Lewis J. Thomas

Noise and Edge Artifacts in Maximum-Likelihood Reconstructions for Emission Tomography

Images produced in emission tomography with the expectation-maximization algorithm have been observed to become more noisy and to have large distortions near edges as iterations proceed and the images converge towards the maximum-likelihood estimate. It is our conclusion that these artifacts are fundamental to reconstructions based on maximum-likelihood estimation as it has been applied usually; they are not due to the use of the expectation-maximization algorithm, which is but one numerical approach for finding the maximum-likelihood estimate. In this paper, we develop a mathematical approach for suppressing both the noise and edge artifacts by modifying the maximum-likelihood approach to include constraints which the estimate must satisfy.

A Matheematical Model for Positron-Emission Tomography Systems Having Time-of-Flight Measurements

Improvements in high speed electronics and scintillation-crystal technology now permit usable differential time-of-flight measurements to be made in tomography systems that employ coincidence detection of the annihilation photons created with positron emitting radionuclides. A mathematical model for these new measurements is developed in this paper. Reconstruction algorithms and their signal-to-noise ratio performance are given.

Regularized linear method for reconstruction of three-dimensional microscopic objects from optical sections

The inverse problem involving the determination of a three-dimensional biological structure from images obtained by means of optical-sectioning microscopy is ill posed. Although the linear least-squares solution can be obtained rapidly by inverse filtering, we show here that it is unstable because of the inversion of small eigenvalues of the microscopes point-spread-function operator. We have regularized the problem by application of the linear-precision-gauge formalism of Joyce and Root [J. Opt. Soc. Am. A 1, 149 (1984)]. In our method the solution is regularized by being constrained to lie in a subspace spanned by the eigenvectors corresponding to a selected number of large eigenvalues. The trade-off between the variance and the regularization error determines the number of eigenvalues inverted in the estimation. The resulting linear method is a one-step algorithm that yields, in a few seconds, solutions that are optimal in the mean-square sense when the correct number of eigenvalues are inverted. Results from sensitivity studies show that the proposed method is robust to noise and to underestimation of the width of the point-spread function. The method proposed here is particularly useful for applications in which processing speed is critical, such as studies of living specimens and time-lapse analyses. For these applications existing iterative methods are impractical without expensive and/or specially designed hardware.

Artifacts in computational optical-sectioning microscopy.

We tested the most complete optical model available for computational optical-sectioning microscopy and obtained four main results. First, we observed good agreement between experimental and theoretical point-spread functions (PSFs) under a variety of imaging conditions. Second, using these PSFs, we found that a linear restoration method yielded reconstructed images of a well-defined phantom object (a 10-microns-diameter fluorescent bead) that closely resembled the theoretically determined, best-possible linear reconstruction of the object. Third, this best linear reconstruction suffered from a (to our knowledge) previously undescribed artifactual axial elongation whose principal cause was not increased axial blur but rather the conical shape of the null space intrinsic to nonconfocal three-dimensional (3D) microscopy. Fourth, when 10-microns phantom beads were embedded at different depths in a transparent medium, reconstructed bead images were progressively degraded with depth unless they were reconstructed with use of a PSF determined at the beads depth. We conclude that (1) the optical model for optical sectioning is reasonably accurate; (2) if PSF shift variance cannot be avoided by adjustment of the optics, then reconstruction methods must be modified to account for this effect; and (3) alternative microscopical or nonlinear algorithmic approaches are required for overcoming artifacts imposed by the missing cone of frequencies that is intrinsic to nonconfocal 3D microscopy.

