David G. Brown

Describing small‐scale structure in random media using pulse‐echo ultrasound

A method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J.J. Faran, J. Acoust. Soc. Am. 23, 405-418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere-in-agar and polystyrene sphere-in-agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.

Unified SNR analysis of medical imaging systems

The ideal observer signal to noise ratio (snr) has been derived from statistical decision theory for all of the major medical imaging modalities. This snr provides an absolute scale for image system performance assessment and leads to instrumentation design goals and constraints for imaging system optimisation since no observer can surpass the performance of the ideal observer. The dependence of detectable detail size on exposure or imaging time follows immediately from the analysis. A framework emerges for comparing data acquisition techniques, e.g. reconstruction from projections versus Fourier methods in nmr imaging, and time of flight positron emission tomography (tofpet) versus conventional pet. The approach of studying the ideal observer is motivated by measurements on human observers which show that they can come close to the performance of the idea) observer, except when the image noise has negative correlations-as in images reconstructed from projections-where they suffer a small but significant penalty.

Statistical properties of radio-frequency and envelope-detected signals with applications to medical ultrasound

Both radio-frequency (rf) and envelope-detected signal analyses have lead to successful tissue discrimination in medical ultrasound. The extrapolation from tissue discrimination to a description of the tissue structure requires an analysis of the statistics of complex signals. To that end, first- and second-order statistics of complex random signals are reviewed, and an example is taken from rf signal analysis of the backscattered echoes from diffuse scatterers. In this case the scattering form factor of small scatterers can be easily separated from long-range structure and corrected for the transducer characteristics, thereby yielding an instrument-independent tissue signature. The statistics of the more economical envelope- and square-law-detected signals are derived next and found to be almost identical when normalized autocorrelation functions are used. Of the two nonlinear methods of detection, the square-law or intensity scheme gives rise to statistics that are more transparent to physical insight. Moreover, an analysis of the intensity-correlation structure indicates that the contributions to the total echo signal from the diffuse scatter and from the steady and variable components of coherent scatter can still be separated and used for tissue characterization. However, this analysis is not system independent. Finally, the statistical methods of this paper may be applied directly to envelope signals in nuclear-magnetic-resonance imaging because of the approximate equivalence of second-order statistics for magnitude and intensity.

Analysis Of Ultrasound Image Texture Via Generalized Rician Statistics

Tissue signatures are obtained from the first- and second-order statistics of ultrasonic B-scan texture. Laboratory measurements and early clinical results show that the image may be segmented to discriminate between different normal tissues and to detect abnormal conditions based on a multidimensional feature space. These features describe the intrinsic backscatter properties of the tissues imaged and may be used as the basis of an automatic tissue characterization algorithm.

Application of information theory to the assessment of computed tomography.

The imaging process has two fundamental stages: detection and display. The detection stage can be quantified rigourously using Shannons information theory. This requires the contrast scale (CS), modulation transfer function (MTF), and noise power spectrum [N(f)] to be combined into a signal-to-noise ratio (SNR). This results in two fundamental summary figures of merit: the density of noise equivalent quanta (NEQ) in the image and the information bandwidth integral (IBWI). These algorithm-independent measures are used to quantify the recording stage. The display stage is less well understood since it couples to an external observer. Several types of decision makers are treated. Examples are drawn from first and second generation CT, demonstrating that thye are nearly quantum limited for large signals, indicating how their algorithms are matched or mismatched to the geometry, and calculating the contrast-detail diagrams for those decision makers.

Unified approach to the detection and classification of speckle texture in diagnostic ultrasound

Second order statistics have been derived for the speckle in diagnostic ultrasound that arises from diffuse (incoherent) scattering in the presence of distributed and organized specular (coherent) scattering. They serve as the basis for a three-dimensional feature space in which tissue textures can be classified. The covariance matrix of the measurements in this space is a generalization of the speckle spot number or sampling concept that arises in the study of signal or lesion detectability.

Protein-Based Multiplex Assays: Mock Presubmissions to the US Food and Drug Administration

As a part of ongoing efforts of the NCI-FDA Interagency Oncology Task Force subcommittee on molecular diagnostics, members of the Clinical Proteomic Technology Assessment for Cancer program of the National Cancer Institute have submitted 2 protein-based multiplex assay descriptions to the Office of In Vitro Diagnostic Device Evaluation and Safety, US Food and Drug Administration. The objective was to evaluate the analytical measurement criteria and studies needed to validate protein-based multiplex assays. Each submission described a different protein-based platform: a multiplex immunoaffinity mass spectrometry platform for protein quantification, and an immunological array platform quantifying glycoprotein isoforms. Submissions provided a mutually beneficial way for members of the proteomics and regulatory communities to identify the analytical issues that the field should address when developing protein-based multiplex clinical assays.

Statistical properties of estimates of signal-to-noise ratio and number of scatterers per resolution cell

Elementary theory underlying the relationship between the number of scatterers per resolution cell (N) and echo intensity signal-to-noise ratio (SNR) is reviewed. A relationship between the probability density functions for estimates of N and SNR2 is derived. This relationship is validated using a computer simulation. Phantom and in vitro experiments are described. In one set of experiments on phantoms, empirical distributions of estimates of N and SNR2 are measured and compared to theoretical predictions. The utility of SNR2 for discrimination of phantoms with different values for N is assessed using receiver operating characteristic (ROC) analysis. In another set of experiments, the frequency dependence of the SNR2 estimate is investigated for a two-component phantom and for excised dog kidney. It is shown that the frequency dependence of the SNR can help to identify the presence of two or more scattering components that are spatially mixed. With regard to kidney data, measurements performed both parallel and perpendicular to the predominant nephron orientation are reported. The observed anisotropy is compared to the anisotropy of backscatter coefficient encountered in previous investigations.

Multivariate Gaussian Pattern Classification: Effects of Finite Sample Size and the Addition of Correlated of Noisy Features on Summary Measures of Goodness

The addition of correlated or noisy features to a given feature set can degrade estimates of certain figures of merit used to characterize the class separability offered by the set. We review three such figures of merit and consider the effects of correlation and noise on their estimation from a finite training set. These effects cause some measures to be biased optimistically, others pessimistically. Previous studies of these biases have tended to overlook the large variances involved, particularly in low-dimensional space. Several methods of bias reduction are compared. A method due to Fukunaga and Hayes is compared with the “jackknife”; only the former reduces the bias without increasing the variance of the estimate for problems considered here.

Higher-order tasks: Human vs. machine performance

The linear prewhitening matched filter (PWMF) is the optimal decision function for discriminating exactly-specified signals in additive Gaussian noise. When the signals are less well specified the optimal decision function contains higher than linear terms in the data. Several examples of detection and discrimination tasks are presented for which only the linear term is required and other examples for which higher order terms are necessary. Even in the nonlinear case decision functions can often be approximated by linear operations on the data followed by logical operations. This combination of linear weights plus logic operations is typical of neural network models, which are thought to be elementary models of human processing mechanisms. A number of experiments suggest that there is no decrease in performance of humans for some complex tasks that ideally require such nonlinear operations. However, there are other such tasks where human performance is degraded and this appears to be due more to the complexity of the task and the nature of the correlations in the image than the order of the task. This suggests applications in diagnostic imaging where it might be advantageous for a machine viewer to substitute or work in conjunction with the human observer.