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PubMed2002

Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure.

We review the derivation of the fast orthogonal search algorithm, first proposed by Korenberg, with emphasis on its application to the problem of estimating coefficient matrices of vector autoregressive models. New aspects of the algorithm not previously considered are examined. One of these is the application of the algorithm to estimate coefficient matrices of a vector autoregressive process with time-varying coefficients when multiple realizations of the said process are available. Computer simulations were also performed to characterize the statistical properties of the estimates. The results show that even for shorter time series the algorithm works well and obtains good estimates of the time-varying parameters. Statistical characterization indicates that the standard deviation of the estimates decreases as 1 square root N (N being the length of the time series), a typical behavior of least-squares estimators. Another key aspect of the approach, which has previously been considered, is its direct extension to the parameter estimation of vector nonlinear autoregressive models. Nonlinear terms can be added to the model and the same algorithm can be applied to effectively estimate their associated parameters. Using chaotic time series generated from the Lorenz equations, the algorithm produces a model that captures the nonlinear structure of the data and exhibits the same chaotic attractor as that of the original system.

Algorithms↗

PubMed2003

The merits of a parallel genetic algorithm in solving hard optimization problems.

A parallel genetic algorithm for optimization is outlined, and its performance on both mathematical and biomechanical optimization problems is compared to a sequential quadratic programming algorithm, a downhill simplex algorithm and a simulated annealing algorithm. When high-dimensional non-smooth or discontinuous problems with numerous local optima are considered, only the simulated annealing and the genetic algorithm, which are both characterized by a weak search heuristic, are successful in finding the optimal region in parameter space. The key advantage of the genetic algorithm is that it can easily be parallelized at negligible overhead.

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PubMed2000

Evaluation of an algorithm for the assessment of the MTF using an edge method.

An algorithm to calculate the presampling modulation transfer function (MTF) of an imaging system from an angled edge image has its own inherent transfer function. Factors such as the angle of the sampling aperture to the edge, registration of edge function profiles using the determined edge angle, differentiation, smoothing, and folding all combine to produce the frequency response of the algorithm. In this work, the profile registration transfer function accounting for an error in the determined edge angle has been derived. This has been incorporated with other, previously reported, algorithm component transfer functions to fully characterize the MTF calculation algorithm. When registering profiles, small errors in the edge angle determination were found to result in large errors in the MTF, as the misalignment errors increase with the number of profiles. For example, registering 50 profiles a 0.07 degree error in a 7 degree edge angle (1% error) produces a 36% error in the MTF at the system cutoff frequency f=f(c) when profiles are oversampled at a frequency f(s)=8f(c)(f(c) is defined as the maximum frequency reproducible without aliasing when sampling at the limiting system Nyquist frequency f(s) = 2f(c)). These results highlight the importance of quantifying the transfer function of the algorithm used to determine an imaging system modulation transfer function. The MTF calculation algorithm and the transfer function analysis have been incorporated into a Windows-based software program to be made available for general use.

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PubMed2001

A cone beam filtered backprojection (CB-FBP) reconstruction algorithm for a circle-plus-two-arc orbit.

The circle-plus-arc orbit possesses advantages over other "circle-plus" orbits for the application of x-ray cone beam (CB) volume CT in image-guided interventional procedures requiring intraoperative imaging, in which movement of the patient table is to be avoided. A CB circle-plus-two-arc orbit satisfying the data sufficiency condition and a filtered backprojection (FBP) algorithm to reconstruct longitudinally unbounded objects is presented here. In the circle suborbit, the algorithm employs Feldkamp's formula and another FBP implementation. In the arc suborbits, an FBP solution is obtained originating from Grangeat's formula, and the reconstruction computation is significantly reduced using a window function to exclude redundancy in Radon domain. The performance of the algorithm has been thoroughly evaluated through computer-simulated phantoms and preliminarily evaluated through experimental data, revealing that the algorithm can regionally reconstruct longitudinally unbounded objects exactly and efficiently, is insensitive to the variation of the angle sampling interval along the arc suborbits, and is robust over practical x-ray quantum noise. The algorithm's merits include: only 1D filtering is implemented even in a 3D reconstruction, only separable 2D interpolation is required to accomplish the CB backprojection, and the algorithm structure is appropriate for parallel computation.

