Biomedical subjects

M A Anastasio

Publications and source records attributed to M A Anastasio.

6 recordsLinked to original sources

PubMed2001

Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution.

The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, we demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.

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PubMed2000

Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography.

Diffraction tomography (DT) is an inversion scheme used to reconstruct the spatially variant refractive-index distribution of a scattering object. We developed computationally efficient algorithms for image reconstruction in three-dimensional (3D) DT. A unique and important aspect of these algorithms is that they involve only a series of two-dimensional reconstructions and thus greatly reduce the prohibitively large computational load required by conventional 3D reconstruction algorithms. We also investigated the noise characteristics of these algorithms and developed strategies that exploit the statistically complementary information inherent in the measured data to achieve a bias-free reduction of the reconstructed image variance. We performed numerical studies that corroborate our theoretical assertions.

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PubMed1999

Multiobjective genetic optimization of diagnostic classifiers with implications for generating receiver operating characteristic curves.

It is well understood that binary classifiers have two implicit objective functions (sensitivity and specificity) describing their performance. Traditional methods of classifier training attempt to combine these two objective functions (or two analogous class performance measures) into one so that conventional scalar optimization techniques can be utilized. This involves incorporating a priori information into the aggregation method so that the resulting performance of the classifier is satisfactory for the task at hand. We have investigated the use of a niched Pareto multiobjective genetic algorithm (GA) for classifier optimization. With niched Pareto GA's, an objective vector is optimized instead of a scalar function, eliminating the need to aggregate classification objective functions. The niched Pareto GA returns a set of optimal solutions that are equivalent in the absence of any information regarding the preferences of the objectives. The a priori knowledge that was used for aggregating the objective functions in conventional classifier training can instead be applied post-optimization to select from one of the series of solutions returned from the multiobjective genetic optimization. We have applied this technique to train a linear classifier and an artificial neural network (ANN), using simulated datasets. The performances of the solutions returned from the multiobjective genetic optimization represent a series of optimal (sensitivity, specificity) pairs, which can be thought of as operating points on a receiver operating characteristic (ROC) curve. All possible ROC curves for a given dataset and classifier are less than or equal to the ROC curve generated by the niched Pareto genetic optimization.

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PubMed1999

Minimal-scan filtered backpropagation algorithms for diffraction tomography.

The filtered backpropagation (FBPP) algorithm, originally developed by Devaney [Ultrason. Imaging 4, 336 (1982)], has been widely used for reconstructing images in diffraction tomography. It is generally known that the FBPP algorithm requires scattered data from a full angular range of 2 pi for exact reconstruction of a generally complex-valued object function. However, we reveal that one needs scattered data only over the angular range 0 < or = phi < or = 3 pi/2 for exact reconstruction of a generally complex-valued object function. Using this insight, we develop and analyze a family of minimal-scan filtered backpropagation (MS-FBPP) algorithms, which, unlike the FBPP algorithm, use scattered data acquired from view angles over the range 0 < or = phi < or = 3 pi/2. We show analytically that these MS-FBPP algorithms are mathematically identical to the FBPP algorithm. We also perform computer simulation studies for validation, demonstration, and comparison of these MS-FBPP algorithms. The numerical results in these simulation studies corroborate our theoretical assertions.

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PubMed1998

Optimization and FROC analysis of rule-based detection schemes using a multiobjective approach.

Computerized detection schemes have the potential of increasing diagnostic accuracy in medical imaging by alerting radiologists to lesions that they initially overlooked. These schemes typically employ multiple parameters such as threshold values or filter weights to arrive at a detection decision. In order for the system to have high performance, the values of these parameters need to be set optimally. Conventional optimization techniques are designed to optimize a scalar objective function. The task of optimizing the performance of a computerized detection scheme, however, is clearly a multiobjective problem: we wish to simultaneously improve the sensitivity and false-positive rate of the system. In this work we investigate a multiobjective approach to optimizing computerized rule-based detection schemes. In a multiobjective optimization, multiple objectives are simultaneously optimized, with the objective now being a vector-valued function. The multiobjective optimization problem admits a set of solutions, known as the Pareto-optimal set, which are equivalent in the absence of any information regarding the preferences of the objectives. The performances of the Pareto-optimal solutions can be interpreted as operating points on an optimal free-response receiver operating characteristic (FROC) curve, greater than or equal to the points on any possible FROC curve for a given dataset and detection scheme. It is demonstrated that generating FROC curves in this manner eliminates several known problems with conventional FROC curve generation techniques for rule-based detection schemes. We employ the multiobjective approach to optimize a rule-based scheme for clustered microcalcification detection that has been developed in our laboratory.

Algorithms↗

PubMed1998

A genetic algorithm-based method for optimizing the performance of a computer-aided diagnosis scheme for detection of clustered microcalcifications in mammograms.

Computer-aided diagnosis (CAD) schemes have the potential of substantially increasing diagnostic accuracy in mammography by providing the advantages of having a second reader. Our laboratory has developed a CAD scheme for detecting clustered microcalcifications in digital mammograms that is being tested clinically at the University of Chicago Hospitals. Our CAD scheme contains a large number of parameters such as filter weights, threshold levels, and region of interest (ROI) sizes. The choice of these parameter values determines the overall performance of the system and thus must be carefully set. Unfortunately, when the number of parameters becomes large, it is very difficult to obtain the optimal performance, especially when the values of the parameters are correlated with each other. In this study, we address the problem of identifying the optimal overall performance by developing an automated method for the determination of the parameter values that maximize the performance of a mammographic CAD scheme. Our method utilizes a genetic algorithm to search through the possible parameter values, and provides the set of parameters that minimize a cost function which measures the performance of the scheme. Using a database of 89 digitized mammograms, our method demonstrated that the sensitivity of our CAD scheme can be increased from 80% to 87% at a false positive rate of 1.0 per image. We estimate the average performance of our CAD scheme on unknown cases by performing jackknife tests; this was previously not feasible when the parameters of the CAD scheme were determined in a nonautomated manner.

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