Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM

We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)

Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM

We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)

Distributed multi-agent Gaussian regression via finite-dimensional approximations

We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with limited computational and communication capabilities and to gather $M$ noisy measurements in total on input locations independently drawn from a known common probability density. The optimal solution would require agents to exchange all the $M$ input locations and measurements and then invert an $M \times M$ matrix, a non-scalable task. Differently, we propose two suboptimal approaches using the first $E$ orthonormal eigenfunctions obtained from the \ac{KL} expansion of the chosen kernel, where typically $E \ll M$. The benefits are that the computation and communication complexities scale with $E$ and not with $M$, and computing the required statistics can be performed via standard average consensus algorithms. We obtain probabilistic non-asymptotic bounds that determine a priori the desired level of estimation accuracy, and new distributed strategies relying on Stein's unbiased risk estimate (SURE) paradigms for tuning the regularization parameters and applicable to generic basis functions (thus not necessarily kernel eigenfunctions) and that can again be implemented via average consensus. The proposed estimators and bounds are finally tested on both synthetic and real field data

Reconstruction, Classification, and Segmentation for Computational Microscopy

This thesis treats two fundamental problems in computational microscopy: image reconstruction for magnetic resonance force microscopy (MRFM) and image classification for electron backscatter diffraction (EBSD). In MRFM, as in many inverse problems, the true point spread function (PSF) that blurs the image may be only partially known. The image quality may suffer from this possible mismatch when standard image reconstruction techniques are applied. To deal with the mismatch, we develop novel Bayesian sparse reconstruction methods that account for possible errors in the PSF of the microscope and for the inherent sparsity of MRFM images. Two methods are proposed: a stochastic method and a variational method. They both jointly estimate the unknown PSF and unknown image. Our proposed framework for reconstruction has the flexibility to incorporate sparsity inducing priors, thus addressing ill-posedness of this non-convex problem, Markov-Random field priors, and can be extended to other image models. To obtain scalable and tractable solutions, a dimensionality reduction technique is applied to the highly nonlinear PSF space. The experiments clearly demonstrate that the proposed methods have superior performance compared to previous methods. In EBSD we develop novel and robust dictionary-based methods for segmentation and classification of grain and sub-grain structures in polycrystalline materials. Our work is the first in EBSD analysis to use a physics-based forward model, called the dictionary, to use full diffraction patterns, and that efficiently classifies patterns into grains, boundaries, and anomalies. In particular, unlike previous methods, our method incorporates anomaly detection directly into the segmentation process. The proposed approach also permits super-resolution of grain mantle and grain boundary locations. Finally, the proposed dictionary-based segmentation method performs uncertainty quantification, i.e. p-values, for the classified grain interiors and grain boundaries. We demonstrate that the dictionary-based approach is robust to instrument drift and material differences that produce small amounts of dictionary mismatch.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102296/1/seunpark_1.pd

Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery

Regularized System Identification

This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authors’ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book