Quantitative real-time imaging of myocardium based on ultrasonic integrated backscatter

The integrated backscatter calculation over the full, two-dimensional echocardiographic sector is implemented to produce images from closed-chest dogs. This new real-time integrated backscatter measurement system allows a continuous determination of integrated backscatter from all myocardial regions in the ultrasonic view. By replacing the conventional video processor in a commercial two-dimensional echocardiographic imager with this new real-time backscatter measurement system, it is possible to produce real-time two-dimensional images based on integrated backscatter.<<ETX>>

An improved wall filter for flow imaging of low velocity flow

In medical ultrasound, flow velocity estimation for blood flow imaging (color flow) relies on first filtering out signals due to stationary scatterers so that a simple autocorrelation frequency estimator can be used to determine flow. Usually, this “wall filter” is implemented as either a conventional FIR or IIR filter. Unfortunately, in the case of very low velocity flow, these wall filters may remove signals from the moving scatterers of interest. In this work we present a novel filtering scheme that involves first shifting (via a complex multiplication) the undesired signals to zero frequency and then removing these signals by simply subtracting the average of these signals from each of them. The result is a high-pass filter which is very narrow, yet does not reduce the number of samples available to the autocorrelation velocity estimator

Detection of Remote Myocardial Infarction With Quantitative Real-Time Ultrasonic Characterization

We have previously shown that the intrinsic properties of myocardium can be characterized quantitatively by the assessment of ultrasonic integrated backscatter. In this study we utilized a novel, real-time, two-dimensional system capable of quantitative integrated backscatter imaging to determine whether zones of remote myocardial infarction in dogs could be delineated definitively by ultrasonic tissue characterization. Detection of such zones in patients is needed as a basis for management decisions related to thrombolysis, angioplasty, and coronary surgery. Integrated backscatter was measured through the closed chest from 25 myocardial sites. Zones of infarction exhibited time-averaged integrated backscatter values approximately 10 dB (9.5 +/- 0.5 dB, standard error of the mean) greater than those in normal regions (p less than 0.001). In addition, the physiologic cardiac cycle--dependent variation of integrated backscatter was blunted significantly in zones of infarction [0.8 dB +/- 0.3 vs. 3.8 +/- 0.6 (p less than 0.01) for normal regions]. Ultrasonic results matched the histopathologic features assessed directly. Thus quantitative ultrasonic tissue characterization can differentiate infarcted tissue from normal myocardium and offers promise for quantitative detection of histopathology in vivo.

Two-Dimensional Imaging of Selected Ply Orientations in Quasi-Isotropic Composite Laminates Using Polar Backscattering

The polar backscatter technique of Bar-Cohen and Crane offers the potential of selectively interrogating plies of a single orientation in composite material composed of lamina exhibiting multiple orientations. In this work we report an application of this novel measurement technique to quantitative two-dimensional imaging of impact and fatigue damage in graphite epoxy composite materials. For each composite investigated, 4 images were generated based on the ultrasonic backscatter obtained at a fixed, nonperpendicular polar angle and azimuthal angles perpendicular to the 45, 0, -45, and -90 degree fiber orientations in the quasi-isotropic composites. Results of investigation of samples that were damaged by impact and fatigue suggest that polar backscatter offers the potential of a ply-by-ply examination of the location and extent of damage.

Filter matrix estimation in automated DNA sequencing

In four-color fluorescence-based automated DNA sequencing, a 4/spl times/4 filter matrix parameterizes the relationship between the dye-intensity signals of interest and the data collected by an optical imaging system. The filter matrix is important because the estimated DNA sequence is based on the dye intensities that can only be recovered via inversion of the matrix. Here, the authors present a calibration method for the estimation of the columns of this matrix, using data generated through a special experiment in which DNA samples are labeled with only one fluorescent dye at a time. Simulations and applications of the method to real data are provided, with promising results.

6C-6 Qualitative Properties of an Entropy-Based Signal Detector

Detection of molecular epitopes associated with neo- vasculature in a growing tumor presents a unique challenge for ultrasonic clinical imaging systems. In this study, we attempt to solve the problem of detection of site-specific contrast through the use of signal receivers (i.e., mathematical operations that reduce an entire radio frequency (RF) waveform or a portion of it to a single number) based on information-theoretic quantities, such as Shannon Entropy (H), or its counterpart for continuous signal (Hf). These receivers appear to be sensitive to diffuse, low amplitude features of the signal that often are obscured by noise, or else lost in large specular echoes and, hence, not usually perceivable by a human observer. Qualitative and quantitative properties of the finite part, Hf, of the Shannon entropy of a continuous waveform f(t) in the continuum limit are derived in order to illuminate its use for waveform characterization.