Digital mammography: mixed feature neural network with spectral entropy decision for detection of microcalcifications

Computer-aided detection of breast cancer on mammograms: a swarm intelligence optimized wavelet neural network approach

Breast cancer is the second leading cause of cancer death in women. Accurate early detection can effectively reduce the mortality rate caused by breast cancer. Masses and microcalcification clusters are an important early signs of breast cancer. However, it is often difficult to distinguish abnormalities from normal breast tissues because of their subtle appearance and ambiguous margins. Computer aided diagnosis (CAD) helps the radiologist in detecting the abnormalities in an efficient way. This paper investigates a new classification approach for detection of breast abnormalities in digital mammograms using Particle Swarm Optimized Wavelet Neural Network (PSOWNN). The proposed abnormality detection algorithm is based on extracting Laws Texture Energy Measures from the mammograms and classifying the suspicious regions by applying a pattern classifier. The method is applied to real clinical database of 216 mammograms collected from mammogram screening centers. The detection performance of the CAD system is analyzed using Receiver Operating Characteristic (ROC) curve. This curve indicates the trade-offs between sensitivity and specificity that is available from a diagnostic system, and thus describes the inherent discrimination capacity of the proposed system. The result shows that the area under the ROC curve of the proposed algorithm is 0.96853 with a sensitivity 94.167% of and specificity of 92.105%.

A Comparative Study on Microcalcification Detection Methods with Posterior Probability Estimation based on Gaussian Mixture Models

Automatic detection of microcalcifications in mammograms constitutes a helpful tool in breast cancer diagnosis. Radiologist's confidence level on microcalcification detection would be improved if a probability estimate of its presence could be obtained from computer-aided diagnosis. In this paper we explore detection performance of a simple Bayesian classifier based on Gaussian mixture probability density functions (pdf). Posterior probability of microcalcification presence may be estimated from the probabilistic model. Two model selection algorithms have been tested, one based on the Minimum Message Length criterion and the other on discriminative criteria obtained from the classifier performance. In addition, we propose a complementing model selection algorithm in order to improve the initial system performance obtained with these methods. Simulation results show that our model gets a good compromise between classification performance and probability estimation accuracy.

A novel wavelet-statistics based feature detection system for detecting microcalcifications

This paper describes a wavelet-statistics based feature detection system as applied to microcalcification detection. While a number of researches have been conducted towards microcalcification detection using wavelet analysis and auxiliary information, most of this auxiliary information was obtained from within the spatial domain. In this research, a continuous wavelet transform was used to segment features and compute energy maps of these segmented features. The kurtoses of these features were computed in the wavelet domain. This statistical information together with the energy maps forms the inputs to a rule-based classifier. Physiological information from the spatial domain was used to exclude false-positives. The system was tested using a ROI from the LLNL database. The result is one false-positive within the cluster as classified by the radiologist.

Feature Reduction in Graph Analysis

A common approach to improve medical image classification is to add more features to the classifiers; however, this increases the time required for preprocessing raw data and training the classifiers, and the increase in features is not always beneficial. The number of commonly used features in the literature for training of image feature classifiers is over 50. Existing algorithms for selecting a subset of available features for image analysis fail to adequately eliminate redundant features. This paper presents a new selection algorithm based on graph analysis of interactions among features and between features to classifier decision. A modification of path analysis is done by applying regression analysis, multiple logistic and posterior Bayesian inference in order to eliminate features that provide the same contributions. A database of 113 mammograms from the Mammographic Image Analysis Society was used in the experiments. Tested on two classifiers - ANN and logistic regression - cancer detection accuracy (true positive and false-positive rates) using a 13-feature set selected by our algorithm yielded substantially similar accuracy as using a 26-feature set selected by SFS and results using all 50-features. However, the 13-feature greatly reduced the amount of computation needed.

Analysis of location specific observer performance data: validated extensions of the jackknife free-response (JAFROC) method

RATIONALE AND OBJECTIVES

The free-response paradigm is being increasingly used in the assessment of medical imaging systems. The currently implemented method of analyzing the data, namely jackknife free-response (JAFROC) analysis, has some validation and applicability limitations. The purpose of this work is to address these limitations.

