Mark A. Anastasio

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.

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: the authors wish to simultaneously improve the sensitivity and false-positive rate of the system. In this work the authors 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 (FROG) curve, greater than or equal to the points on any possible FROG curve for a given dataset and detection scheme. It is demonstrated that generating FROG curves in this manner eliminates several known problems with conventional FROG curve generation techniques for rule-based detection schemes. The authors employ the multiobjective approach to optimize a rule-based scheme for clustered mirocalcification detection that has been developed in the authors laboratory.

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.

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.

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

The authors analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, they 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, the authors demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.

Noise propagation in diffraction tomography: comparison of conventional algorithms with a new reconstruction algorithm

In ultrasonic diffraction tomography, ultrasonic waves are used to probe the object of interest at various angles. The incident waves scatter when encountering inhomogeneities, unlike conventional X-ray CT. Theoretically, when the scattering inhomogeneities are considered weak, the scattering object can be reconstructed by algorithms developed from a generalized central slice theorem. The authors develop a hybrid algorithm for reconstruction of a scattering object by transforming the scattered data into a conventional X-ray-like sinogram thus allowing standard X-ray reconstruction algorithms, such as filtered back-projection, to be applied. The authors investigate the statistical properties of the filtered back-propagation, direct Fourier, and newly proposed hybrid reconstruction algorithms by performing analytical as well as numerical studies.

Multiobjective genetic optimization of diagnostic classifiers used in the computerized detection of mass lesions in mammography

We have recently proposed and developed a multiobjective approach to training classification systems. In this approach, the objectives, i.e., the sensitivity and specificity, of a classifier are simultaneously optimized, resulting in a series of solutions that are equivalent in the absence of any a priori knowledge regarding the relative merits of the two objectives. These solutions form a receiver operating characteristic (ROC) curve that is, theoretically, the best possible ROC curve that can be obtained using the given classifier and given training dataset. We have applied this technique to the optimization of classifiers for the computerized detection of mass lesions in digitized mammograms. Comparisons will be made between the results obtained using the multiobjective approach and results obtained using more conventional approaches. We employed a database of 60 consecutive, non-palpable mass lesion cases. Features relating to the geometry, intensity, and gradients of the images were calculated for each visible lesion and for many false detections. Using a conventionally trained linear classifier we were able to achieve an Az of 0.84 while the multiobjective approach to training a linear classifier yielded an Az of 0.87 in the task of distinguishing between true lesions and false detections. Using a multiobjective approach to train a rule-based classifier with 5 thresholding rules resulted in an Az of 0.88 in the task of distinguishing between true lesions and false detections.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A new reconstruction approach for reflection mode diffraction tomography

Reflection mode diffraction tomography (RM DT) is an inversion scheme used to reconstruct the acoustical refractive index distribution of a scattering object. In this work, we reveal the existence of statistically complementary information inherent in the backscattered data and propose reconstruction algorithms that exploit this information for achieving a bias-free reduction of image variance in RM DT images. Such a reduction of image variance can potentially enhance the detectability of subtle image features when the signal-to-noise ratio of the measured scattered data is low in RM DT. The proposed reconstruction algorithms are mathematically identical, but they propagate noise and numerical errors differently. We investigate theoretically, and validate numerically, the noise properties of images reconstructed using one of the reconstruction algorithms for several different multifrequency sources and uncorrelated data noise.

Full- and minimal-scan reconstruction algorithms for fan-beam diffraction tomography

Diffraction tomography (DT) is a tomographic inversion technique that reconstructs the spatially variant refractive-index distribution of a scattering object. In fan-beam DT, the interrogating radiation is not a plane wave but rather a cylindrical wave front emanating from a line source located a finite distance from the scattering object. We reveal and examine the redundant information that is inherent in the fan-beam DT data function. Such redundant information can be exploited to reduce the reconstructed image variance or, alternatively, to reduce the angular scanning requirements of the fan-beam DT experiment. We develop novel filtered backpropagation and estimate-combination reconstruction algorithms for full-scan and minimal-scan fan-beam DT. The full-scan algorithms utilize measurements taken over the angular range 0 </= phi </= 2pi, whereas the minimal-scan reconstruction algorithms utilize only measurements taken over the angular range 0 </= phi </= phi(min), where pi </= phi(min) </= 3pi/2 is a specified function that describes the fan-beam geometry. We demonstrate that the full- and minimal-scan fan-beam algorithms are mathematically equivalent. An implementation of the algorithms and numerical results obtained with noiseless and noisy simulated data are presented.

Fourier-based optimal recovery method for antialiasing interpolation

We propose a Fourier-based interpolation method designed to suppress the oscillatory artifacts that occur when interpolating an un- dersampled function. In the proposed method, we formulate the problem as an optimal recovery problem incorporating a priori knowledge of the aliasing. Our computer simulations demonstrate that the proposed method can produce good interpolation results even when the functions are severely undersampled.