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)

Unsupervised Image Restoration and Edge Location Using Compound Gauss-Markov Random Fields and the MDL Principle

Discontinuity-preserving Bayesian image restoration typically involves two Markov random fields: one representing the image intensities/gray levels to be recovered and another one signaling discontinuities/edges to be preserved. The usual strategy is to perform joint maximum a posteriori (MAP) estimation of the image and its edges, which requires the specification of priors for both fields. In this paper, instead of taking an edge prior, we interpret discontinuities (in fact their locations) as deterministic unknown parameters of the compound Gauss--Markov random field (CGMRF), which is assumed to model the intensities. This strategy should allow inferring the discontinuity locations directly from the image with no further assumptions. However, an additional problem emerges: The number of parameters (edges) is unknown. To deal with it, we invoke the minimum description length (MDL) principle; according to MDL, the best edge configuration is the one that allows the shortest description of the image and its edges. Taking the other model parameters (noise and CGMRF variances) also as unknown, we propose a new unsupervised discontinuity-preserving image restoration criterion. Implementation is carried out by a continuation-type iterative algorithm which provides estimates of the number of discontinuities, their locations, the noise variance, the original image variance, and the original image itself (restored image). Experimental results with real and synthetic images are reported

Analysis and development of self localization and autonomous driving systems for the industrial and automotive environment.

The goal of the present thesis is dual. First the self localization problem is investigated in the industrial environment and a working prototype, consisting in an AGV able to perform self localization and autonomous driving under certain conditions, has been developed. Then the self localization problem is considered as a part of wider and currently very active research problem: the Simultaneous Localization And Mapping (SLAM), considered in the automotive environment.L'obiettivo della presente Tesi è duplice. Inizialmente il problema della self localization viene analizzato nel contesto industriale e un prototipo funzionante è stato realizzato, consistente in un AGV in grado di auto localizzarsi in certe condizioni. In seguito il problema della self localization è stato considerato come parte di un problema più ampio e ad oggi particolarmente: il Simultaneous Localization And Mapping (SLAM), nel contesto automobilistico

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