Person:
Vidakovic, Brani

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Author: Ruggeri, Fabrizio ×

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    Wavelet-based 3-D Multifractal Spectrum with Applications in Breast MRI Images
    (Georgia Institute of Technology, 2008) Derado, Gordana ; Lee, Kichun ; Nicolis, Orietta ; Bowman, F. DuBois ; Newell, Mary ; Ruggeri, Fabrizio ; Vidakovic, Brani
    Breast cancer is the second leading cause of death in women in the United States. Breast Magnetic Resonance Imaging (BMRI) is an emerging tool in breast cancer diagnostics and research, and it is becoming routine in clinical practice. Recently, the American Cancer Society (ACS) recommended that women at very high risk of developing breast cancer have annual BMRI exams, in addition to annual mammograms, to increase the likelihood of early detection. (Saslow et al. [20]). Many medical images demonstrate a certain degree of self-similarity over a range of scales. The multifractal spectrum (MFS) summarizes possibly variable degrees of scaling in one dimensional signals and has been widely used in fractal analysis. In this work, we develop a generalization of MFS to three dimensions and use dynamics of the scaling as discriminatory descriptors for the classification of BMRI images to benign and malignant. Methodology we propose was tested using breast MRI images for four anonymous subjects (two cancer, and two cancer-free cases). The dataset consists of BMRI scans obtained on a 1.5T GE Signa MR (with VIBRANT) scanner at Emory University. We demonstrate that meaningful descriptors show potential for classifying inference.
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    Larger Posterior Mode Wavelet Thresholding and Applications
    (Georgia Institute of Technology, 2005-07-01) Cutillo, Luisa ; Jung, Yoon Young ; Ruggeri, Fabrizio ; Vidakovic, Brani
    This paper explores the thresholding rules induced by a variation of the Bayesian MAP principle. The MAP rules are Bayes actions that maximize the posterior. The proposed rule is thresholding and always picks the mode of the posterior larger in absolute value, thus the name LPM. We demonstrate that the introduced shrinkage performs comparably to several popular shrinkage techniques. The exact risk properties of the thresholding rule are explored, as well. We provide extensive simulational analysis and apply the proposed methodology to real-life experimental data coming from the field of Atomic Force Microscopy.
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    Bayesian False Discovery Rate Wavelet Shrinkage: Theory and Applications
    (Georgia Institute of Technology, 2005) Lavrik, Ilya A. ; Jung, Yoon Young ; Ruggeri, Fabrizio ; Vidakovic, Brani
    Statistical inference in the wavelet domain remains vibrant area of contemporary statistical research because desirable properties of wavelet representations and the need of scientific community to process, explore, and summarize massive data sets. Prime examples are biomedical, geophysical, and internet related data. In this paper we develop wavelet shrinkage methodology based on testing multiple hypotheses in the wavelet domain. The shrinkage/thresholding approach by implicit or explicit simultaneous testing of many hypotheses had been considered by many researchers and goes back to the early 1990’s. Even the early proposal, the universal thresholding, could be interpreted as a test of multiple hypotheses in the wavelet domain. We propose two new approaches to wavelet shrinkage/thresholding. (i) In the spirit of Efron and Tibshirani’s recent work on local false discovery rate, we propose the theoretical counterpart Bayesian Local False Discovery Rate, BLFDR, where the underlying model assumes unknown variances. This approach to wavelet shrinkage can also be connected with shrinkage based on Bayes factors. (ii) The second proposal to wavelet shrinkage explored in this paper is Bayesian False Discovery Rate, BaFDR. This proposal is based on ordering of posterior probabilities of hypotheses in Bayesian testing of multiple hypotheses. We demonstrate that both approaches result in competitive shrinkage methods by contrasting them to some popular shrinkage techniques
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    BAMS Method: Theory and Simulations
    (Georgia Institute of Technology, 2001-08) Vidakovic, Brani ; Ruggeri, Fabrizio
    In this paper we address the problem of model-induced wavelet shrinkage. Assuming the independence model according to which the wavelet coefficients are treated individually, we discuss a level-adaptive Bayesian model in the wavelet domain that has two important properties: (i) it realistically describes empirical properties of signals and images in the wavelet domain, and (ii) it results in simple optimal shrinkage rules to be used in fast wavelet denoising. The proposed denoising paradigm BAMS (short for Bayesian Adaptive Multiresolution Shrinker) is illustrated on an array of Donoho and Johnstone's standard test functions and is compared to some standard wavelet-based smoothing methods.
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    Denoising Ozone Concentration Measurements with BAMS Filtering
    (Georgia Institute of Technology, 2001) Katul, Gabriel ; Ruggeri, Fabrizio ; Vidakovic, Brani
    We propose a method for filtering self-similar geophysical signals corrupted by an antoregressive noise using a combination of non-decimated wavelet transform and a Bayesian model. In the application part, we consider separating the instrumentation noise from high frequency ozone concentration measurements sampled in the atmospheric boundary layer. The elicitation of priors needed to specify the statistical model in this application is guided by the well-known Kolmogorov K41-theory, which describes the statistical structure of the high frequency scalar concentration fluctuations.