Guy E. Mailloux

Restoration of the velocity field of the heart from two-dimensional echocardiograms

A method to quantify the motion of the heart from digitized sequences of two-dimensional echocardiograms (2-D) echos was recently proposed. This method computes on every point of the 2-D echoes, the 2-D apparent velocity vector (or optical flow) which characterizes its interframe motion. However, further analysis is required to determine what part of this motion is due to translation, rotation, contraction, and deformation of the myocardium. A method to locally obtain this information is presented. The proposed method assumes that the interframe velocity field U(xy), V(x,y) can be locally described by linear equations in the form U(x,y)=a+Ax+By; V(x,y)=b+Cx+Dy. The additional constraint was introduced in the computation of the local velocity field by the method of projections onto convex sets. Since this constraint is only valid locally, the myocardium must be first divided into sectors and the velocity fields computed independently for each sector.

A projection operator for the restoration of divergence-free vector fields

The theory of image restoration by projection onto convex sets can also be applied to the restoration of vector fields. These can have properties that restrict them to lie in well-defined closed convex sets. One of the properties, divergence freedom, is considered, and the theory and numerical implementation of its projection operator are presented. The performance of the operator is illustrated by restoring, from partial information, two simulated divergence-free vector fields. This projection operator finds an important application in the restoration of velocity fields or optical flows computed from an image sequence when the real velocity field is known, a priori to be divergence-free. >

Regional epicardial dynamics computed from coronary cineangiograms

A method to compute the region epicardial deformation from coronary cineangiograms is presented. For this purpose, a close relationship is assumed between the motion of the epicardium and the motion of the embedded coronary arterial tree which is visible on cineangiograms. The interframe motion of the coronary arteries is computed by an optical flow approach assuming a locally linear two-dimensional (2-D) motion field. One can thus extract from the composite linear field meaningful components, such as the local 2-D biaxial deformation of the epicardial surface and the related epicardial thickening. Once the region of interest (ROI) is selected, the method is essentially operator free and provides a tool to characterize the epicardial dynamics. The method is five to ten times faster than conventional iterative optical flow methods, while providing essentially the same results. The method was applied to monoplane angiography, using a projection with the ROI parallel to the image plane (to minimize the foreshortening) to reduce the effect of third-dimension movement on the computed deformation field.<<ETX>>

An expectation maximization reconstruction algorithm for emission tomography with non-uniform entropy prior

A Bayesian image reconstruction algorithm is proposed for emission tomography. It incorporates the Poisson nature of the noise in the projection data and uses a non-uniform entropy as an a priori probability distribution of the image in a maximum a posteriori (MAP) approach. The expectation maximization (EM) method was applied to find the MAP estimator. The Newton-Raphson numerical method whose convergence and positive solutions are proven, was used to solve the EM problem. The prior mean at iteration k was determined by smoothing the image obtained at iteration k-1. Comparisons between the ML and the MAP algorithm were carried out with a numerical phantom that contains a narrow valley region. The ML solution after 50 iterations was chosen as the initial solution for the MAP algorithm, since the global performance of the ML algorithm deteriorates with increasing number of iterations while its local performance in the valley region is always improving. The resulting algorithm is a compromise between ML who has the best local performance in the valley region and the MAP who has the best global performance.

Deriving the multiplicative algebraic reconstruction algorithm (MART) by the method of convex projection (POCS)

It is shown that the MART (multiplicative algebraic reconstruction technique) algorithm can be derived by POCS. This gives MART a new theoretical interpretation and a proof of convergence to a stable solution even when other convex constraints are introduced. However, MART, as a multiplicative algorithm, depends on the initial solution. It is noted that, far from being a flaw, this property can be used to introduce further a priori knowledge about the image to be reconstructed, to maximize the entropy, to keep the ratio between the regions of the original image constant, or to set to zero the area outside the reconstruction volume. MART should be preferred to MENT (a maximum entropy algorithm) for entropy maximization, for it performs as well but is much faster. ART is much less influenced by the initial solution than MART.<<ETX>>

Use of an optical flow algorithm to quantify and correct patient motion during tomographic acquisition

We have developed an automatic procedure for the detection, quantification and correction of translational motion during single photon emission computerized tomography (SPECT). The method computes the optical flow vector field between two successive views. The optical flow vector field assigns to each pixel of a tomographic view a two dimensional velocity that describes its motion across the image plane between two successive views. Motion can be corrected by shifting the moved views back by the amount of the measured motion distance. The method is applied to human studies where obvious motion was detected from visual inspection of a rotating cine display. Visually artifactual perfusion defects are eliminated after motion correction. The optical flow method can accurately detect the presence of motion, localize the camera angle at which motion occurred and measure the distance of motion.

Accelerated iterative reconstruction based on the maximum a posteriori expectation maximization

It is demonstrated that the ML-EM (maximum-likelihood expectation-maximization) algorithm is a particular case of the modified Newton method whose convergence is proved and can be optimally accelerated by an overrelaxation parameter. In order to overcome the checkerboard effect, this accelerated ML-EM algorithm can be penalized with a Gaussian a priori distribution in the framework of a MAP (maximum a posteriori) approach. The experimental results obtained here indicate that significant savings in computation time may be achieved using the accelerated MAP algorithm.<<ETX>>

Obtaining blood velocity profile from coronary arteriograms via optimally controlled optical flow

Physical constraints are used to adapt known optical flow algorithms to study blood circulation in healthy and stenosed arteries by tracking dye dispersion using radiological image sequences. To this end, the multiplier methods of constrained optimization are put forward. Instabilities are handled through the Lions regularization process. Simulated radiological images taking into account blood flow and contrast substance dispersion are computed to test the proposed algorithms. Results from simulations as well as from clinical radiological data are presented. Results on simulated images indicate a good fluid flow estimation. Results on clinical images appear to be qualitatively correct. The proposed method has many advantages. It allows the introduction of any physical a priori knowledge modeled with partial differential equations, permits clear distinction between mathematical (smoothness) and physical constraints, and provides efficient image flow algorithms.<<ETX>>

Comparison between cross-correlation and optical flow methods for patient motion detection in SPECT

An automatic procedure for the detection and quantification of motion during single photon emission computerized tomography (SPECT) is proposed. The method computes the optical flow vector field between two successive views. The proposed method is also compared with the cross-correlation method.

Three-dimensional correction of experimentally determined gamma camera response

The response of a gamma camera depends on the source to-camera distance. It results in a two-dimensional blurring of the projection image and in an increasing loss in resolution with increasing distance from the face of the collimator. Here, the authors present a method for experimentally estimating a parametric model for the point source response of a gamma camera with parallel hole collimator. This model is used to incorporate the three-dimensional spatially varying camera response into the projection and back-projection operations of the tomographic reconstruction maximum likelihood algorithm which also compensates for the three-dimensional uniform attenuation. Using phantom experiments, the authors demonstrated a substantial improvement in the quality and the quantitative accuracy of the single photon emission computed tomography images.<<ETX>>