A combined reconstruction–classification method for diffuse optical tomography

We present a combined classification and reconstruction algorithm for diffuse optical tomography (DOT). DOT is a nonlinear ill-posed inverse problem. Therefore, some regularization is needed. We present a mixture of Gaussians prior, which regularizes the DOT reconstruction step. During each iteration, the parameters of a mixture model are estimated. These associate each reconstructed pixel with one of several classes based on the current estimate of the optical parameters. This classification is exploited to form a new prior distribution to regularize the reconstruction step and update the optical parameters. The algorithm can be described as an iteration between an optimization scheme with zeroth-order variable mean and variance Tikhonov regularization and an expectation-maximization scheme for estimation of the model parameters. We describe the algorithm in a general Bayesian framework. Results from simulated test cases and phantom measurements show that the algorithm enhances the contrast of the reconstructed images with good spatial accuracy. The probabilistic classifications of each image contain only a few misclassified pixels.

[1]  Jonathan Warrell,et al.  Epitomized priors for multi-labeling problems , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[2]  D Calvetti,et al.  An adaptive smoothness regularization algorithm for optical tomography. , 2008, Optics express.

[3]  Simon R. Arridge,et al.  Parameter and structure reconstruction in optical tomography , 2008 .

[4]  Simon R. Arridge,et al.  3-D shape and contrast reconstruction in optical tomography with level sets , 2008 .

[5]  Yiannis Aloimonos,et al.  Who killed the directed model? , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[6]  M. Schweiger,et al.  Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information , 2006 .

[7]  M. Schweiger,et al.  Comparison between a time-domain and a frequency-domain system for optical tomography. , 2006, Journal of biomedical optics.

[8]  Simon R. Arridge,et al.  Reconstruction of subdomain boundaries of piecewise constant coefficients of the radiative transfer equation from optical tomography data , 2006 .

[9]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[10]  Simon R. Arridge,et al.  Three-dimensional reconstruction of shape and piecewise constant region values for optical tomography using spherical harmonic parametrization and a boundary element method , 2006 .

[11]  S R Arridge,et al.  Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique. , 2006, Optics letters.

[12]  E. Somersalo,et al.  Approximation errors and model reduction with an application in optical diffusion tomography , 2006 .

[13]  Faming Liang,et al.  Statistical and Computational Inverse Problems:Statistical and Computational Inverse Problems , 2006 .

[14]  Michael J. Black,et al.  Fields of Experts: a framework for learning image priors , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[15]  M. Schweiger,et al.  Gauss–Newton method for image reconstruction in diffuse optical tomography , 2005, Physics in medicine and biology.

[16]  S R Arridge,et al.  Recent advances in diffuse optical imaging , 2005, Physics in medicine and biology.

[17]  E. Somersalo,et al.  Statistical and computational inverse problems , 2004 .

[18]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[19]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[20]  Britton Chance,et al.  Diffuse optical tomography with a priori anatomical information , 2003, SPIE BiOS.

[21]  Anand Rangarajan,et al.  Joint-MAP Bayesian tomographic reconstruction with a gamma-mixture prior , 2002, IEEE Trans. Image Process..

[22]  Christopher K. I. Williams,et al.  Combining Belief Networks and Neural Networks for Scene Segmentation , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Jerry L Prince,et al.  Automated Sulcal Segmentation Using Watersheds on the Cortical Surface , 2002, NeuroImage.

[24]  S Arridge,et al.  Recovery of piecewise constant coefficients in optical diffusion tomography. , 2000, Optics express.

[25]  S R Arridge,et al.  Simultaneous reconstruction of internal tissue region boundaries and coefficients in optical diffusion tomography , 2000, Physics in medicine and biology.

[26]  Owen Carmichael,et al.  Learning Low-level Vision Learning Low-level Vision , 2000 .

[27]  M. Escobar,et al.  Markov Chain Sampling Methods for Dirichlet Process Mixture Models , 2000 .

[28]  Simon R. Arridge,et al.  RECOVERY OF REGION BOUNDARIES OF PIECEWISE CONSTANT COEFFICIENTS OF AN ELLIPTIC PDE FROM BOUNDARY DATA , 1999 .

[29]  S. Arridge.  Optical tomography in medical imaging , 1999 .

[30]  Anand Rangarajan,et al.  Joint-MAP reconstruction/segmentation for transmission tomography using mixture-models as priors , 1998, 1998 IEEE Nuclear Science Symposium Conference Record. 1998 IEEE Nuclear Science Symposium and Medical Imaging Conference (Cat. No.98CH36255).

[31]  S R Arridge,et al.  The finite-element method for the propagation of light in scattering media: frequency domain case. , 1997, Medical physics.

[32]  Moncef Gabbouj,et al.  Parallel Image Component Labeling With Watershed Transformation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  K D Paulsen,et al.  Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization. , 1996, Applied optics.

[34]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[35]  M. Schweiger,et al.  The finite element method for the propagation of light in scattering media: boundary and source conditions. , 1995, Medical physics.

[36]  Timothy F. Cootes,et al.  Use of active shape models for locating structures in medical images , 1994, Image Vis. Comput..

[37]  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..

[38]  M. Schweiger,et al.  A finite element approach for modeling photon transport in tissue. , 1993, Medical physics.

[39]  James S. Duncan,et al.  Boundary Finding with Parametrically Deformable Models , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  P.K Sahoo,et al.  A survey of thresholding techniques , 1988, Comput. Vis. Graph. Image Process..

[41]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[42]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[43]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[44]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[45]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[46]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .