lesion detection in 3D PET. , 2014, Physics in medicine and biology.

[22]  W. W. Moses,et al.  List-mode maximum-likelihood reconstruction applied to positron emission mammography (PEM) with irregular sampling , 2000, IEEE Transactions on Medical Imaging.

[23]  Alvaro R. De Pierro,et al.  A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography , 1995, IEEE Trans. Medical Imaging.