MATERIALS AND METHODS

The general principles of modality evaluation and methodology validation are reviewed. A model for simulating free-response data was used to test the statistical validity of several methods of analyzing the data. The methods differed only in the choice of the figure of merit used to quantify performance. Statistical validity was judged by investigating the behaviors of the methods under null hypothesis conditions of no difference between modalities.

RESULTS

The validity of the different methods of analyzing the data was found to be dependent on the choice of figure of merit. A figure of merit is identified that accommodates abnormal images with multiple (one or more) lesions, detections of which could have different clinical significances (weights). This figure of merit is shown to be statistically valid. An extension of the analysis to single reader interpretations of images from different modalities is also shown to be statistically valid.

CONCLUSION

With the validated enhancements, JAFROC is expected to be of greater utility to users of the free-response method. The extension to single-reader interpretations should be of particular value to developers of image processing algorithms, including developers of computer-aided diagnosis algorithms.

MACHINE LEARNING FOR DETECTION AND DIAGNOSIS OF DISEASE

Machine learning offers a principled approach for developing sophisticated, automatic, and objective algorithms for analysis of high-dimensional and multimodal biomedical data. This review focuses on several advances in the state of the art that have shown promise in improving detection, diagnosis, and therapeutic monitoring of disease. Key in the advancement has been the development of a more in-depth understanding and theoretical analysis of critical issues related to algorithmic construction and learning theory. These include trade-offs for maximizing generalization performance, use of physically realistic constraints, and incorporation of prior knowledge and uncertainty. The review describes recent developments in machine learning, focusing on supervised and unsupervised linear methods and Bayesian inference, which have made significant impacts in the detection and diagnosis of disease in biomedicine. We describe the different methodologies and, for each, provide examples of their application to specific domains in biomedical diagnostics.

Detection of microcalcifications in digital mammograms using wavelet filter and Markov random field model

Clustered microcalcifcations (MCs) in digitized mammograms has been widely recognized as an early sign of breast cancer in women. This work is devoted to developing a computer-aided diagnosis (CAD) system for the detection of MCs in digital mammograms. Such a task actually involves two key issues: detection of suspicious MCs and recognition of true MCs. Accordingly, our approach is divided into two stages. At first, all suspicious MCs are preserved by thresholding a filtered mammogram via a wavelet filter according to the MPV (mean pixel value) of that image. Subsequently, Markov random field parameters based on the Derin-Elliott model are extracted from the neighborhood of every suspicious MCs as the primary texture features. The primary features combined with three auxiliary texture quantities serve as inputs to classifiers for the recognition of true MCs so as to decrease the false positive rate. Both Bayes classifier and back-propagation neural network were used for computer experiments. The data used to test this method were 20 mammograms containing 25 areas of clustered MCs marked by radiologists. Our method can readily remove 1341 false positives out of 1356, namely, 98.9% false positives were removed. Additionally, the sensitivity (true positives rate) is 92%, with only 0.75 false positives per image. From our experiments, we conclude that, with a proper choice of classifier, the texture feature based on Markov random field parameters combined with properly designed auxiliary features extracted from the texture context of the MCs can work outstandingly in the recognition of MCs in digital mammograms.

SVM based system for classification of microcalcifications in digital mammograms

This paper presents a SVM based computer-aided diagnosis (CAD) system for the characterization of clustered microcalcifications in digitized mammograms. First, the region of interest (ROI) in mammogram is enhanced using morphological enhancement (MORPHEN) method. Second, pixels in potential microcalcification regions are segmented out by using edge detection and morphological operations. Third, features based on shape, texture and statistical properties are extracted from each region. Finally, these features are fed to a SVM based classifier for identifying the clusters as either benign or malignant. The SVM with RBF kernel gave A(z)=0.9803 with 97% accuracy and the SVM with polynomial kernel gave A(z)=0.9541 with 95% accuracy.

