16,503 research outputs found
Structured random measurements in signal processing
Compressed sensing and its extensions have recently triggered interest in
randomized signal acquisition. A key finding is that random measurements
provide sparse signal reconstruction guarantees for efficient and stable
algorithms with a minimal number of samples. While this was first shown for
(unstructured) Gaussian random measurement matrices, applications require
certain structure of the measurements leading to structured random measurement
matrices. Near optimal recovery guarantees for such structured measurements
have been developed over the past years in a variety of contexts. This article
surveys the theory in three scenarios: compressed sensing (sparse recovery),
low rank matrix recovery, and phaseless estimation. The random measurement
matrices to be considered include random partial Fourier matrices, partial
random circulant matrices (subsampled convolutions), matrix completion, and
phase estimation from magnitudes of Fourier type measurements. The article
concludes with a brief discussion of the mathematical techniques for the
analysis of such structured random measurements.Comment: 22 pages, 2 figure
Single-shot compressed ultrafast photography: a review
Compressed ultrafast photography (CUP) is a burgeoning single-shot computational imaging technique that provides an imaging speed as high as 10 trillion frames per second and a sequence depth of up to a few hundred frames. This technique synergizes compressed sensing and the streak camera technique to capture nonrepeatable ultrafast transient events with a single shot. With recent unprecedented technical developments and extensions of this methodology, it has been widely used in ultrafast optical imaging and metrology, ultrafast electron diffraction and microscopy, and information security protection. We review the basic principles of CUP, its recent advances in data acquisition and image reconstruction, its fusions with other modalities, and its unique applications in multiple research fields
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Dynamic Mode Decomposition for Compressive System Identification
Dynamic mode decomposition has emerged as a leading technique to identify
spatiotemporal coherent structures from high-dimensional data, benefiting from
a strong connection to nonlinear dynamical systems via the Koopman operator. In
this work, we integrate and unify two recent innovations that extend DMD to
systems with actuation [Proctor et al., 2016] and systems with heavily
subsampled measurements [Brunton et al., 2015]. When combined, these methods
yield a novel framework for compressive system identification [code is publicly
available at: https://github.com/zhbai/cDMDc]. It is possible to identify a
low-order model from limited input-output data and reconstruct the associated
full-state dynamic modes with compressed sensing, adding interpretability to
the state of the reduced-order model. Moreover, when full-state data is
available, it is possible to dramatically accelerate downstream computations by
first compressing the data. We demonstrate this unified framework on two model
systems, investigating the effects of sensor noise, different types of
measurements (e.g., point sensors, Gaussian random projections, etc.),
compression ratios, and different choices of actuation (e.g., localized,
broadband, etc.). In the first example, we explore this architecture on a test
system with known low-rank dynamics and an artificially inflated state
dimension. The second example consists of a real-world engineering application
given by the fluid flow past a pitching airfoil at low Reynolds number. This
example provides a challenging and realistic test-case for the proposed method,
and results demonstrate that the dominant coherent structures are well
characterized despite actuation and heavily subsampled data
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