786 research outputs found
Sensing Matrix Design and Sparse Recovery on the Sphere and the Rotation Group
In this paper, {the goal is to design deterministic sampling patterns on the
sphere and the rotation group} and, thereby, construct sensing matrices for
sparse recovery of band-limited functions. It is first shown that random
sensing matrices, which consists of random samples of Wigner D-functions,
satisfy the Restricted Isometry Property (RIP) with proper preconditioning and
can be used for sparse recovery on the rotation group. The mutual coherence,
however, is used to assess the performance of deterministic and regular sensing
matrices. We show that many of widely used regular sampling patterns yield
sensing matrices with the worst possible mutual coherence, and therefore are
undesirable for sparse recovery. Using tools from angular momentum analysis in
quantum mechanics, we provide a new expression for the mutual coherence, which
encourages the use of regular elevation samples. We construct low coherence
deterministic matrices by fixing the regular samples on the elevation and
minimizing the mutual coherence over the azimuth-polarization choice. It is
shown that once the elevation sampling is fixed, the mutual coherence has a
lower bound that depends only on the elevation samples. This lower bound,
however, can be achieved for spherical harmonics, which leads to new sensing
matrices with better coherence than other representative regular sampling
patterns. This is reflected as well in our numerical experiments where our
proposed sampling patterns perfectly match the phase transition of random
sampling patterns.Comment: IEEE Trans. on Signal Processin
Tight bounds on the mutual coherence of sensing matrices for Wigner D-functions on regular grids
Many practical sampling patterns for function approximation on the rotation
group utilizes regular samples on the parameter axes. In this paper, we relate
the mutual coherence analysis for sensing matrices that correspond to a class
of regular patterns to angular momentum analysis in quantum mechanics and
provide simple lower bounds for it. The products of Wigner d-functions, which
appear in coherence analysis, arise in angular momentum analysis in quantum
mechanics. We first represent the product as a linear combination of a single
Wigner d-function and angular momentum coefficients, otherwise known as the
Wigner 3j symbols. Using combinatorial identities, we show that under certain
conditions on the bandwidth and number of samples, the inner product of the
columns of the sensing matrix at zero orders, which is equal to the inner
product of two Legendre polynomials, dominates the mutual coherence term and
fixes a lower bound for it. In other words, for a class of regular sampling
patterns, we provide a lower bound for the inner product of the columns of the
sensing matrix that can be analytically computed. We verify numerically our
theoretical results and show that the lower bound for the mutual coherence is
larger than Welch bound. Besides, we provide algorithms that can achieve the
lower bound for spherical harmonics
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
Fast computation of spherical phase-space functions of quantum many-body states
Quantum devices are preparing increasingly more complex entangled quantum
states. How can one effectively study these states in light of their increasing
dimensions? Phase spaces such as Wigner functions provide a suitable framework.
We focus on phase spaces for finite-dimensional quantum states of single qudits
or permutationally symmetric states of multiple qubits. We present methods to
efficiently compute the corresponding phase-space functions which are at least
an order of magnitude faster than traditional methods. Quantum many-body states
in much larger dimensions can now be effectively studied by experimentalists
and theorists using these phase-space techniques.Comment: 12 pages, 3 figure
Signal Processing and Propagation for Aeroacoustic Sensor Networking,” Ch
Passive sensing of acoustic sources is attractive in many respects, including the relatively low signal bandwidth of sound waves, the loudness of most sources of interest, and the inherent difficulty of disguising or concealing emitted acoustic signals. The availability of inexpensive, low-power sensing and signal-processing hardware enables application of sophisticated real-time signal processing. Among th
Fundamental limits to optical response in absorptive systems
At visible and infrared frequencies, metals show tantalizing promise for
strong subwavelength resonances, but material loss typically dampens the
response. We derive fundamental limits to the optical response of absorptive
systems, bounding the largest enhancements possible given intrinsic material
losses. Through basic conservation-of-energy principles, we derive
geometry-independent limits to per-volume absorption and scattering rates, and
to local-density-of-states enhancements that represent the power radiated or
expended by a dipole near a material body. We provide examples of structures
that approach our absorption and scattering limits at any frequency, by
contrast, we find that common "antenna" structures fall far short of our
radiative LDOS bounds, suggesting the possibility for significant further
improvement. Underlying the limits is a simple metric, for a material with susceptibility , that enables
broad technological evaluation of lossy materials across optical frequencies.Comment: 21 pages and 6 figures (excluding appendices, references
Fundamental Limits of Nanophotonic Design
Nanoscale fabrication techniques, computational inverse design, and fields
from silicon photonics to metasurface optics are enabling transformative use of
an unprecedented number of structural degrees of freedom in nanophotonics. A
critical need is to understand the extreme limits to what is possible by
engineering nanophotonic structures. This thesis establishes the first general
theoretical framework identifying fundamental limits to light--matter
interactions. It derives bounds for applications across nanophotonics,
including far-field scattering, optimal wavefront shaping, optical beam
switching, and wave communication, as well as the miniaturization of optical
components, including perfect absorbers, linear optical analog computing units,
resonant optical sensors, multilayered thin films, and high-NA metalenses. The
bounds emerge from an infinite set of physical constraints that have to be
satisfied by polarization fields in response to an excitation. The constraints
encode power conservation in single-scenario scattering and requisite field
correlations in multi-scenario scattering. The framework developed in this
thesis, encompassing general linear wave scattering dynamics, offers a new way
to understand optimal designs and their fundamental limits, in nanophotonics
and beyond.Comment: PhD thesi
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Forward and Inverse Modeling of GPS Multipath for Snow Monitoring
Snowpacks provide reservoirs of freshwater, storing solid precipitation and delaying runoff to be released later in the spring and summer when it is most needed. The goal of this dissertation is to develop the technique of GPS multipath reflectometry (GPS-MR) for ground-based measurement of snow depth. The phenomenon of multipath in GPS constitutes the reception of reflected signals in conjunction with the direct signal from a satellite. As these coherent direct and reflected signals go in and out of phase, signal-to-noise ratio (SNR) exhibits peaks and troughs that can be related to land surface characteristics. In contrast to other GPS reflectometry modes, in GPS-MR the poorly separated composite signal is collected utilizing a single antenna and correlated against a single replica. SNR observations derived from the newer L2-frequency civilian GPS signal (L2C) are used, as recorded by commercial off-the-shelf receivers and geodetic-quality antennas in existing GPS sites. I developed a forward/inverse approach for modeling GPS multipath present in SNR observations. The model here is unique in that it capitalizes on known information about the antenna response and the physics of surface scattering to aid in retrieving the unknown snow conditions in the antenna surroundings. This physically-based forward model is utilized to simulate the surface and antenna coupling. The statistically-rigorous inverse model is considered in two parts. Part I (theory) explains how the snow characteristics are parameterized; the observation/parameter sensitivity; inversion errors; and parameter uncertainty, which serves to indicate the sensing footprint where the reflection originates. Part II (practice) applies the multipath model to SNR observations and validates the resulting GPS retrievals against independent in situ measurements during a 1-3 year period in three different environments - grasslands, alpine, and forested. The assessment yields a correlation of 0.98 and an RMS error of 6-8 cm, with the GPS under-estimating in situ snow depth by approximately 15%. GPS daily site averages were found effective in mitigating random noise without unduly smoothing the sharp transitions as captured in new snow events. This work corroborates the readiness of quality-controlled GPS-MR for snow depth monitoring, reinforcing its maturity for operational usage
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