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Application of the EM algorithm to radiographic images.

The expectation maximization (EM) algorithm has received considerable attention in the area of positron emitted tomography (PET) as a restoration and reconstruction technique. In this paper, the restoration capabilities of the EM algorithm when applied to radiographic images is investigated. This application does not involve reconstruction. The performance of the EM algorithm is quantitatively evaluated using a "perceived" signal-to-noise ratio (SNR) as the image quality metric. This perceived SNR is based on statistical decision theory and includes both the observer's visual response function and a noise component internal to the eye-brain system. For a variety of processing parameters, the relative SNR (ratio of the processed SNR to the original SNR) is calculated and used as a metric to compare quantitatively the effects of the EM algorithm with two other image enhancement techniques: global contrast enhancement (windowing) and unsharp mask filtering. The results suggest that the EM algorithm's performance is superior when compared to unsharp mask filtering and global contrast enhancement for radiographic images which contain objects smaller than 4 mm.

Algorithms

Experimental verification of a three-dimensional dose calculation algorithm using a specially designed heterogeneous phantom.

A solid heterogeneous phantom made up of 25- and 50-mm cubes of materials with different electron densities was used to verify the accuracy of a three-dimensional (3-D) dose calculation algorithm. This algorithm uses 3-D information obtained from contiguous CT (computed tomography) slices, spaced 5 mm apart. Primary and scatter doses at a point are calculated by using information from ray-tracing CT voxels. The algorithm was developed on a Stardent model 1500 Supergraphic workstation. Cubes of materials with different electron densities were stacked up to simulate finite heterogeneities in three dimensions. This design allows verification of the algorithm for surface contour corrections and finite heterogeneities in the treatment field. Thermoluminescent lithium fluoride chips were placed in grooves milled on the cubes for dose measurement at various points. Different experiments were performed to investigate both the accuracy of the dose calculation algorithm and the utility of the versatile test phantom.

Algorithms

A generalized pencil beam algorithm for optimization of radiation therapy.

An iterative pencil beam algorithm for optimization of multidimensional radiation therapy dose plans has been developed. The algorithm allows the use of both physical and radiobiological treatment objective functions and allows arbitrary sampling such as straight Cartesian grids with linear or nonlinear sampling functions or random sampling. The algorithm can account for and optimally combine almost all the degrees of freedom at an advanced radiotherapy clinic, such as different beam modalities and spectra, beam directions, beam fluence distributions, and time-dose fractionations. The algorithm allows for external charged and neutral beams as well as intracavitary and interstitial sources to be optimally combined. A quantity termed the generalized fluence vector is introduced, combining fluences and energy fluences from external beams as well as the radiation source densities of intracavitary and interstitial sources or external source distributions. The positivity constraint on the generalized fluence can therefore be applied directly during the optimization procedure. The convergence properties and the required iteration time of the algorithm are discussed. Several examples with combinations of photon and electron beams of different energies and directions of incidence are presented. The optimization has been made with the treatment objective to maximize the probability of achieving tumor control without causing severe complications in healthy normal tissues.

Algorithms

Algorithm for image reconstruction in multi-slice helical CT.

Efforts are being made to develop a new type of CT system that can scan volumes over a large range within a short time with thin slice images. One of the most promising approaches is the combination of helical scanning with multi-slice CT, which involves several detector arrays stacked in the z direction. However, the algorithm for image reconstruction remains one of the biggest problems in multi-slice CT. Two helical interpolation methods for single-slice CT, 360LI and 180LI, were used a starting points and extended to multi-slice CT. The extended methods, however, had a serious image quality problem due to the following three reasons: (1) excessively close slice positions of the complementary and direct data, resulting in a larger sampling interval; (2) the existence of several discontinuous changeovers in pairs of data samples for interpolation; and (3) the existence of cone angles. Therefore we have proposed a new algorithm to overcome the problem. It consists of the following three parts: (1) optimized sampling scan; (2) filter interpolation; and (3) fan-beam reconstruction. Optimized sampling scan refers to a special type of multi-slice helical scan developed to shift the slice position of complementary data and to acquire data with a much smaller sampling interval in the z direction. Filter interpolation refers to a filtering process performed in the z direction using several data. The normal fan-beam reconstruction technique is used. The section sensitivity profile (SSP) and image quality for four-array multi-slice CT were investigated by computer simulations. Combinations of three types of optimized sampling scan and various filter widths were used. The algorithm enables us to achieve acceptable image quality and spatial resolution at a scanning speed that is about three times faster than that for single-slice CT. The noise characteristics show that the proposed algorithm efficiently utilizes the data collected with optimized sampling scan. The new algorithm allows suitable combinations of scan and filter parameters to be selected to meet the purpose of each examination.

