Biomedical subjects

Anand Rangarajan

Publications and source records attributed to Anand Rangarajan.

7 recordsLinked to original sources

PubMed2004

An accelerated convergent ordered subsets algorithm for emission tomography.

We propose an algorithm, E-COSEM (enhanced complete-data ordered subsets expectation-maximization), for fast maximum likelihood (ML) reconstruction in emission tomography. E-COSEM is founded on an incremental EM approach. Unlike the familiar OSEM (ordered subsets EM) algorithm which is not convergent, we show that E-COSEM converges to the ML solution. Alternatives to the OSEM include RAMLA, and for the related maximum a posteriori (MAP) problem, the BSREM and OS-SPS algorithms. These are fast and convergent, but require ajudicious choice of a user-specified relaxation schedule. E-COSEM itself uses a sequence of iteration-dependent parameters (very roughly akin to relaxation parameters) to control a tradeoff between a greedy, fast but non-convergent update and a slower but convergent update. These parameters are computed automatically at each iteration and require no user specification. For the ML case, our simulations show that E-COSEM is nearly as fast as RAMLA.

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PubMed2004

Unsupervised learning of an atlas from unlabeled point-sets.

One of the key challenges in deformable shape modeling is the problem of estimating a meaningful average or mean shape from a set of unlabeled shapes. We present a new joint clustering and matching algorithm that is capable of computing such a mean shape from multiple shape samples which are represented by unlabeled point-sets. An iterative bootstrap process is used wherein multiple shape sample point-sets are nonrigidly deformed to the emerging mean shape, with subsequent estimation of the mean shape based on these nonrigid alignments. The process is entirely symmetric with no bias toward any of the original shape sample point-sets. We believe that this method can be especially useful for creating atlases of various shapes present in medical images. We have applied the method to create mean shapes from nine hand-segmented 2D corpus callosum data sets and 10 hippocampal 3D point-sets.

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PubMed2003

Bayesian multimodality non-rigid image registration via conditional density estimation.

We present a Bayesian multimodality non-rigid image registration method. Since the likelihood is unknown in the general multimodality setting, we use a density estimator as a drop in replacement to the true likelihood. The prior is a standard small deformation penalty on the displacement field. Since mutual information-based methods are in widespread use for multimodality registration, we attempt to relate the Bayesian approach to mutual information-based approaches. To this end, we derive a new criterion which when satisfied, guarantees that the displacement field which minimizes the Bayesian maximum a posteriori (MAP) objective also maximizes the true mutual information (with a small deformation penalty) as the number of pixels tends to infinity. The criterion imposes an upper bound on the number of configurations of the displacement field. Finally, we compare the results of the Bayesian approach with mutual information, joint entropy and joint probability approaches on synthetic data and simulated T1 and T2 2D MR images.

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PubMed2003

A unified non-rigid feature registration method for brain mapping.

This paper describes the design, implementation and results of a unified non-rigid feature registration method for the purposes of anatomical MRI brain registration. An important characteristic of the method is its ability to fuse different types of anatomical features into a single point-set representation. We demonstrate the application of the method using two different types of features: the outer cortical surface and major sulcal ribbons. Non-rigid registration of the combined feature point-sets is then performed using a new robust non-rigid point matching algorithm. The point matching algorithm implements an iterative joint clustering and matching (JCM) strategy which effectively reduces the computational complexity without sacrificing accuracy. We have conducted carefully designed synthetic experiments to gauge the effect of using different types of features either separately or together. A validation study examining the accuracy of non-rigid alignment of many brain structures is also presented. Finally, we present anecdotal results on the alignment of two subject MRI brain data.

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PubMed2003

Entropy-based dual-portal-to-3-DCT registration incorporating pixel correlation.

For patient setup verification in external beam radiotherapy (EBRT) of prostate cancer, we developed an information theoretic registration framework, called the minimax entropy registration framework, to simultaneously and iteratively segment portal images and register them to three-dimensional (3-D) computed tomography (CT) image data. The registration framework has two steps, the max step and the min step, and evaluates appropriate entropies to estimate segmentations of the portal images and to find the transformation parameters. In the initial version of the algorithm (Bansal et al. 1999), we assumed image pixels to be independently distributed, an assumption not true in general. Thus, to better segment the portal images and to improve the accuracy of the estimated registration parameters, in this initial formulation of the problem, the correlation among pixel intensities is modeled using a one-dimensional Markov random process. Line processes are incorporated into the model to improve the estimation of segmentation of the portal images. In the max step, the principle of maximum entropy is invoked to estimate the probability distribution on the segmentations. The estimated distribution is then incorporated into the min step to estimate the registration parameters. Performance of the proposed framework is evaluated and compared to that of a mutual information-based registration algorithm using both simulated and real patient data. In the proposed registration framework, registration of the 3-D CT image and the portal images is guided by an estimated segmentation of the pelvic bone. However, as the prostate can move with respect to the pelvic structure, further localization of the prostate using ultrasound image data is required, an issue to be further explored in future.

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PubMed2003

A new convex edge-preserving median prior with applications to tomography.

In a Bayesian tomographic maximum a posteriori (MAP) reconstruction, an estimate of the object f is computed by iteratively minimizing an objective function that typically comprises the sum of a log-likelihood (data consistency) term and prior (or penalty) term. The prior can be used to stabilize the solution and to also impose spatial properties on the solution. One such property, preservation of edges and locally monotonic regions, is captured by the well-known median root prior (MRP), an empirical method that has been applied to emission and transmission tomography. We propose an entirely new class of convex priors that depends on f and also on m, an auxiliary field in register with f. We specialize this class to our median prior (MP). The approximate action of the median prior is to draw, at each iteration, an object voxel toward its own local median. This action is similar to that of MRP and results in solutions that impose the same sorts of object properties as does MRP. Our MAP method is not empirical, since the problem is stated completely as the minimization of a joint (on f and m) objective. We propose an alternating algorithm to compute the joint MAP solution and apply this to emission tomography, showing that the reconstructions are qualitatively similar to those obtained using MRP.

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PubMed2003

The concave-convex procedure.

The concave-convex procedure (CCCP) is a way to construct discrete-time iterative dynamical systems that are guaranteed to decrease global optimization and energy functions monotonically. This procedure can be applied to almost any optimization problem, and many existing algorithms can be interpreted in terms of it. In particular, we prove that all expectation-maximization algorithms and classes of Legendre minimization and variational bounding algorithms can be reexpressed in terms of CCCP. We show that many existing neural network and mean-field theory algorithms are also examples of CCCP. The generalized iterative scaling algorithm and Sinkhorn's algorithm can also be expressed as CCCP by changing variables. CCCP can be used both as a new way to understand, and prove the convergence of, existing optimization algorithms and as a procedure for generating new algorithms.

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