Biomedical subjects

A J den Dekker

Publications and source records attributed to A J den Dekker.

13 recordsLinked to original sources

PubMed2005

Maximum likelihood estimation of structure parameters from high resolution electron microscopy images. Part I: a theoretical framework.

This paper is the first part of a two-part paper on maximum likelihood (ML) estimation of structure parameters from electron microscopy images. In principle, electron microscopy allows structure determination with a precision that is orders of magnitude better than the resolution of the microscope. This requires, however, a quantitative, model-based method. In our opinion, the ML method is the most appropriate one since it has optimal statistical properties. This paper aims to provide microscopists with the necessary tools to apply this method so as to determine structure parameters as precisely as possible. It reviews the theoretical framework, including model assessment, the derivation of the ML estimator of the parameters, the limits to precision and the construction of confidence regions and intervals for ML parameter estimates. In a companion paper [Van Aert et al., Ultramicroscopy, this issue, 2005], a practical example will be worked out.

Journal Article↗

PubMed2005

Maximum likelihood estimation of structure parameters from high resolution electron microscopy images. Part II: a practical example.

This paper is the second part of a two-part paper on maximum likelihood (ML) estimation of structure parameters from electron microscopy images. In order to show the practical applicability of the theoretical methods described in the first part of this two-part paper, an experimental study of an aluminium crystal is presented. In this study, structure parameters, atom column distances in particular, are estimated from high-resolution transmission electron microscopy (HRTEM) images using the ML method. The necessary steps to be made in the application of this method will be worked out one by one, including model assessment, the computation of the ML parameter estimates, and the construction of confidence intervals for these parameter estimates.

Journal Article↗

PubMed2005

Generalized likelihood ratio tests for complex fMRI data: a simulation study.

Statistical tests developed for the analysis of (intrinsically complex valued) functional magnetic resonance time series, are generally applied to the data's magnitude components. However, during the past five years, new tests were developed that incorporate the complex nature of fMRI data. In particular, a generalized likelihood ratio test (GLRT) was proposed based on a constant phase model. In this work, we evaluate the sensitivity of GLRTs for complex data to small misspecifications of the phase model by means of simulation experiments. It is argued that, in practical situations, GLRTs based on magnitude data are likely to perform better compared to GLRTs based on complex data in terms of detection rate and constant false alarm rate properties.

Algorithms↗

PubMed2004

Maximum likelihood estimation of signal amplitude and noise variance from MR data.

In MRI, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian-distributed noise. After applying an inverse Fourier transform, the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets. This article addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the maximum likelihood method. As a performance criterion, the mean-squared error (MSE) is used.

Algorithms↗

PubMed2004

How to optimize the experimental design of quantitative atomic resolution TEM experiments?

A quantitative measure is proposed to evaluate and optimize the design of quantitative atomic resolution TEM experiments. It aims at precise measurement of unknown structure parameters. Specifically, the proposed measure quantifies the statistical precision with which positions of atom columns can be estimated. The optimal design is then given by the combination of microscope settings for which this precision is highest. The proposed measure is also used to find out if new instrumental developments improve the precision as compared to existing methods.

Microscopy, Electron↗

PubMed2004

Physical limits on atomic resolution.

It is shown that the ultimate resolution is not limited by the bandwidth of the microscope but by the bandwidth (i.e., the scattering power) of the object. In the case of a crystal oriented along a zone axis, the scattering is enhanced by the channeling of the electrons. However, if the object is aperiodic along the beam direction, the bandwidth is much more reduced. A particular challenge are the amorphous objects. For amorphous materials, the natural bandwidth is that of the single atom and of the order of 1 angstrom(-1), which can be reached with the present generation of medium voltage microscopes without aberration correctors. A clear distinction is made between resolving a structure and refining, that is, between resolution and precision. In the case of an amorphous structure, the natural bandwidth also puts a limit on the number of atom coordinates that can be refined quantitatively. As a consequence, amorphous structures cannot be determined from one projection, but only by using atomic resolution tomography. Finally a theory of experiment design is presented that can be used to predict the optimal experimental setting or the best instrumental improvement. Using this approach it is suggested that the study of amorphous objects should be done at low accelerating voltage with correction of both spherical and chromatic aberration.