Algorithms

A simple algorithm for planar image registration in radiation therapy.

A simple algorithm is presented for planar image registration and the method is applied to the simulator and portal image registration for patient setup verification in radiation therapy. Basically, the algorithm follows the concept proposed by Balter et al. [Med. Phys. 19, 329-334 (1992)], which converts the problem of open curve registration into matching a series of points along the curves. Balter's algorithm consists of three steps: (1) to determine a common starting point for each curve pair, (2) acquire two corresponding point sets along each curve, and (3) obtain a global transform matrix by matching two point sets. We integrate all three steps into one simple procedure which fits the sampled points along the intended curve pair by taking the relative path length shift as an independent fitting parameter. After being modified, the algorithm is able to take the different magnification factors of images into account, and it avoids curvature calculations. Numerical simulation as well as clinical and phantom images have been utilized to test the accuracy of the algorithm. The typical errors are less than 1 mm in translation and 1 degree in rotation. We also made a comparison study with the chamfer method. The results of the two methods agree to within 0.5 mm in translation and 0.5 degree in rotation.

Algorithms

A new genetic algorithm technique in optimization of permanent 125I prostate implants.

Real time optimized treatment planning at the time of the implant is desirable for ultrasound-guided transperineal 125I permanent prostate implants. Currently available optimization algorithms are too slow to be used in the operating room. The goal of this work is to develop a robust optimization algorithm, which is suitable for such application. Three different genetic algorithms (sGA, sureGA and securGA) were developed and compared in terms of the number of function evaluations and the corresponding fitness. The optimized dose distribution was achieved by searching the best seed distribution through the minimization of a cost function. The cost function included constraints on the periphery dose of the planned target volume, the dose uniformity within the target volume, and the dose to the critical structure. Adjustment between the peripheral dose, the dose uniformity and critical structure dose can be achieved by varying the weighting factors in the cost function. All plans were evaluated in terms of the dose nonuniformity ratio, the conformation number and the dose volume histograms. Among these three GA algorithms, the securGA provided the best performance. Within 2500 function evaluations, the near optimum results were obtained. For a large target volume (5 cm x 4 cm x 4.5 cm) including urethra with 20 needles, the computer time needed for the optimization was less than 5 min on a HP735 workstation. The results showed that once the best set of parameters was found, they were applicable for all sizes of prostate volume. For a fixed needle geometry, the optimized plan showed much better dose distribution than that of nonoptimized plan. If the critical structure was considered in the optimization, the dose to the critical structure could be minimized. In the cases of irregular and skewed needle geometry, the optimized treatment plans were almost as good as ideal needle geometry. It is concluded that this new genetic algorithm (securGA) allows for an efficient and rapid optimization of dose distribution, which is suitable for real time treatment planning optimization for ultrasound-guided prostate implant.

Algorithms

Objective speech quality assessment and the RPE-LTP coding algorithm in different noise and language conditions.

The formulation of reliable signal processing algorithms for speech coding and synthesis require the selection of a prior criterion of performance. Though coding efficiency (bits/second) or computational requirements can be used, a final performance measure must always include speech quality. In this paper, three objective speech quality measures are considered with respect to quality assessment for American English, noisy American English, and noise-free versions of seven languages. The purpose is to determine whether objective quality measures can be used to quantify changes in quality for a given voice coding method, with a known subjective performance level, as background noise or language conditions are changed. The speech coding algorithm chosen is regular-pulse excitation with long-term prediction (RPE-LTP), which has been chosen as the standard voice compression algorithm for the European Digital Mobile Radio system. Three areas are considered for objective quality assessment which include: (i) vocoder performance for American English in a noise-free environment, (ii) speech quality variation for three additive background noise sources, and (iii) noise-free performance for seven languages which include English, Japanese, Finnish, German, Hindi, Spanish, and French. It is suggested that although existing objective quality measures will never replace subjective testing, they can be a useful means of assessing changes in performance, identifying areas for improvement in algorithm design, and augmenting subjective quality tests for voice coding/compression algorithms in noise-free, noisy, and/or non-English applications.

