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AeroDyn Theory Manual
AeroDyn is a set of routines used in conjunction with an aeroelastic simulation code to predict the aerodynamics of horizontal axis wind turbines. These subroutines provide several different modelsExpand
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Breaking the coherence barrier: A new theory for compressed sensing
TLDR
We introduce a mathematical framework that generalizes the three standard pillars of compressed sensing - namely, sparsity, incoherence and uniform random subsampling - to three new concepts: asymptotic sparsity and multilevel random sampling. Expand
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Generalized Sampling and Infinite-Dimensional Compressed Sensing
TLDR
We introduce and analyze a framework and corresponding method for compressed sensing in infinite dimensions. Expand
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On the Solvability Complexity Index, the n-pseudospectrum and approximations of spectra of operators
We show that it is possible to compute spectra and pseudospectra of linear operators on separable Hilbert spaces given their matrix elements. The core in the theory is pseudospectral analysis and inExpand
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On asymptotic structure in compressed sensing
TLDR
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymmptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing. Expand
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A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases
TLDR
We introduce a generalized framework for sampling and reconstruction in separable Hilbert spaces. Expand
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On instabilities of deep learning in image reconstruction - Does AI come at a cost?
TLDR
In this paper, we demonstrate a crucial phenomenon: Deep learning typically yields unstable methods for image reconstruction with potential to change the field. Expand
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Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing
TLDR
We introduce a mathematical framework that bridges a substantial gap between compressed sensing theory and its current use in real-world applications. Expand
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Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
TLDR
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. Expand
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Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum
TLDR
We propose a theory and set of methods for infinite-dimensional compressed sensing, or as we shall also refer to it, compressed sensing over the continuum. Expand
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