Introduction to linear and nonlinear programming

System Identification I

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.

http://www.sparseprocesses.org/sparseprocesses-chap1-2-3.pdf

An Introduction to Sparse Stochastic Processes

Medical activity requires responsibility not only based on knowledge and clinical skills, but also in managing a vast amount of information related to patient care. It is through the appropriate treatment of information that experts can consistently build a strong policy of welfare. The primary goal of decision support systems (DSSs) is to give information to the experts where and when it is needed. These systems provide knowledge, models, and data processing tools to help the experts make better decisions in several situations. They aim to resolve several problems in health services to help patients and their families manage their health care by providing better access to these services. This paper presents a deep review of the state of the art of smart DSSs. It also elaborates on the latest developments in intelligent systems to support decision-makers in health care. The most promising findings brought in literature are analyzed and summarized according to their taxonomy, application area, year of publication, and the approaches and technologies used. Smart systems can assist decision-makers to improve the effectiveness of their decisions using the integration of data mining techniques and model-based systems. It significantly improves the current approaches, enabling the combination of knowledge from experts and knowledge extracted from data.

A Comprehensive Review on Smart Decision Support Systems for Health Care

Ultrasonic tissue characterization has become an area of intensive research. This procedure generally relies on the analysis of the unprocessed echo signal. Because the ultrasound echo is degraded by the non-ideal system point spread function, a deconvolution step could be employed to provide an estimate of the tissue response that could then be exploited for a more accurate characterization. In medical ultrasound, deconvolution is commonly used to increase diagnostic reliability of ultrasound images by improving their contrast and resolution. Most successful algorithms address deconvolution in a maximum a posteriori estimation framework; this typically leads to the solution of l2-norm or l1-norm constrained optimization problems, depending on the choice of the prior distribution. Although these techniques are sufficient to obtain relevant image visual quality improvements, the obtained reflectivity estimates are, however, not appropriate for classification purposes. In this context, we introduce in this paper a maximum a posteriori deconvolution framework expressly derived to improve tissue characterization. The algorithm overcomes limitations associated with standard techniques by using a nonstandard prior model for the tissue response. We present an evaluation of the algorithm performance using both computer simulations and tissue-mimicking phantoms. These studies reveal increased accuracy in the characterization of media with different properties. A comparison with state-of-the-art Wiener and l1-norm deconvolution techniques attests to the superiority of the proposed algorithm.

/pdf/a-restoration-framework-for-ultrasonic-tissue-2g6uaeihom.pdf

A restoration framework for ultrasonic tissue characterization

Computer-aided detection (CAD) schemes are decision making support tools, useful to overcome limitations of problematic clinical procedures. Trans-rectal ultrasound image based CAD would be extremely important to support prostate cancer diagnosis. An effective approach to realize a CAD scheme for this purpose is described in this work, employing a multi-feature kernel classification model based on generalized discriminant analysis. The mutual information of feature value and tissue pathological state is used to select features essential for tissue characterization. System-dependent effects are reduced through predictive deconvolution of the acquired radio-frequency signals. A clinical study, performed on ground truth images from biopsy findings, provides a comparison of the classification model applied before and after deconvolution, showing in the latter case a significant gain in accuracy and area under the receiver operating characteristic curve.

Predictive Deconvolution and Hybrid Feature Selection for Computer-Aided Detection of Prostate Cancer

The problem of estimating continuous-domain autoregressive moving-average processes from sampled data is considered. The proposed approach incorporates the sampling process into the problem formulation while introducing exponential models for both the continuous and the sampled processes. We derive an exact evaluation of the discrete-domain power-spectrum using exponential B-splines and further suggest an estimation approach that is based on digitally filtering the available data. The proposed functional, which is related to Whittle's likelihood function, exhibits several local minima that originate from aliasing. The global minimum, however, corresponds to a maximum-likelihood estimator, regardless of the sampling step. Experimental results indicate that the proposed approach closely follows the Cramer-Rao bound for various aliasing configurations.

/pdf/a-sampling-theory-approach-for-continuous-arma-hdjqzsz5sk.pdf

A Sampling Theory Approach for Continuous ARMA Identification

A Computer-Aided Detection (CAD) scheme to support prostate cancer diagnosis based on ultrasound images is presented. The approach described in this work employs a multifeature classification model. To indentify features highly correlated to the pathologic state of the tissue we use a Feature Selection algorithm based on mutual information. System-dependent effects are removed through predictive deconvolution and this operation results in increasing quality of images and discriminating power of features. A comparison of the classification model applied before and after deconvolution shows a gain in accuracy and area under the ROC curve. The use of deconvolution as preprocessing step in CAD schemes can improve prostate cancer detection.

Computer Aided Detection of prostate cancer based on GDA and predictive deconvolution

We address the problem of identifying continuous-time auto regressive (CAR) models from sampled data. The exponential nature of CAR autocorrelation functions is taken into account by means of exponential B-splines modelling, allowing one to associate the available digital data with a CAR model. A maximum likelihood (ML) estimator is then derived for identifying the optimal parameters; it relies on an exact discretization of the sampled version of the continuous-time model. We provide both time- and frequency-domain interpretations of the proposed estimator, while introducing a weighting function that describes the CAR power spectrum by means of discrete Fourier transform values. We present experimental results demonstrating that the proposed exponential-based ML estimator outperforms currently available polynomial-based methods, while achieving Cramer-Rao lower bound values even for relatively low sampling rates.

/pdf/continuous-time-ar-model-identification-does-sampling-rate-1jv4utho6u.pdf

S. Maggio

Papers

A restoration framework for ultrasonic tissue characterization

Predictive Deconvolution and Hybrid Feature Selection for Computer-Aided Detection of Prostate Cancer

A Sampling Theory Approach for Continuous ARMA Identification

Computer Aided Detection of prostate cancer based on GDA and predictive deconvolution

Continuous-time AR model identification: Does sampling rate really matter?