Adult

An active noise control algorithm for controlling multiple sinusoids.

The filtered-x LMS algorithm and its modified versions have been successfully applied in suppressing acoustic noise such as single and multiple tones and broadband random noise. This paper presents an adaptive algorithm based on the filtered-x LMS algorithm which may be applied in attenuating tonal acoustic noise. In the proposed method, the weights of the adaptive filter and estimation of the phase shift due to the acoustic path from a loudspeaker to a microphone are computed simultaneously for optimal control. The algorithm possesses advantages over other filtered-x LMS approaches in three aspects: (1) each frequency component is processed separately using an adaptive filter with two coefficients, (2) the convergence parameter for each sinusoid can be selected independently, and (3) the computational load can be reduced by eliminating the convolution process required to obtain the filtered reference signal. Simulation results for a single-input/single-output (SISO) environment demonstrate that the proposed method is robust to the changes of the acoustic path between the actuator and the microphone and outperforms the filtered-x LMS algorithm in simplicity and convergence speed.

Acoustics

Genetic algorithms: principles of natural selection applied to computation.

A genetic algorithm is a form of evolution that occurs on a computer. Genetic algorithms are a search method that can be used for both solving problems and modeling evolutionary systems. With various mapping techniques and an appropriate measure of fitness, a genetic algorithm can be tailored to evolve a solution for many types of problems, including optimization of a function of determination of the proper order of a sequence. Mathematical analysis has begun to explain how genetic algorithms work and how best to use them. Recently, genetic algorithms have been used to model several natural evolutionary systems, including immune systems.

Algorithms

Algorithm for use of nucleic acid probes for identifying Mycobacterium tuberculosis from BACTEC 12B bottles.

Nucleic acid probes (Gen-Probe, San Diego, Calif.) can be used to identify mycobacteria in BACTEC 12B broth cultures prior to detection of growth on solid media. We developed an algorithm that can be used to make an initial choice of a probe (either Mycobacterium tuberculosis complex [MTB] or M. avium complex [MAC]) for use in testing respiratory specimens. The algorithm was based on both the fluorochrome smear result of the concentrated specimen and the time from inoculation until the BACTEC 12B broth culture is flagged (growth index 10) as presumptively positive. The MTB probe is used first for all 4+ smear specimens, 3+ smear specimens positive in 5 days, 2+ and 1+ smear specimens positive in 7 days, and smear-negative specimens positive in 11 days. The MAC probe is used for all other specimens. The algorithm is used when other information about the culture (e.g., previous positive cultures and colonial morphology of growth on solid media) is unknown. Use of the algorithm to probe 102 respiratory BACTEC 12B broth cultures (35 with MTB; 1 with MTB, MAC, and M. gordonae; 47 with MAC; and 19 with other mycobacterial species) from 1 September through 30 November 1992 resulted in the initial use of the MTB probe for 35 (97%) of the cultures positive for MTB and the use of the MAC probe for 35 (73%) of the cultures positive for MAC. Use of the algorithm aided in the efficient use of laboratory resources without delaying the time to identification of MTB isolates.

Algorithms

Clinical evaluation of scanning laser polarimetry: I. Intraoperator reproducibility and design of a blood vessel removal algorithm.

AIMS: To evaluate the reproducibility of the retardation values (change in polarisation) obtained with the scanning-laser polarimeter in a series of normal subjects and glaucoma patients. To improve the analysis of the raw data by devising and evaluating a blood vessel removal algorithm. METHODS: Scanning laser polarimetry was performed on 10 normal subjects and 10 glaucoma patients. A series of six images was obtained from each eye. The normal subjects were re-imaged 3 months after their initial assessment. The retardation values obtained from each eye were analysed using the authors' own methods, including the use of an algorithm to remove blood vessels from the polar profiles. The reproducibility of these measurements and the performance of the blood vessel removal algorithm were assessed. RESULTS: The "individual point" coefficient of variation was approximately 12.5% for normal subjects and 17.0% for glaucoma patients. The "integral" coefficient of variation for these groups was approximately 5.5% and 9.5% respectively. The reproducibility of the measurements did not improve with an increased number of measurements. There was no difference in the reproducibility of the measurements in normal subjects over time. The blood vessel removal algorithm improved the reproducibility of the measurements when the shape of the profile was assessed. CONCLUSION: The intraoperator reproducibility of retardation values obtained with the scanning laser polarimeter is satisfactory for its use as a clinical tool. The use of a blood vessel removal algorithm improves the reproducibility of the measurements and also assists the clinician in the interpretation of the polar profiles. Furthermore, it allows the construction of normal database polar profiles, thereby enabling the identification, location and quantification of retinal nerve fibre layer damage in an "at risk" individual's polar profile.