Image segmentation feature selection and pattern classification for mammographic microcalcifications

Since microcalcifications in X-ray mammograms are the primary indicator of breast cancer, detection of microcalcifications is central to the development of an effective diagnostic system. This paper proposes a two-stage detection procedure. In the first stage, a data driven, closed form mathematical model is used to calculate the location and shape of suspected microcalcifications. When tested on the Nijmegen University Hospital (Netherlands) database, data analysis shows that the proposed model can effectively detect the occurrence of microcalcifications. The proposed mathematical model not only eliminates the need for system training, but also provides information on the borders of suspected microcalcifications for further feature extraction. In the second stage, 61 features are extracted for each suspected microcalcification, representing texture, the spatial domain and the spectral domain. From these features, a sequential forward search (SFS) algorithm selects the classification input vector, which consists of features sensitive only to microcalcifications. Two types of classifiers-a general regression neural network (GRNN) and a support vector machine (SVM)--are applied, and their classification performance is compared using the Az value of the Receiver Operating Characteristic curve. For all 61 features used as input vectors, the test data set yielded Az values of 97.01% for the SVM and 96.00% for the GRNN. With input features selected by SFS, the corresponding Az values were 98.00% for the SVM and 97.80% for the GRNN. The SVM outperformed the GRNN, whether or not the input vectors first underwent SFS feature selection. In both cases, feature selection dramatically reduced the dimension of the input vectors (82% for the SVM and 59% for the GRNN). Moreover, SFS feature selection improved the classification performance, increasing the Az value from 97.01 to 98.00% for the SVM and from 96.00 to 97.80% for the GRNN.

CAD-aided mammogram training

RATIONALE AND OBJECTIVES

Although computer-aided detection (CAD) improves the diagnosis rate of early breast cancer, it has not been well integrated into radiology residency and technician training program. Moreover, CAD performance studies ignore the reader's training and experience with CAD. The purpose of this study was to investigate whether CAD training via a cognitive-perceptual based hypermedia program has effects on the performance studies of mammogram reading.

MATERIALS AND METHODS

Three observers read a pretest set of 80 breast cancer cases (43 negative, 23 benign, and 14 malignant cancer cases). During 4 weeks' training, the observers used a hypermedia instructional program in CAD-aided mammography interpretation. The program includes modules of CAD attention-focusing schemes, CAD procedural knowledge, and case-based simulations in mammography interpretation in consensus with CAD. By the end of the fourth week of the training, they reviewed a posttest set of cases. Data were analyzed with multireader, multicase receiver operating characteristic methods.

RESULTS

Three readers performed better in mammogram reading after training in CAD knowledge than they did before CAD training. CAD training and experience improved the performance of CAD-aided mammography interpretation.

CONCLUSION

A statistically significant difference was found in each observer's performance in CAD-aided mammogram reading before and after the training. CAD training will influence the perception, recognition, and interpretation of early breast cancer and CAD performance studies. Furthermore, the young generation of radiologic professionals can have more training in various attention-focusing features, declarative knowledge, procedural knowledge, and conditional knowledge of CAD and incorporate them into their knowledge base and strategic processing for the purpose of improving the accuracy of mammography interpretation performance.

Spectral phase based medical image processing

RATIONALE AND OBJECTIVES

To exploit the spectral phase characteristics of digital or digitized mammograms for early detection of microcalcifications, shape, and sizes of suspected lesions and to demonstrate its use for training radiologists to discriminate signal features in different spatially varying backgrounds.

MATERIALS AND METHODS

We propose two algorithms: in the phase-only image (POI) reconstruction algorithm the spectral phase of the digital mammogram is extracted from its Fourier spectrum. This is coupled with unit magnitude and inverse Fourier transformed to reconstruct the POI thus enhancing the features of interest such as microcalcifications, shape, and sizes of suspected lesions. In the algorithm for image reconstruction from a priori phase-only information, spectral phase is used to extract signal features of the digital mammogram and then this is combined with spectral magnitude that is extracted and averaged over an ensemble of unrelated digital mammograms.

RESULTS

The results for several digital phantoms and mammograms show that POI reconstructs only high spatial frequencies related to the features such as microcalcifications, shape, and size of masses like cysts and tumors. The results on image reconstruction from a priori phase-only information demonstrate the changes in the visibility of signal features when buried in a wide variety of real world mammogram backgrounds with different densities.

