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.

Inverse Metabolic Engineering of Synechocystis PCC 6803 for Improved Growth Rate and Poly-3-hydroxybutyrate Production

Synechocystis PCC 6803 is a photosynthetic bacterium that has the potential to make bioproducts from carbon dioxide and light. Biochemical production from photosynthetic organisms is attractive because it replaces the typical bioprocessing steps of crop growth, milling, and fermentation, with a one-step photosynthetic process. However, low yields and slow growth rates limit the economic potential of such endeavors. Rational metabolic engineering methods are hindered by limited cellular knowledge and inadequate models of Synechocystis. Instead, inverse metabolic engineering, a scheme based on combinatorial gene searches which does not require detailed cellular models, but can exploit sequence data and existing molecular biological techniques, was used to find genes that (1) improve the production of the biopolymer poly-3-hydroxybutyrate (PHB) and (2) increase the growth rate. A fluorescence activated cell sorting assay was developed to screen for high PHB producing clones. Separately, serial sub-culturing was used to select clones that improve growth rate. Novel gene knock-outs were identified that increase PHB production and others that increase the specific growth rate. These improvements make this system more attractive for industrial use and demonstrate the power of inverse metabolic engineering to identify novel phenotype-associated genes in poorly understood systems.