Algorithms

A simple algorithm to predict the development of radiological erosions in patients with early rheumatoid arthritis: prospective cohort study.

OBJECTIVE: To produce a practical algorithm to predict which patients with early rheumatoid arthritis will develop radiological erosions. DESIGN: Primary care based prospective cohort study. SETTING: All general practices in the Norwich Health Authority, Norfolk. SUBJECTS: 175 patients notified to the Norfolk Arthritis Register were visited by a metrologist soon after they had presented to their general practitioners with inflammatory polyarthritis, and again after a further 12 months. All the patients satisfied the American Rheumatism Association's 1987 criteria for rheumatoid arthritis and were seen by a metrologist within six months of the onset of symptoms. The study population was randomly split into a prediction sample (n = 105) for generating the algorithm and a validation sample (n = 70) for testing it. MAIN OUTCOME MEASURES: Predictor variables measured at baseline included rheumatoid factor status, swelling of specific joint areas, duration of morning stiffness, nodules, disability score, age, sex, and disease duration when the patient first presented. The outcome variable was the presence of radiological erosions in the hands or feet, or both, after 12 months. RESULTS: A simple algorithm based on a combination of three variables--a positive rheumatoid factor test, swelling of at least two large joints, and a disease duration of more than three months--was best able to predict erosions. When the accuracy of this algorithm was tested with the validation sample, the erosion status of 79% of patients was predicted correctly. CONCLUSIONS: A simple algorithm based on three easily measured items of information can predict which patients are at high risk and which are at low risk of developing radiological erosions.

Adult

Predicting operative risk for coronary artery surgery in the United Kingdom: a comparison of various risk prediction algorithms.

OBJECTIVE: To compare the ability of four risk models to predict operative mortality after coronary artery bypass graft surgery (CABG) in the United Kingdom. DESIGN: Prospective study. SETTING: Two cardiothoracic centres in the United Kingdom. SUBJECTS: 1774 patients having CABG. MAIN OUTCOME MEASURES: Risk factors were recorded for all patients, along with in-hospital mortality. Predicted mortality was derived from the American Society of Thoracic Surgeons (STS) risk program, Ontario Province risk score (PACCN), Parsonnet score, and the UK Society of Cardiothoracic Surgeons risk algorithm. RESULTS: There were significant differences (p < 0.05) between the British and American populations from which the STS risk algorithm was derived with respect to most variables. The observed mortality in the British population was 3.7% (65 of 1774). The mean predicted mortality by STS score, PACCN, Parsonnet score, and UK algorithms were 1.1%, 1.6%, 4.6%, and 4.7% respectively. The overall predictive ability of the models as measured by the area under the receiver operating characteristic curve were 0.64, 0.60, 0.73, and 0.75, respectively. CONCLUSIONS: There are differences between the British and American populations for CABG and the North American algorithms are not useful for predicting mortality in the United Kingdom. The UK Society of Cardiothoracic Surgeons algorithm is the best of the models tested but still only has limited predictive ability. Great care must be exercised when using methods of this type for comparisons of units and surgeons.

Aged

The ClusNet algorithm and time series prediction.

This paper describes a novel neural network architecture named ClusNet. This network is designed to study the trade-offs between the simplicity of instance-based methods and the accuracy of the more computational intensive learning methods. The features that make this network different from existing learning algorithms are outlined. A simple proof of convergence of the ClusNet algorithm is given. Experimental results showing the convergence of the algorithm on a specific problem is also presented. In this paper, ClusNet is applied to predict the temporal continuation of the Mackey-Glass chaotic time series. A comparison between the results obtained with ClusNet and other neural network algorithms is made. For example, ClusNet requires one-tenth the computing resources of the instance-based local linear method for this application while achieving comparable accuracy in this task. The sensitivity of ClusNet prediction accuracies on specific clustering algorithms is examined for an application. The simplicity and fast convergence of ClusNet makes it ideal as a rapid prototyping tool for applications where on-line learning is required.

