Probabilistic Solution of Inverse Problems

In this thesis we study the general problem of reconstructing a function, defined on a finite lattice from a set of incomplete, noisy and/or ambiguous observations. The goal of this work is to demonstrate the generality and practical value of a probabilistic (in particular, Bayesian) approach to this problem, particularly in the context of Computer Vision. In this approach, the prior knowledge about the solution is expressed in the form of a Gibbsian probability distribution on the space of all possible functions, so that the reconstruction task is formulated as an estimation problem. Our main contributions are the following: (1) We introduce the use of specific error criteria for the design of the optimal Bayesian estimators for several classes of problems, and propose a general (Monte Carlo) procedure for approximating them. This new approach leads to a substantial improvement over the existing schemes, both regarding the quality of the results (particularly for low signal to noise ratios) and the computational efficiency. (2) We apply the Bayesian appraoch to the solution of several problems, some of which are formulated and solved in these terms for the first time. Specifically, these applications are: teh reconstruction of piecewise constant surfaces from sparse and noisy observationsl; the reconstruction of depth from stereoscopic pairs of images and the formation of perceptual clusters. (3) For each one of these applications, we develop fast, deterministic algorithms that approximate the optimal estimators, and illustrate their performance on both synthetic and real data. (4) We propose a new method, based on the analysis of the residual process, for estimating the parameters of the probabilistic models directly from the noisy observations. This scheme leads to an algorithm, which has no free parameters, for the restoration of piecewise uniform images. (5) We analyze the implementation of the algorithms that we develop in non-conventional hardware, such as massively parallel digital machines, and analog and hybrid networks.

Hypothesis Formation and Evaluation in Medical Diagnosis

This thesis describes some aspects of a computer system for doing medical diagnosis in the specialized field of kidney disease. Because such a system faces the spectre of combinatorial explosion, this discussion concentrates on heuristics which control the number of concurrent hypotheses and efficient "compiled" representations of medical knowledge. In particular, the differential diagnosis of hematuria (blood in the urine) is discussed in detail. A protocol of a simulated doctor/patient interaction is presented and analyzed to determine the crucial structures and processes involved in the diagnosis procedure. The data structure proposed for representing medical information revolves around elementary hypotheses which are activated when certain disposing of findings, activating hypotheses, evaluating hypotheses locally and combining hypotheses globally is examined for its heuristic implications. The thesis attempts to fit the problem of medical diagnosis into the framework of other Artifcial Intelligence problems and paradigms and in particular explores the notions of pure search vs. heuristic methods, linearity and interaction, local vs. global knowledge and the structure of hypotheses within the world of kidney disease.

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.

Workforce Issues in the Greater Boston Health Care Industry: Implications for Work and Family

Interviews with more than 40 leaders in the Boston area health care industry have identified a range of broadly-felt critical problems. This document synthesizes these problems and places them in the context of work and family issues implicit in the organization of health care workplaces. It concludes with questions about possible ways to address such issues. The defining circumstance for the health care industry nationally as well as regionally at present is an extraordinary reorganization, not yet fully negotiated, in the provision and financing of health care. Hoped-for controls on increased costs of medical care – specifically the widespread replacement of indemnity insurance by market-based managed care and business models of operation--have fallen far short of their promise. Pressures to limit expenditures have produced dispiriting conditions for the entire healthcare workforce, from technicians and aides to nurses and physicians. Under such strains, relations between managers and workers providing care are uneasy, ranging from determined efforts to maintain respectful cooperation to adversarial negotiation. Taken together, the interviews identify five key issues affecting a broad cross-section of occupational groups, albeit in different ways: Staffing shortages of various kinds throughout the health care workforce create problems for managers and workers and also for the quality of patient care. Long work hours and inflexible schedules place pressure on virtually every part of the healthcare workforce, including physicians. Degraded and unsupportive working conditions, often the result of workplace "deskilling" and "speed up," undercut previous modes of clinical practice. Lack of opportunities for training and advancement exacerbate workforce problems in an industry where occupational categories and terms of work are in a constant state of flux. Professional and employee voices are insufficiently heard in conditions of rapid institutional reorganization and consolidation. Interviewees describe multiple impacts of these issues--on the operation of health care workplaces, on the well being of the health care workforce, and on the quality of patient care. Also apparent in the interviews, but not clearly named and defined, is the impact of these issues on the ability of workers to attend well to the needs of their families--and the reciprocal impact of workers' family tensions on workplace performance. In other words, the same things that affect patient care also affect families, and vice versa. Some workers describe feeling both guilty about raising their own family issues when their patients' needs are at stake, and resentful about the exploitation of these feelings by administrators making workplace policy. The different institutions making up the health care system have responded to their most pressing issues with a variety of specific stratagems but few that address the complexities connecting relations between work and family. The MIT Workplace Center proposes a collaborative exploration of next steps to probe these complications and to identify possible locations within the health care system for workplace experimentation with outcomes benefiting all parties.