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PubMed2001

An algorithm for automatic, computed-tomography-based source localization after prostate implant.

Permanent implant of the prostate using I-125 and Pd-103 seeds is a popular choice of treatment for early-stage prostate cancer in the United States. Evaluation of the quality of the implant is best based on the calculated dose distribution from postimplant computed tomography (CT) images. This task, however, has been time-consuming and inaccurate. We have developed an algorithm for automatic source localization from postimplant CT images. The only requirement of this algorithm is knowledge of the number of seeds present in the prostate, thus minimizing the need for human intervention. The algorithm processes volumetric CT data from the patient, and pixels of higher CT numbers are categorized into classes of definite and potential source pixels. A multithresholding technique is used to further determine the number of seeds and their precise locations in the CT volume data. A graphic user interface was developed to facilitate operator review of and intervention in the calculation and the results of the algorithm. This algorithm was tested on two phantoms containing nonradioactive seeds, one with 20 seeds in discrete locations and another with 100 seeds with small distances between seeds. The tests showed that the algorithm was able to identify the seed locations to within 1 mm of their physical locations for discrete seed locations. It was further able to separate seeds at close proximity to each other while maintaining an average seed localization error of less than 2 mm, with no operator intervention required.

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PubMed2002

Energy-loss straggling algorithms for Monte Carlo electron transport.

A new method is presented for the modeling of the electron (positron) energy-loss straggling in Monte Carlo transport simulations. First, the Vavilov energy-loss distribution is calculated for electrons and positrons using the Møller and Bhabha collision cross-sections, respectively. The maximum energy transfer in a single collision (E(S)) is considered as variable. Binding effects from low-energy collisions are modeled using the Blunck and Westphal model. Secondly, new algorithms are developed to fit the Vavilov distribution. These algorithms are based on the first three moments of the energy-loss distribution. They are suitable for rapid random sampling of the energy loss. The new algorithms are validated against the Vavilov distribution for electrons and positrons, water and lead, kinetic energy E0 of 0.1, 1, and 10 MeV and several values of E(S) (10, 50, 100, and 200 keV). The developed algorithms are incorporated in a new version of the GEPTS Monte Carlo code called GEPTS(III). Collisions involving energy transfers larger than E(S) are simulated individually and the energy loss due to soft collisions (energy transfers less than E(S)) is sampled using the new algorithms. The straggling effect is therefore taken into account whatever the chosen E(S) value. GEPTS(III) and EGSnrc are used for the calculation of (1) electron dose distributions in water and (2) energy spectra for electrons passing through water and tungsten slabs. Electron beams of 1, 2, 5, 10, and 20 MeV along with varying E(S) values are considered. Electron dose distributions in water are rather insensitive to the soft collision straggling. The use of the new algorithms results in a slight gain in computation time when relatively large E(S) values are used (e.g., E(S) = 1 MeV for 10 MeV electrons). However, the calculation of electron energy spectra is very sensitive to the soft collision straggling. GEPTS(III) (E(S) = 200 keV) is about 5 and 11 times faster than EGSnrc (E(S) = 1 keV) for the case of 2 and 20 MeV electrons passing through 0.025 and 0.25 cm water slabs, respectively. Contrary to EGSnrc, GEPTS(III) accounts for the energy-spectrum broadening due to the binding effects. The resulting differences between the two codes are significant for 5 and 10 MeV electrons passing through a 0.01 cm tungsten slab. Gains in GEPTS(III) computation times (approximately a factor 5) are also observed for tungsten. In short, GEPTS(III) provides significant advantages (rapidity and accuracy) for electron transport simulations, especially those dealing with energy-spectrum calculations, as encountered in clinical electron beam modeling studies. In other respects, the developed approach is more suitable than class-II codes for the use of accurate electron cross sections (numerical data) at low energy (<100 keV).