CONCLUSION

The POI can aid radiologists in early detection of microcalcifications, lesions, and other masses of interest in digital mammograms. This reconstruction method is self-adaptive to changes in the background. The image reconstruction from a priori phase-only information can help the radiologist as a training tool in his decision-making process. Preliminary experiments indicate the potential of the techniques for early diagnosis of breast cancer. Clinical studies on these algorithm procedures are in progress for application as a diagnostic CAD tool in digital mammography. These methods can in general be applied to other medical images such as CT and MRI images.

3-D ultrasound texture classification using run difference matrix

Ultrasonography is one of the most useful diagnostic tools for human soft tissue and it is in routine use in nearly all hospitals and many physicians' offices and clinics. However, the diagnosis mostly depends upon the personal experiences of the physicians. Moreover, the surface features and internal architecture of a tumor are not easy to be demonstrated simultaneously using the conventional two-dimensional (2-D) ultrasound. Recently, three-dimensional (3-D) ultrasound has been developed and allows the physician to view the 3-D anatomy. 3-D breast US can provide transverse, longitudinal planes as well as in addition simultaneously the coronal plane. This additional information has been proved to be helpful for clinical applications. In this paper, a new approach of texture classification of 3-D ultrasound breast diagnosis using run difference matrix with neural networks is developed. The test 3-D US image database includes 54 malignant and 161 benign tumors. In the experiments, the area index A(z) under the ROC curve of the proposal 3-D RDM method can achieve 0.9680. The accuracy, sensitivity, specificity, positive predictive value and negative predictive value of the proposed 3-D RDM method is 91.9%(148/161), 88.9%(48/54), 93.5%(100/107), 87.3%(48/55), and 94.3%(100/105), respectively.

Ipsilateral-mammogram computer-aided detection of breast cancer

In this paper, an ipsilateral multi-view computer-aided detection (CAD) scheme is presented for mass detection in digital mammograms by exploiting correlative information of suspicious lesions between mammograms of the same breast. After nonlinear tree-structured filtering for image noise suppression, two wavelet-based methods, directional wavelet transform and tree-structured wavelet transform for image enhancement, and adaptive fuzzy C-means algorithm for segmentation are employed on each mammograms of the same breast, respectively, concurrent analysis is developed for iterative analysis of ipsilateral multi-view mammograms by inter-projective feature matching analysis. A supervised artificial neural network is developed as a classifier, in which the back-propagation algorithm combined with Kalman filtering is used as training algorithm, and free-response receiver operating characteristic analysis is used to test the performance of the developed unilateral CAD system. Performance comparison has been conducted between the final ipsilateral multi-view CAD system and our previously developed single-mammogram-based CAD system. The study results demonstrate the advantages of ipsilateral multi-view CAD method combined with concurrent analysis over current single-view CAD system on false positive reduction.

An improved method of region grouping for microcalcification detection in digital mammograms

A very important issue, namely region grouping, in computer-assisted diagnostic detection of microcalcification clusters (MCC) in digital mammograms is addressed in this work. In the diagnosis of breast cancer, MCC, instead of single and isolated microcalcifications, are considered clinically significant. Grouping individual regions segmented from digital mammograms, therefore, should be a component in an automatic MCC detection system. Actually this component may concern several system modules, such as segmentation, feature extraction, performance estimation aiming at both algorithm optimization and consistent evaluation and ultimately computerized malignancy estimation of calcified lesions. The previous work in the literature used a kernel-based method for region grouping. We proposed a distance-based and dense-to-sparse grouping method. The grouping result should be independent of the size, shape and orientation of real clusters. The application, namely cluster-oriented analysis including an adaptive segmentation method and cluster level feature extraction scheme, is discussed. A preliminary study was performed on a set of 30 full mammograms at 60 microm resolution, containing 40 MCC. The introduction of the cluster level feature extraction and a simple rule-based method reduces false positives from 7.1 to 2.4 per image at the sensitivity of 92.5%. This grouping method provides a solid basis for effective feature extraction-analysis and candidate cluster classification.

