Generalized blind deconvolution with missing data
- A blind deconvolution problem seeks two signals that convolve (approximately) to some known data signal. Such problems appear in application areas that can be described by a convolution model, e.g., a linear time invariant (LTI) system or a convolutional (shift invariant) dictionary. Data signals may have multiple rows and columns, entries drawn from a non-numeric set, missing or corrupt values, or any combination of these. In this dissertation, we present a general-purpose method for formulating blind deconvolution problems when data signals suffer from real-world issues, e.g., have arbitrary data type, are corrupt or incomplete, include additional constraints, and so on. Our approach extends Generalized Low Rank Models (an exploratory analysis tool for heterogeneous data tables) to the signal setting. By extension, missing values can be overlooked with a careful choice of optimization formulation and later imputed. We use alternating proximal gradient descent to leverage the Fast Fourier transform and parallelize updates over rows and columns of the data. We introduce a new problem, histogram unmixing, that is particularly well-suited for our framework. Finally we report results for some numerical experiments, demonstrating the improvement of our method over a naive approach.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Electrical Engineering.
|Statement of responsibility
|Submitted to the Department of Electrical Engineering.
|Thesis (Ph.D.)--Stanford University, 2017.
- © 2017 by Corinne Elizabeth Horn
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