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PubMed2003

Automated detection of lung nodules in CT scans: effect of image reconstruction algorithm.

We have investigated the effect of computed tomography (CT) image reconstruction algorithm on the performance of our automated lung nodule detection method. Commercial CT scanners offer a choice of several algorithms for the reconstruction of projection data into transaxial images. Different algorithms produce images with substantially different properties that are apparent not only quantitatively, but also through visual assessment. During some clinical thoracic CT examinations, patient scans are reconstructed with multiple reconstruction algorithms. Thirty-eight such cases were collected to form two databases: one with patient projection data reconstructed with the "standard" reconstruction algorithm and the other with the same patient projection data reconstructed with the "lung" reconstruction algorithm. The automated nodule detection method was applied to both databases. This method is based on gray-level-thresholding techniques to segment the lung regions from each CT section to create a segmented lung volume. Further gray-level-thresholding techniques are applied within the segmented lung volume to identify a set of lung nodule candidates. Rule-based and linear discriminant classifiers are used to differentiate between lung nodule candidates that correspond to actual nodules and those that correspond to non-nodules. The automated method that was applied to both databases was exactly the same, except that the classifiers were calibrated separately for each database. For comparison, the classifier then was trained on one database and tested independently on the other database. When applied to the databases in this manner, the automated method demonstrated overall a similar level of performance, indicating an encouraging degree of robustness.

Adult↗

PubMed2003

A Grangeat-type half-scan algorithm for cone-beam CT.

Modern CT and micro-CT scanners are rapidly moving from fan-beam toward cone-beam geometry. Half-scan CT algorithms are advantageous in terms of temporal resolution, and widely used in fan-beam and cone-beam geometry. While existing half-scan algorithms for cone-beam CT are in the Feldkamp framework, in this paper we compensate missing data explicitly in the Grangeat framework, and formulate a half-scan algorithm in the circular scanning case. The half-scan spans 180 degrees plus two cone angles that guarantee sufficient data for reconstruction of the midplane defined by the source trajectory. The smooth half-scan weighting functions are designed for the suppression of data inconsistency. Numerical simulation results are reported for verification of our formulas and programs. This Grangeat-type half-scan algorithm produces excellent image quality, without off-mid-plane artifacts associated with Feldkamp-type half-scan algorithms. The Grangeat-type half-scan algorithm seems promising for quantitative and dynamic biomedical applications of CT and micro-CT.

Algorithms↗

PubMedDate not supplied

A comparison of the speeds of three convolution algorithms.

The speeds of three computer algorithms suitable for use in three-dimensional radiotherapy planning codes were compared. Two of the algorithms are based on ray-tracing methods, the first algorithm uses a fast ray-tracing procedure directly and the second employs a table lookup procedure; the table was originally calculated by ray tracing. The third algorithm was a convolution procedure using the fast Fourier transform. Benchmark programs were written to compare the fundamental running speeds of the three algorithms operating on three-dimensional arrays of various sizes. The convolution procedure employing the three-dimensional fast Fourier transform had the shortest running times on a VAX/750 (Digital Equipment Corp.) computer. We concluded that this algorithm holds significant potential for practical three-dimensional dose calculations.

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PubMed1994

A cone beam SPECT reconstruction algorithm with a displaced center of rotation.