Crystallization↗

PubMed2003

Is atomic resolution transmission electron microscopy able to resolve and refine amorphous structures?

Atomic resolution transmission electron microscopy, even with an aberration free microscope, is only able to resolve and refine amorphous structures at the atomic level for very small foil thicknesses. Then, a precision of the order of 0.01 A is possible, but this may require long recording times, especially for light atoms. For larger thicknesses, amorphous structures can in principle only be resolved and refined using electron tomography.

Journal Article↗

PubMed2002

Optimal experimental design of STEM measurement of atom column positions.

A quantitative measure is proposed to evaluate and optimize the design of a high-resolution scanning transmission electron microscopy (STEM) experiment. The proposed measure is related to the measurement of atom column positions. Specifically, it is based on the statistical precision with which the positions of atom columns can be estimated. The optimal design, that is, the combination of tunable microscope parameters for which the precision is highest. is derived for different types of atom columns. The proposed measure is also used to find out if an annular detector is preferable to an axial one and if a C(s)-corrector pays off in quantitative STEM experiments. In addition, the optimal settings of the STEM are compared to the Scherzer conditions for incoherent imaging and their dependence on the type of object is investigated.

Journal Article↗

PubMed2001

Does a monochromator improve the precision in quantitative HRTEM?

This paper addresses the question as to what extent the incorporation of a monochromator in an electron microscope can enhance the performance of high resolution transmission electron microscopy (HRTEM). The monochromator will reduce the chromatic aberration, and hence the information limit, at the expense of beam current, leading to a decrease in signal intensity and a corresponding decrease in signal-to-noise ratio (SNR). Both aspects, information limit and SNR, have been included in a quantitative evaluation based on the statistical precision with which the position of an atom column can be estimated. It is shown that the effect of a monochromator on the attainable precision depends on the microscope and monochromator parameters, as well as on the characteristics of the object.

Journal Article↗

PubMed1999

Adaptive anisotropic noise filtering for magnitude MR data.

Conventional noise filtering schemes applied to magnitude magnetic resonance (MR) images tacitly assume Gauss distributed noise. Magnitude MR data, however, are Rice distributed. Not incorporating this knowledge leads inevitably to biased results, in particular when applying such filters in regions with low signal-to-noise ratio. In this work, we show how the Rice data probability distribution can be incorporated so as to construct a noise filter that is far less biased.

Anisotropy↗

PubMed1998

Estimation of the noise in magnitude MR images.

Magnitude magnetic resonance data are Rician distributed. In this note a new method is proposed to estimate the image noise variance for this type of data distribution. The method is based on a double image acquisition, thereby exploiting the knowledge of the Rice distribution moments.

Magnetic Resonance Imaging↗

PubMed1998

Maximum-likelihood estimation of Rician distribution parameters.

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR.

Computer Simulation↗

PubMedDate not supplied

High-resolution electron microscopy and electron tomography: resolution versus precision.

The performance of high-resolution electron microscopy and electron tomography is usually discussed in terms of two-point resolution, expressing the possibility of perceiving separately two image points of an object. However, the concept resolution obtains another meaning if one uses prior knowledge about the object and the imaging procedure in the form of a parametric model describing the expectations of the observations. The unknown parameters, such as the positions of the components in an object, can be measured quantitatively by fitting this model to the observations. Due to the statistical nature of the experiment, the resulting solutions for the positions of the components and therefore for the distance between the components will never be exact. An alternative to resolution is then the precision with which the distance can be measured. In the present paper, it is shown that the precision depends on the size of the components, the distance between the components, the resolution of the instrument, and the number of electron counts. For electron tomography, it also depends on the orientation of the object with respect to the rotation axis.

Image Processing, Computer-Assisted↗