Diagnosis of breast tumors with sonographic texture analysis using wavelet transform and neural networks

To increase the ability of ultrasonographic technology for the differential diagnosis of solid breast tumors, we describe a novel computer-aided diagnosis (CADx) system using neural networks for classification of breast tumors. Tumor regions and surrounding tissues are segmented from the physician-located region-of-interest (ROI) images by applying our proposed segmentation algorithm. Cooperating with the segmentation algorithm, three feasible features, including variance contrast, autocorrelation contrast and distribution distortion of wavelet coefficients, were extracted from the ROI images for further classification. A multilayered perceptron (MLP) neural network trained using error back-propagation algorithm with momentum was then used for the differential diagnosis of breast tumors on sonograms. In the experiment, 242 cases (including benign breast tumors from 161 patients and carcinomas from 82 patients) were sampled with k-fold cross-validation (k = 10) to evaluate the performance. The receiver operating characteristic (ROC) area index for the proposed CADx system is 0.9396 +/- 0.0183, the sensitivity is 98.77%, the specificity is 81.37%, the positive predictive value is 72.73% and the negative predictive value is 99.24%. Experimental results showed that our diagnosis model performed very well for breast tumor diagnosis.

An automatic microcalcification detection system based on a hybrid neural network classifier

A hybrid intelligent system is presented for the identification of microcalcification clusters in digital mammograms. The proposed method is based on a three-step procedure: (a) preprocessing and segmentation, (b) regions of interest (ROI) specification, and (c) feature extraction and classification. The reduction of false positive cases is performed using an intelligent system containing two sub-systems: a rule-based and a neural network sub-system. In the first step of the classification schema 22 features are automatically computed which refer either to individual microcalcifications or to groups of them. Further reduction in the number of features is achieved through principal component analysis (PCA). The proposed methodology is tested using the Nijmegen and the Mammographic Image Analysis Society (MIAS) mammographic databases. Results are presented as the receiver operating characteristic (ROC) performance and are quantified by the area under the ROC curve (A(z)). In particular, the A(z) value for the Nijmegen dataset is 0.91 and for the MIAS is 0.92. The detection specificity of the two sets is 1.80 and 1.15 false positive clusters per image, at the sensitivity level higher than 0.90, respectively.

Learning contextual relationships in mammograms using a hierarchical pyramid neural network

This paper describes a pattern recognition architecture, which we term hierarchical pyramid/neural network (HPNN), that learns to exploit image structure at multiple resolutions for detecting clinically significant features in digital/digitized mammograms. The HPNN architecture consists of a hierarchy of neural networks, each network receiving feature inputs at a given scale as well as features constructed by networks lower in the hierarchy. Networks are trained using a novel error function for the supervised learning of image search/detection tasks when the position of the objects to be found is uncertain or ill defined. We have evaluated the HPNN's ability to eliminate false positive (FP) regions of interest generated by the University of Chicago's (UofC) Computer-aided diagnosis (CAD) systems for microcalcification and mass detection. Results show that the HPNN architecture, trained using the uncertain object position (UOP) error function, reduces the FP rate of a mammographic CAD system by approximately 50% without significant loss in sensitivity. Investigation into the types of FPs that the HPNN eliminates suggests that the pattern recognizer is automatically learning and exploiting contextual information. Clinical utility is demonstrated through the evaluation of an integrated system in a clinical reader study. We conclude that the HPNN architecture learns contextual relationships between features at multiple scales and integrates these features for detecting microcalcifications and breast masses.

Data mining with decision trees for diagnosis of breast tumor in medical ultrasonic images

To increase the ability of ultrasonographic (US) technology for the differential diagnosis of solid breast tumors, we describe a novel computer-aided diagnosis (CADx) system using data mining with decision tree for classification of breast tumor to increase the levels of diagnostic confidence and to provide the immediate second opinion for physicians. Cooperating with the texture information extracted from the region of interest (ROI) image, a decision tree model generated from the training data in a top-down, general-to-specific direction with 24 co-variance texture features is used to classify the tumors as benign or malignant. In the experiments, accuracy rates for a experienced physician and the proposed CADx are 86.67% (78/90) and 95.50% (86/90), respectively.