A filtered backprojection (FBP) algorithm is derived based on Feldkamp's FBP algorithm for a cone beam geometry that has a displaced center of rotation. In cone beam single photon emission computed tomography (CB-SPECT) the center of rotation displacement can degrade the reconstructed images. The center of rotation displacement of interest is mechanical shift, which is the displacement of the midplane of the cone beam collimator off the rotation center. Mechanical shift is characterized by two orthogonal components: the shift of the midplane of the cone beam collimator along the direction of the axis of rotation, and the distance between the midline of the cone beam collimator and the axis of rotation. This new algorithm corrects mechanical shift directly by incorporating mechanical shift into the algorithm. This new algorithm is evaluated using both Monte Carlo simulated data and experimentally acquired data. The results demonstrate that this algorithm is able to correct for blurring and the "doughnut" type artifacts caused by system mechanical shift and improve the image resolution.

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PubMed1998

Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments.

The "stop and shoot" method of producing intensity modulation using combinations of static multileaf collimator (MLC) segments has a number of advantages including precise dose delivery, easy verification, and general availability. However, due to the potential limitation of prolonged treatment time, it is essential to keep the number of required segments to a reasonable number. We propose an algorithm to minimize the number of segments for an intensity modulated field. In this algorithm, the sequence of delivery intensity is proposed to be a series of powers of 2, depending on the maximum intensity level in the matrix. The MLC leaf position sequence is designed directly on the two-dimensional intensity matrix to irradiate the largest possible area in each segment. The algorithm can be applied directly to MLC systems with different motion constraints. This algorithm has been evaluated by generating 1000 random 15 x 15 cm intensity matrices, each having from 3 to 16 intensity levels. Five clinical intensity modulated fields generated from the NOMOS CORVUS planning system for a complex clinical head and neck case were also tested with this and two other algorithms. The results of both the statistical and clinical studies showed that for all the intensity matrices tested, the proposed algorithm results in the smallest number of segments with a moderately increased monitor units. Thus it is well-suited for use in static MLC intensity modulation beam delivery. For MLC systems with interleaf motion constraint, we prove mathematically that this constraint reduces the tongue and groove effect at the expense of an increase of 25% in the number of segments.

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PubMed1998

New classes of helical weighting algorithms with applications to fast CT reconstruction.

The focus of this paper is on CT helical weighting algorithms using one source rotation, or 2 pi, worth of projection data. Currently known 2 pi helical weighting algorithms include a fan-angle dependency, and do not lend themselves to fast reconstruction, for two reasons. First, it can be shown that the weight distributions present a line of discontinuity across the sinogram (projection space), which defines two separate sinogram regions. Second, the expressions for the weighting functions differ for those two regions. Accordingly, reconstruction of P different image planes (all using a given projection) requires P weightings and filterings of that projection. In this paper, it is shown that, by first generalizing the concept of the interpolation/extrapolation function used in the weighting, to the concept of distance function, and second by selecting particular classes of such distance functions, the discontinuity across the sinogram can be eliminated. By imposing specific sufficient conditions on such distance functions, single analytical expressions across the entire 2 pi sinogram are obtained. Decomposition of these particular "single" distance functions leads to two-filtering reconstruction algorithms, for which a given projection needs to be filtered only two times for an arbitrary number P of reconstruction planes. Finally, another generalization of the concept of helical weighting leads to one-filtering weight functions that depend only on the sum of the projection--and fan angles. Accordingly, after rebinning the fan-beam projections to parallel projections, the corresponding 2 pi helical weighting algorithms do not include a dependency over the ray parameter. Equivalently, for these algorithms, weighting commutes with filtering, and reconstruction of an arbitrary number P of image planes requires only one filtering per projection. These algorithms are shown to be consistent with the hypothesis of a linear z variation of the projections.

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PubMed2000

Photon scatter in portal images: accuracy of a fluence based pencil beam superposition algorithm.