Algorithms

On the use of neural network techniques to analyze sleep EEG data. Third communication: robustification of the classificator by applying an algorithm obtained from 9 different networks.

This is the third communication on the use of neural network techniques to classify sleep stages. In our first communication we presented the algorithms and the selection of the feature space and its reduction by using evolutionary and genetic procedures. In our second communication we trained the evolutionary optimized networks on the basis of multiple subject data in context with some smoothing algorithms in analogy of Rechtschaffen and Kales (RK). In this third communication we could demonstrate that the robustness concerning individual specific features of automatically generated sleep profiles could be reasonably improved by an additional modification of the procedure used by SASCIA (Sleep Analysis System to Challenge Innovative Artificial Networks). The outputs of nine different networks that were created by the data of 9 different subjects were used simultaneously for classification. The medians of the values obtained in each output measure were selected for the allocation to a sleep stage. The fitness criteria of 16 automatically generated sleep profiles showed reasonable concordance with the expert profile. Even though in single cases the concordance between conventional RK classifications and automatically generated profiles were a few percentages lower, the average correct classification of the 12 classified subjects improved substantially, thus proving that the classifier is more robust against individuum-specific variability. Despite the fact that the expert generally employs three channels (EEG, EMG and EOG), at least to build up sleep profiles, the SASCIA system was able to produce profiles on the basis of only one EEG channel with 80% concordance and a correlation coefficient of 0.86. The feature selections were performed by genetic algorithms and the topologies of the networks were optimized by evolutionary algorithms. This algorithm will now be used for larger sample forward classification.

Algorithms

A medical algorithm for detecting physical disease in psychiatric patients.

An algorithm for screening psychiatric patients for physical disease was empirically derived from a comprehensive assessment of 509 patients in California's mental health system. The first 343 patients were used to develop the algorithm, and the remaining 166 were used as a test group. Calculations were made for several versions of the algorithm, and the data were compared with the diagnoses listed in the patients' admission mental health record. The algorithmic procedure was more accurate and more cost-effective than the medical evaluation procedures used by the state mental health system. When applied to the test group, the algorithm detected up to 90 percent of patients who had an active, important physical disease at a cost of $156 per patient. The mental health system had detected 58 percent of test-group patients with a disease at a cost of $230 per patient.

Algorithms

Fast scan conversion algorithms for displaying ultrasound sector images.

Two fast algorithms for interpolation of ultrasonic sector-scans were developed. Both algorithms are based on line-drawing algorithms and are free from multiplications in the innermost loops. The algorithms were compared to the following conventional interpolators: 2-D windowed sinc, bicubic spline, 4 x 4 point bicubic spline, bilinear, and nearest neighbor. The most accurate of the two new algorithms is about eight times faster than nearest neighbor interpolation. The quantitative errors are of the same order as the errors of the nearest neighbor interpolator. The subjective image quality is between nearest neighbor and bilinear interpolation.

Algorithms

Uses of the EM algorithm in the analysis of data on HIV/AIDS and other infectious diseases.

The analysis of data on infectious diseases is a natural setting for applications of the EM algorithm, because the infection process is only partially observable. Difficulties in determining the expectation at the E step have been side-stepped by adopting pragmatic models which reflect only part of the mechanism that generates the data. In the HIV/AIDS context the EM algorithm has helped in the reconstruction of the unobserved HIV infection curve, the so-called backprojection problem, as well as in the estimation of the distribution for the incubation period until AIDS, in estimating the infectivity of HIV in partnerships and in estimating parameters describing the decline in the immune system. There is a need for smooth estimates of functions in these applications, suggesting the use of the EMS algorithm or use of the EM algorithm to maximize a penalized likelihood. For data on other infectious diseases the application of the EM algorithm has so far been restricted to analyses of data on the size of outbreaks in a sample of households.

Acquired Immunodeficiency Syndrome