Cardiac motion estimation by joint alignment of tagged MRI sequences.

Image registration has been proposed as an automatic method for recovering cardiac displacement fields from tagged Magnetic Resonance Imaging (tMRI) sequences. Initially performed as a set of pairwise registrations, these techniques have evolved to the use of 3D+t deformation models, requiring metrics of joint image alignment (JA). However, only linear combinations of cost functions defined with respect to the first frame have been used. In this paper, we have applied k-Nearest Neighbors Graphs (kNNG) estimators of the α-entropy (H(α)) to measure the joint similarity between frames, and to combine the information provided by different cardiac views in an unified metric. Experiments performed on six subjects showed a significantly higher accuracy (p<0.05) with respect to a standard pairwise alignment (PA) approach in terms of mean positional error and variance with respect to manually placed landmarks. The developed method was used to study strains in patients with myocardial infarction, showing a consistency between strain, infarction location, and coronary occlusion. This paper also presents an interesting clinical application of graph-based metric estimators, showing their value for solving practical problems found in medical imaging.

Comparing pairwise and simultaneous joint registrations of decorrelating interval exams using entropic graphs.

The interest in registering a set of images has quickly risen in the field of medical image analysis. Mutual information (MI) based methods are well-established for pairwise registration but their extension to higher dimensions (multiple images) has encountered practical implementation difficulties. We extend the use of alpha mutual information (alphaMI) as the similarity measure to simultaneously register multiple images. alphaMI of a set of images can be directly estimated using entropic graphs spanning feature vectors extracted from the images, which is demonstrated to be practically feasible for joint registration. In this paper we are specifically interested in monitoring malignant tumor changes using simultaneous registration of multiple interval MR or CT scans. Tumor scans are typically a decorrelating sequence due to the cycles of heterogeneous cell death and growth. The accuracy of joint and pairwise registration using entropic graph methods is evaluated by registering several sets of interval exams. We show that for the parameters we investigated simultaneous joint registration method yields lower average registration errors compared to pairwise. Different degrees of decorrelation in the serial scans are studied and registration performance suggests that an appropriate scanning interval can be determined for efficiently monitoring lesion changes. Different levels of observation noise are added to the image sequences and the experimental results show that entropic graph based methods are robust and can be used reliably for multiple image registration.

Myocardial motion estimation in tagged MR sequences by using alphaMI-based non rigid registration.

Tagged Magnetic Resonance Imaging (MRI) is currently the reference MR modality for myocardial motion and strain analysis. NMI-based non rigid registration has proven to be an accurate method to retrieve cardiac deformation fields. The use of alphaMI permits higher dimensional features to be implemented in myocardial deformation estimation through image registration. This paper demonstrates that this is feasible with a set of Haar wavelet features of high dimension. While we do not demonstrate performance improvement for this set of features, there is no significant degradation as compared to implementing the registration method with the traditional NMI metric. We use Entropic Spanning Graphs (ESGs) to estimate the alphaMI of the wavelet feature vectors WFVs since this is not possible with histograms. To the best of our knowledge, this is the first time that ESGs are used for non rigid registration.

Comparison of GLR and invariant detectors under structured clutter covariance.

This paper addresses a target detection problem in radar imaging for which the covariance matrix of unknown Gaussian clutter has block diagonal structure. This block diagonal structure is the consequence of a target lying along a boundary between two statistically independent clutter regions. Here, we design adaptive detection algorithms using both the generalized likelihood ratio (GLR) and the invariance principles. There has been considerable interest in applying invariant hypothesis testing as an alternative to the GLR test. This interest has been motivated by several attractive properties of invariant tests including: exact robustness to variation of nuisance parameters and possible finite-sample min-max optimality. However, in our deep-hide target detection problem, there are regimes for which neither the GLR nor the invariant tests uniformly outperforms the other. We discuss the relative advantages of GLR and invariance procedures in the context of this radar imaging and target detection application.

Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms.

Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type algorithms. This paper presents space-alternating generalized EM (SAGE) algorithms for image reconstruction, which update the parameters sequentially using a sequence of small "hidden" data spaces, rather than simultaneously using one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. We introduce new hidden-data spaces that are less informative than the conventional complete-data space for Poisson data and that yield significant improvements in convergence rate. This acceleration is due to statistical considerations, not numerical overrelaxation methods, so monotonic increases in the objective function are guaranteed. We provide a general global convergence proof for SAGE methods with nonnegativity constraints.

Model-based estimation for dynamic cardiac studies using ECT.

The authors develop a strategy for joint estimation of physiological parameters and myocardial boundaries using ECT (emission computed tomography). They construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. The authors then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. They also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model-based joint ML estimator and compare this performance to the Cramer-Rao lower bound. Finally, the authors discuss model assumptions and potential uses of the joint estimation strategy.

Model-based estimation with boundary side information or boundary regularization [cardiac emission CT].

The authors have previously developed a model-based strategy for joint estimation of myocardial perfusion and boundaries using ECT (emission computed tomography). They have also reported difficulties with boundary estimation in low contrast and low count rate situations. Here they propose using boundary side information (obtainable from high resolution MRI and CT images) or boundary regularization to improve both perfusion and boundary estimation in these situations. To fuse boundary side information into the emission measurements, the authors formulate a joint log-likelihood function to include auxiliary boundary measurements as well as ECT projection measurements. In addition, they introduce registration parameters to align auxiliary boundary measurements with ECT measurements and jointly estimate these parameters with other parameters of interest from the composite measurements. In simulated PET O-15 water myocardial perfusion studies using a simplified model, the authors show that the joint estimation improves perfusion estimation performance and gives boundary alignment accuracy of <0.5 mm even at 0.2 million counts. They implement boundary regularization through formulating a penalized log-likelihood function. They also demonstrate in simulations that simultaneous regularization of the epicardial boundary and myocardial thickness gives comparable perfusion estimation accuracy with the use of boundary side information.

Information analysis of single photon emission computed tomography with count losses.

An analysis is presented of the information transfer from emitter-space to detector-space in single photon emission computed tomography (SPECT) systems. The analysis takes into account the fact that count loss side information is generally not available at the detector. Side information corresponds to the number gamma-rays lost deleted due to lack of interaction with the detector data. It is shown that the information transfer depends on the structure of the likelihood function of the emitter locations associated with the detector data. This likelihood function is the average of a set of ideal-detection likelihood functions, each matched to a particular set of possible deleted gamma-ray paths. A lower bound is derived for the information gain due to incorporating the count loss side information at the detector. This is shown to be significant when the mean emission rate is small or when the gamma-ray deletion probability is strongly dependent on emitter location. Numerical evaluations of the mutual information, with and without side information, associated with information-optimal apertures and uniform parallel-hole collimators are presented.

The mutual information criterion for SPECT aperture evaluation and design.

An aperture performance criterion for single-photon-emission computed tomography (SPECT) that is based on the mutual information (MI) between the source and detector processes is proposed. The MI is a measure of the reduction in uncertainty of the emitter location, given the detector data, and it takes account of the inherent tradeoffs between the effects of sensitivity and resolution on source estimation accuracy. Specific expressions for the MI are derived for one-dimensional linear geometries and two-dimensional, parallel-slice, ring geometries under the assumptions of Poisson emission times, uniform emission angles, no scattering, and a known lost-count correction factor. For one-dimensional geometries a necessary and sufficient condition for an aperture to maximize the mutual information is given. The MI-optimal apertures are derived for various source distributions using an iterative maximization procedure. The MI is then numerically calculated for various ring apertures associated with the parallel-slice SPRINT II system.