The accuracy of a pencil beam algorithm to predict scattered photon fluence into portal imaging systems was studied. A data base of pencil beam kernels describing scattered photon fluence behind homogeneous water slabs (1-50 cm thick) at various air gap distances (0-100 cm) was generated using the EGS Monte Carlo code. Scatter kernels were partitioned according to particle history: singly-scattered, multiply-scattered, and bremsstrahlung and positron annihilation photons. Mean energy and mean angle with respect to the incident photon pencil beam were also scored. This data allows fluence, mean energy, and mean angular data for each history type to be predicted using the pencil beam algorithm. Pencil beam algorithm predictions for 6 and 24 MV incident photon beams were compared against full Monte Carlo simulations for several inhomogeneous phantoms, including approximations to a lateral neck, and a mediastinum treatment. The accuracy of predicted scattered photon fluence, mean energy, and mean angle was investigated as a function of air gap, field size, photon history, incident beam resolution, and phantom geometry. Maximum errors in mean energies were 0.65 and 0.25 MeV for the higher and lower energy spectra, respectively, and 15 degrees for mean angles. The ability of the pencil beam algorithm to predict scatter fluence decreases with decreasing air gap, with the largest error for each phantom occurring at the exit surface. The maximum predictive error was found to be 6.9% with respect to the total fluence on the central axis. By maintaining even a small air gap (approximately 10 cm), the error in predicted scatter fluence may be kept under 3% for the phantoms and beam energies studied here. It is concluded that this pencil beam algorithm is sufficiently accurate (using International Commission on Radiation Units and Measurements Report No. 24 guidelines for absorbed dose) over the majority of clinically relevant air gaps, for further investigation in a portal dose prediction algorithm.

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PubMed1988

Synthesizing a color algorithm from examples.

A lightness algorithm that separates surface reflectance from illumination in a Mondrian world is synthesized automatically from a set of examples, which consist of pairs of input (intensity signal) and desired output (surface reflectance) images. The algorithm, which resembles a new lightness algorithm recently proposed by Land, is approximately equivalent to filtering the image through a center-surround receptive field in individual chromatic channels. The synthesizing technique, optimal linear estimation, requires only one assumption, that the operator that transforms input into output is linear. This assumption is true for a certain class of early vision algorithms that may therefore be synthesized in a similar way from examples. Other methods of synthesizing algorithms from examples, or "learning," such as back-propagation, do not yield a significantly better lightness algorithm.

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PubMed1996

Clinical algorithms for the screening of Chlamydia trachomatis in Turkish women.

OBJECTIVE: To test the diagnostic validity of clinical algorithms for the detection of Chlamydia trachomatis in an urban population of married women in Turkey. DESIGN: Cross-sectional population-based survey. SUBJECTS: A systematic sample of 867 women who reported the use of contraceptive methods. MAIN OUTCOME MEASURES: Sensitivity, specificity and positive predictive value of clinical algorithms for the diagnosis of C trachomatis. RESULTS: C trachomatis was diagnosed in 4.89% of the women. The WHO algorithm for use in settings where no vaginal examination could be performed had a sensitivity of 9% and a specificity of 96%. The corresponding figures for the WHO algorithm incorporating the findings of a speculum examination were 47% and 56% respectively. Algorithms incorporating symptoms or signs other than those suggested by the WHO did not yield satisfactory standards of validity. CONCLUSIONS: The findings of this study do not support the widespread introduction of the use of clinical decision models for screening of women for chlamydia infection in primary health care settings such as family planning or antenatal clinics. The large number of false positive results with the use of the clinical algorithms tested in this study would cause unnecessary costs to the health system and unnecessary interventions to the women treated.

Adult↗

PubMed2000

Validity of the vaginal discharge algorithm among pregnant and non-pregnant women in Nairobi, Kenya.

