Nonlocal Prior Bayesian Tomographic Reconstruction

Abstract Bayesian approaches, or maximum a posteriori (MAP) methods, are effective in providing solutions to ill-posed problems in image reconstruction. Based on Bayesian theory, prior information of the target image is imposed on image reconstruction to suppress noise. Conventionally, the information in most of prior models comes from weighted differences between pixel intensities within a small local neighborhood. In this paper, we propose a novel nonlocal prior such that differences are computed over a broader neighborhoods of each pixel with weights depending on its similarity with respect to the other pixels. In such a way connectivity and continuity of the image is exploited. A two-step reconstruction algorithm using the nonlocal prior is developed. The proposed nonlocal prior Bayesian reconstruction algorithm has been applied to emission tomographic reconstructions using both computer simulated data and patient SPECT data. Compared to several existing reconstruction methods, our approach shows better performance in both lowering the noise and preserving the edges.

[1]  Michael J. Black,et al.  On the unification of line processes, outlier rejection, and robust statistics with applications in early vision , 1996, International Journal of Computer Vision.

[2]  K. Lange.  Convergence of EM image reconstruction algorithms with Gibbs smoothing. , 1990, IEEE transactions on medical imaging.

[3]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[4]  Alfred O. Hero,et al.  Ieee Transactions on Image Processing: to Appear Penalized Maximum-likelihood Image Reconstruction Using Space-alternating Generalized Em Algorithms , 2022 .

[5]  Wufan Chen,et al.  Adaptively regularized constrained total least-squares image restoration , 2000, IEEE Trans. Image Process..

[6]  John R. Votaw,et al.  Regularized image reconstruction algorithms for positron emission tomography , 2004, IEEE Transactions on Medical Imaging.

[7]  Ronald J. Jaszczak,et al.  Bayesian reconstruction and use of anatomical a priori information for emission tomography , 1996, IEEE Trans. Medical Imaging.

[8]  Chin-Tu Chen,et al.  Image Restoration Using Gibbs Priors: Boundary Modeling, Treatment of Blurring, and Selection of Hyperparameter , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  V. Johnson.  A Model for Segmentation and Analysis of Noisy Images , 1994 .

[10]  Jeffrey A. Fessler,et al.  Combined diagonal/Fourier preconditioning methods for image reconstruction in emission tomography , 1995, Proceedings., International Conference on Image Processing.

[11]  Jeffrey A. Fessler,et al.  A paraboloidal surrogates algorithm for convergent penalized-likelihood emission image reconstruction , 1998, 1998 IEEE Nuclear Science Symposium Conference Record. 1998 IEEE Nuclear Science Symposium and Medical Imaging Conference (Cat. No.98CH36255).

[12]  Anand Rangarajan,et al.  Bayesian image reconstruction in SPECT using higher order mechanical models as priors , 1995, IEEE Trans. Medical Imaging.

[13]  Jeffrey A. Fessler,et al.  Edge-preserving tomographic reconstruction with nonlocal regularization , 1998, IEEE Transactions on Medical Imaging.

[14]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[15]  M Berteroi,et al.  Linear inverse problems with discrete data. I. General formulation and singular system analysis , 1985 .

[16]  Hakan Erdogan,et al.  Monotonic algorithms for transmission tomography , 1999, IEEE Transactions on Medical Imaging.

[17]  Anand Rangarajan,et al.  Bayesian Reconstruction for Emissiom Tomography via Deterministic Annealing , 1993, IPMI.

[18]  Ken D. Sauer,et al.  A generalized Gaussian image model for edge-preserving MAP estimation , 1993, IEEE Trans. Image Process..

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

[20]  A. Baudes,et al.  A Nonlocal Algorithm for Image Denoising , 2005, CVPR 2005.

[21]  Stan Z. Li,et al.  Markov Random Field Modeling in Image Analysis , 2001, Computer Science Workbench.

[22]  Jeffrey A. Fessler,et al.  Fast Monotonic Algorithms for Transmission Tomography , 1999, IEEE Trans. Medical Imaging.

[23]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  D S Lalush,et al.  A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm. , 1995, Medical physics.

[25]  Anand Rangarajan,et al.  A new convex edge-preserving median prior with applications to tomography , 2003, IEEE Transactions on Medical Imaging.

[26]  Michel Barlaud,et al.  Deterministic edge-preserving regularization in computed imaging , 1997, IEEE Trans. Image Process..

[27]  M. Bertero,et al.  Ill-posed problems in early vision , 1988, Proc. IEEE.

[28]  Jean-Michel Morel,et al.  A Review of Image Denoising Algorithms, with a New One , 2005, Multiscale Model. Simul..

[29]  Ulla Ruotsalainen,et al.  Generalization of median root prior reconstruction , 2002, IEEE Transactions on Medical Imaging.

[30]  Jeffrey A. Fessler,et al.  Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction , 1999, IEEE Trans. Image Process..