Breast cancer diagnosis using self-organizing map for sonography

The purpose of this study was to evaluate the performance of neural network model self-organizing maps (SOM) in the classification of benign and malignant sonographic breast lesions. A total of 243 breast tumors (82 malignant and 161 benign) were retrospectively evaluated. When a sonogram was performed, the analog video signal was captured to obtain a digitized sonographic image. The physician selected the region of interest in the sonography. An SOM model using 24 autocorrelation texture features classified the tumor as benign or malignant. In the experiment, cases were sampled with k-fold cross-validation (k = 10) to evaluate the performance using receiver operating characteristic (ROC) curves. The ROC area index for the proposed SOM system is 0.9357 +/- 0.0152, the accuracy is 85. 6%, the sensitivity is 97.6%, the specificity is 79.5%, the positive predictive value is 70.8%, and the negative predictive value is 98. 5%. This computer-aided diagnosis system can provide a useful tool and its high negative predictive value could potentially help avert benign biopsies.

A CAD system for the automatic detection of clustered microcalcifications in digitized mammogram films

Clusters of microcalcifications in mammograms are an important early sign of breast cancer. This paper presents a computer-aided diagnosis (CAD) system for the automatic detection of clustered microcalcifications in digitized mammograms. The proposed system consists of two main steps. First, potential microcalcification pixels in the mammograms are segmented out by using mixed features consisting of wavelet features and gray level statistical features, and labeled into potential individual microcalcification objects by their spatial connectivity. Second, individual microcalcifications are detected by using a set of 31 features extracted from the potential individual microcalcification objects. The discriminatory power of these features is analyzed using general regression neural networks via sequential forward and sequential backward selection methods. The classifiers used in these two steps are both multilayer feedforward neural networks. The method is applied to a database of 40 mammograms (Nijmegen database) containing 105 clusters of microcalcifications. A free-response operating characteristics (FROC) curve is used to evaluate the performance. Results show that the proposed system gives quite satisfactory detection performance. In particular, a 90% mean true positive detection rate is achieved at the cost of 0.5 false positive per image when mixed features are used in the first step and 15 features selected by the sequential backward selection method are used in the second step. However, we must be cautious when interpreting the results, since the 20 training samples are also used in the testing step.

Computer-aided diagnosis applied to US of solid breast nodules by using neural networks

PURPOSE

To increase the capabilities of ultrasonographic (US) technology for the differential diagnosis of solid breast tumors by using a neural network.

MATERIALS AND METHODS

One hundred forty US images of solid breast nodules were evaluated. When a sonogram was obtained, an analog video signal from the VCR output of the scanner was transmitted to a notebook computer. A frame grabber connected to the printer port of the computer was then used to digitize the data. The suspicious tumor region on the digitized US image was manually selected. The texture information of the subimage was extracted, and a neural network classifier with autocorrelation features was used to classify the tumor as benign or malignant. In this experiment, 140 pathologically proved tumors (52 malignant and 88 benign tumors) were sampled with k-fold cross-validation (k = 10) to evaluate the performance with receiver operating characteristic curves.

RESULTS

The accuracy of neural networks for classifying malignancies was 95.0% (133 of 140 tumors), the sensitivity was 98% (51 of 52), the specificity was 93% (82 of 88), the positive predictive value was 89% (51 of 57), and the negative predictive value was 99% (82 of 83).

CONCLUSION

This system differentiated solid breast nodules with relatively high accuracy and helped inexperienced operators to avoid misdiagnoses. Because the neural network is trainable, it could be optimized if a larger set of tumor images is supplied.

On the statistical nature of mammograms

We show that digitized mammograms can be considered as evolving from a simple process. A given image results from passing a random input field through a linear filtering operation, where the filter transfer function has a self-similar characteristic. By estimating the functional form of the filter and solving the corresponding filtering equation, the analysis shows that the input field gray value distribution and spectral content can be approximated with parametric methods. The work gives a simple explanation for the variegated image appearance and multimodal character of the gray value distribution common to mammograms. Using the image analysis as a guide, a simulated mammogram is generated that has many statistical characteristics of real mammograms. Additional benefits may follow from understanding the functional form of the filter in conjunction with the input field characteristics that include the approximate parametric description of mammograms, showing the distinction between homogeneously dense and nondense images, and the development of mass analysis methods.

