115 research outputs found
Convolutional Dictionary Learning through Tensor Factorization
Tensor methods have emerged as a powerful paradigm for consistent learning of
many latent variable models such as topic models, independent component
analysis and dictionary learning. Model parameters are estimated via CP
decomposition of the observed higher order input moments. However, in many
domains, additional invariances such as shift invariances exist, enforced via
models such as convolutional dictionary learning. In this paper, we develop
novel tensor decomposition algorithms for parameter estimation of convolutional
models. Our algorithm is based on the popular alternating least squares method,
but with efficient projections onto the space of stacked circulant matrices.
Our method is embarrassingly parallel and consists of simple operations such as
fast Fourier transforms and matrix multiplications. Our algorithm converges to
the dictionary much faster and more accurately compared to the alternating
minimization over filters and activation maps
Subsampled Blind Deconvolution via Nuclear Norm Minimization
Many phenomena can be modeled as systems that preform convolution, including negative effects on data
like translation/motion blurs. Blind Deconvolution (BD) is a process used to reverse the negative effects
of a system by effectively undoing the convolution. Not only can the signal be recovered, but the impulse
response can as well. "Blind" signifies that there is incomplete knowledge of the impulse responses of an
LTI system. Solutions exist for preforming BD but they assume data is fully sampled. In this project we
start from an existing method [1] for BD then extend to the subsampled case. We show that this new
formulation works under similar assumptions. Current results are empirical, but current and future work
focuses providing theoretical guarantees for this algorithm.No embargoAcademic Major: Electrical and Computer Engineerin
Convexity in source separation: Models, geometry, and algorithms
Source separation or demixing is the process of extracting multiple
components entangled within a signal. Contemporary signal processing presents a
host of difficult source separation problems, from interference cancellation to
background subtraction, blind deconvolution, and even dictionary learning.
Despite the recent progress in each of these applications, advances in
high-throughput sensor technology place demixing algorithms under pressure to
accommodate extremely high-dimensional signals, separate an ever larger number
of sources, and cope with more sophisticated signal and mixing models. These
difficulties are exacerbated by the need for real-time action in automated
decision-making systems.
Recent advances in convex optimization provide a simple framework for
efficiently solving numerous difficult demixing problems. This article provides
an overview of the emerging field, explains the theory that governs the
underlying procedures, and surveys algorithms that solve them efficiently. We
aim to equip practitioners with a toolkit for constructing their own demixing
algorithms that work, as well as concrete intuition for why they work
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