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E Clarkson

Publications and source records attributed to E Clarkson.

10 recordsLinked to original sources
PubMed2001

Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution.

The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, we demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.

Algorithms↗
PubMed2001

Chemical-shift imaging utilizing the positional shifts along the readout gradient direction.

In this work, we describe a method that uses the linear phase acquired during the readout period due to chemical shift to generate individual magnetic resonance (MR) images of chemically shifted species. The method utilizes sets of Fourier (or k-space) data acquired with different directions of the readout gradient and a postprocessing algorithm to generate chemical shift images. The methodology is developed for both Cartesian data acquisition and for radial data acquisition. The method is presented here for two chemically shifted species but it can be extended to more species. In this work, we present the theory, show the results in phantoms and in human images, and discuss the artifacts and signal-to-noise ratio of the images obtained with the technique.

Adipose Tissue↗
PubMed1998

A method for approximating the density of maximum-likelihood and maximum a posteriori estimates under a Gaussian noise model.

The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.

Algorithms↗
PubMed1998

Symmetry properties of an imaging system and consistency conditions in image space.

A general definition for a symmetry group of an imaging system is given. A key requirement is that the operators that represent the symmetries in data space are conformal. The result is that the space of consistency conditions is invariant under the action of the given symmetry group. Via the theory of group representations, this fact provides information about the possible forms that these consistency conditions can take. The theory is illustrated by example for the 2D and 3D Radon transforms, the cone-beam transform on a circular orbit and the 2D attenuated Radon transform.

Image Processing, Computer-Assisted↗
PubMed1998

Bounds on null functions of linear digital imaging systems.

Any linear digital imaging system produces a finite amount of data from a continuous object. This means that there are always null functions, so a reconstruction of the object, even without noise in the system, will differ from the actual object. With positivity constraints, the size of a null function is limited, provided that size is measured by the integral of the absolute value of the null function. When smoothing is used in reconstruction, then smoothed null functions become relevant. There are bounds on various measures of the size of smoothed null functions, and these bounds can be quite small. Smoothing will decrease the effects of null functions in object reconstructions, and this effect is greater if the smoothing operator is well matched to the system operator.

Form Perception↗
PubMed1998

Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions.

We continue the theme of previous papers [J. Opt. Soc. Am. A 7, 1266 (1990); 12, 834 (1995)] on objective (task-based) assessment of image quality. We concentrate on signal-detection tasks and figures of merit related to the ROC (receiver operating characteristic) curve. Many different expressions for the area under an ROC curve (AUC) are derived for an arbitrary discriminant function, with different assumptions on what information about the discriminant function is available. In particular, it is shown that AUC can be expressed by a principal-value integral that involves the characteristic functions of the discriminant. Then the discussion is specialized to the ideal observer, defined as one who uses the likelihood ratio (or some monotonic transformation of it, such as its logarithm) as the discriminant function. The properties of the ideal observer are examined from first principles. Several strong constraints on the moments of the likelihood ratio or the log likelihood are derived, and it is shown that the probability density functions for these test statistics are intimately related. In particular, some surprising results are presented for the case in which the log likelihood is normally distributed under one hypothesis. To unify these considerations, a new quantity called the likelihood-generating function is defined. It is shown that all moments of both the likelihood and the log likelihood under both hypotheses can be derived from this one function. Moreover, the AUC can be expressed, to an excellent approximation, in terms of the likelihood-generating function evaluated at the origin. This expression is the leading term in an asymptotic expansion of the AUC; it is exact whenever the likelihood-generating function behaves linearly near the origin. It is also shown that the likelihood-generating function at the origin sets a lower bound on the AUC in all cases.

Area Under Curve↗
PubMed1997

Oxygen consumption, heart rate, and rating of perceived exertion in young adult women during backward walking at different speeds.

Backward walking has gained popularity as an adjunct to treatment for patients undergoing rehabilitation for patellofemoral pain syndrome and anterior cruciate ligament injuries. Researchers have suggested that backward walking decreases the compressive forces at the patellofemoral joint while also preventing overstretching of the anterior cruciate ligament. Prior to this study, precise prescription of backward walking speeds for women was not possible. The purpose of this study was to determine the relationship between heart rate, oxygen consumption, and backward walking speeds. Twenty-five healthy, adult female volunteers participated in this study. Subjects were tested at speeds of 0.96, 1.20, 1.43, 1.67, and 1.91 m/sec. Subjects also performed a graded exercise stress test. Analysis revealed curvilinear relationships between oxygen consumption and speed as well as between heart rate and speed. With these results, clinicians may now prescribe specific speeds of backward walking for women to elicit a desired cardiopulmonary response.

Adult↗