A wavelet-based algorithm for detecting clustered microcalcifications in digital mammograms

A computerized scheme to detect clustered microcalcifications in digital mammograms has been developed. Detection of individual microcalcifications in regions of interest (ROIs) was also performed. The mammograms were previously classified into fatty and dense, according to their breast tissue. The most appropriate wavelet basis and reconstruction levels were selected. To select the wavelet basis, 40 profiles of microcalcifications were decomposed and reconstructed using different types of wavelet functions and different combinations of wavelet coefficients. The symlets with a basis of length 8 were chosen for fatty tissue. For dense tissue, the Daubechies' wavelets with a four-element basis were employed. Two methods to detect individual microcalcifications were evaluated: (a) two-dimensional wavelet transform, and (b) one-dimensional wavelet transform. The second technique yielded the best results, and was used to detect clustered microcalcifications in the complete mammogram. When detecting individual microcalcifications by using two-dimensional wavelet transform we have obtained, for fatty ROIs, a sensitivity of 71.11% at a false positive rate of 7.13 per image. For dense ROIs the sensitivity was 60.76% and the false positive rate, 7.33. The areas (A1) under the AFROC curves were 0.33+/-0.04 and 0.28+/-0.02, respectively. The one-dimensional wavelet transform method yielded 80.44% of sensitivity and 6.43 false positives per image (A1=0.39+/-0.03) for fatty ROIs, and 62.17% and 5.82 false positives per image (A1=0.37+/-0.02) for dense ROIs. For the detection of clusters of microcalcifications in the entire mammogram, the sensitivity was 80.00% with 0.94 false positives per image (A1=0.77+/-0.09) for fatty mammograms, and 72.85% of sensitivity at a false positive detection rate of 2.21 per image (A1=0.64+/-0.07) for dense mammograms. Globally, a sensitivity of 76.43% at a false positive detection rate of 1.57 per image was obtained.

Statistical analysis of functional MRI data in the wavelet domain

The use of the wavelet transform is explored for the detection of differences between brain functional magnetic resonance images (fMRI's) acquired under two different experimental conditions. The method benefits from the fact that a smooth and spatially localized signal can be represented by a small set of localized wavelet coefficients, while the power of white noise is uniformly spread throughout the wavelet space. Hence, a statistical procedure is developed that uses the imposed decomposition orthogonality to locate wavelet-space partitions with large signal-to-noise ratio (SNR), and subsequently restricts the testing for significant wavelet coefficients to these partitions. This results in a higher SNR and a smaller number of statistical tests, yielding a lower detection threshold compared to spatial-domain testing and, thus, a higher detection sensitivity without increasing type I errors. The multiresolution approach of the wavelet method is particularly suited to applications where the signal bandwidth and/or the characteristics of an imaging modality cannot be well specified. The proposed method was applied to compare two different fMRI acquisition modalities. Differences of the respective useful signal bandwidths could be clearly demonstrated; the estimated signal, due to the smoothness of the wavelet representation, yielded more compact regions of neuroactivity than standard spatial-domain testing.

Multiresolution statistical analysis of high-resolution digital mammograms

A multiresolution statistical method for identifying clinically normal tissue in digitized mammograms is used to construct an algorithm for separating normal regions from potentially abnormal regions; that is, small regions that may contain isolated calcifications. This is the initial phase of the development of a general method for the automatic recognition of normal mammograms. The first step is to decompose the image with a wavelet expansion that yields a sum of independent images, each containing different levels of image detail. When calcifications are present, there is strong empirical evidence that only some of the image components are necessary for the purpose of detecting a deviation from normal. The underlying statistic for each of the selected expansion components can be modeled with a simple parametric probability distribution function. This function serves as an instrument for the development of a statistical test that allows for the recognition of normal tissue regions. The distribution function depends on only one parameter, and this parameter itself has an underlying statistical distribution. The values of this parameter define a summary statistic that can be used to set detection error rates. Once the summary statistic is determined, spatial filters that are matched to resolution are applied independently to each selected expansion image. Regions of the image that correlate with the normal statistical model are discarded and regions in disagreement (suspicious areas) are flagged. These results are combined to produce a detection output image consisting only of suspicious areas. This type of detection output is amenable to further processing that may ultimately lead to a fully automated algorithm for the identification of normal mammograms.