OBJECTIVE: To evaluate the validity of different algorithms for the diagnosis of gonococcal and chlamydial infections among pregnant and non-pregnant women consulting health services for vaginal discharge in Nairobi, Kenya. METHODS: Cross sectional study among 621 women with complaints of vaginal discharge in three city council clinics between April and August 1997. Women were interviewed and examined for symptoms and signs of sexually transmitted infections (STIs). Specimens were obtained for laboratory diagnosis of genital infections, HIV, and syphilis. The data were used to evaluate the Kenyan flow chart as well as several other generated algorithms. RESULTS: The mean age was 24 years and 334 (54%) were pregnant. The overall prevalence rates were: 50% candidiasis, 23% trichomoniasis, 9% bacterial vaginosis, 7% gonorrhoea, 9% chlamydia, 7% syphilis, and 22% HIV. In non-pregnant women, gonococcal and chlamydial infection was significantly associated with (1) demographic and behavioural risk markers such as being single, younger than 20 years, multiple sex partners in the previous 3 months; (2) symptom fever; and (3) signs including presence of yellow or bloody vaginal discharge, cervical mucopus, cervical erythema, and friability. Among pregnant women only young age, dysuria, and fever were significantly associated with cervical infection. However, none of these variables was either sensitive or specific enough for the diagnosis of cervical infection. Several algorithms were generated and applied to the study data. The algorithm including risk markers performed slightly better than the current Kenyan algorithm. CONCLUSION: STIs form a major problem in the Nairobi area and should be addressed accordingly. None of the tested algorithms for the treatment of vaginal discharge would constitute a marked improvement of the existing flow chart. Hence, better detection tools for the specific aetiology of vaginal discharge are urgently needed.

Adult↗

PubMed2000

Automating parallel implementation of neural learning algorithms.

Neural learning algorithms generally involve a number of identical processing units, which are fully or partially connected, and involve an update function, such as a ramp, a sigmoid or a Gaussian function for instance. Some variations also exist, where units can be heterogeneous, or where an alternative update technique is employed, such as a pulse stream generator. Associated with connections are numerical values that must be adjusted using a learning rule, and and dictated by parameters that are learning rule specific, such as momentum, a learning rate, a temperature, amongst others. Usually, neural learning algorithms involve local updates, and a global interaction between units is often discouraged, except in instances where units are fully connected, or involve synchronous updates. In all of these instances, concurrency within a neural algorithm cannot be fully exploited without a suitable implementation strategy. A design scheme is described for translating a neural learning algorithm from inception to implementation on a parallel machine using PVM or MPI libraries, or onto programmable logic such as FPGAs. A designer must first describe the algorithm using a specialised Neural Language, from which a Petri net (PN) model is constructed automatically for verification, and building a performance model. The PN model can be used to study issues such as synchronisation points, resource sharing and concurrency within a learning rule. Specialised constructs are provided to enable a designer to express various aspects of a learning rule, such as the number and connectivity of neural nodes, the interconnection strategies, and information flows required by the learning algorithm. A scheduling and mapping strategy is then used to translate this PN model onto a multiprocessor template. We demonstrate our technique using a Kohonen and backpropagation learning rules, implemented on a loosely coupled workstation cluster, and a dedicated parallel machine, with PVM libraries.

Algorithms↗

PubMed1995

Training neural networks by means of genetic algorithms working on very long chromosomes.

In the neural network/genetic algorithm community, rather limited success in the training of neural networks by genetic algorithms has been reported. In a paper by Whitley et al. (1991), he claims that, due to "the multiple representations problem", genetic algorithms will not effectively be able to train multilayer perceptrons, whose chromosomal representation of its weights exceeds 300 bits. In the following paper, by use of a "real-life problem", known to be non-trivial, and by a comparison with "classic" neural net training methods, I will try to show, that the modest success of applying genetic algorithms to the training of perceptrons, is caused not so much by the "multiple representations problems" as by the fact that problem-specific knowledge available is often ignored, thus making the problem unnecessarily tough for the genetic algorithm to solve. Special success is obtained by the use of a new fitness function, which takes into account the fact that the search performed by a genetic algorithm is holistic, and not local as is usually the case when perceptrons are trained by traditional methods.

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