1,764 research outputs found
Reliable recovery of hierarchically sparse signals for Gaussian and Kronecker product measurements
We propose and analyze a solution to the problem of recovering a block sparse
signal with sparse blocks from linear measurements. Such problems naturally
emerge inter alia in the context of mobile communication, in order to meet the
scalability and low complexity requirements of massive antenna systems and
massive machine-type communication. We introduce a new variant of the Hard
Thresholding Pursuit (HTP) algorithm referred to as HiHTP. We provide both a
proof of convergence and a recovery guarantee for noisy Gaussian measurements
that exhibit an improved asymptotic scaling in terms of the sampling complexity
in comparison with the usual HTP algorithm. Furthermore, hierarchically sparse
signals and Kronecker product structured measurements naturally arise together
in a variety of applications. We establish the efficient reconstruction of
hierarchically sparse signals from Kronecker product measurements using the
HiHTP algorithm. Additionally, we provide analytical results that connect our
recovery conditions to generalized coherence measures. Again, our recovery
results exhibit substantial improvement in the asymptotic sampling complexity
scaling over the standard setting. Finally, we validate in numerical
experiments that for hierarchically sparse signals, HiHTP performs
significantly better compared to HTP.Comment: 11+4 pages, 5 figures. V3: Incomplete funding information corrected
and minor typos corrected. V4: Change of title and additional author Axel
Flinth. Included new results on Kronecker product measurements and relations
of HiRIP to hierarchical coherence measures. Improved presentation of general
hierarchically sparse signals and correction of minor typo
Hierarchical compressed sensing
Compressed sensing is a paradigm within signal processing that provides the
means for recovering structured signals from linear measurements in a highly
efficient manner. Originally devised for the recovery of sparse signals, it has
become clear that a similar methodology would also carry over to a wealth of
other classes of structured signals. In this work, we provide an overview over
the theory of compressed sensing for a particularly rich family of such
signals, namely those of hierarchically structured signals. Examples of such
signals are constituted by blocked vectors, with only few non-vanishing sparse
blocks. We present recovery algorithms based on efficient hierarchical
hard-thresholding. The algorithms are guaranteed to converge, in a stable
fashion both with respect to measurement noise as well as to model mismatches,
to the correct solution provided the measurement map acts isometrically
restricted to the signal class. We then provide a series of results
establishing the required condition for large classes of measurement ensembles.
Building upon this machinery, we sketch practical applications of this
framework in machine-type communications and quantum tomography.Comment: This book chapter is a report on findings within the DFG-funded
priority program `Compressed Sensing in Information Processing' (CoSIP
One-Shot Messaging at Any Load Through Random Sub-Channeling in OFDM
Compressive Sensing has well boosted massive random access protocols over the
last decade. In this paper we apply an orthogonal FFT basis as it is used in
OFDM, but subdivide its image into so-called sub-channels and let each
sub-channel take only a fraction of the load. In a random fashion the
subdivision is consecutively applied over a suitable number of time-slots.
Within the time-slots the users will not change their sub-channel assignment
and send in parallel the data. Activity detection is carried out jointly across
time-slots in each of the sub-channels. For such system design we derive three
rather fundamental results: i) First, we prove that the subdivision can be
driven to the extent that the activity in each sub-channel is sparse by design.
An effect that we call sparsity capture effect. ii) Second, we prove that
effectively the system can sustain any overload situation relative to the FFT
dimension, i.e. detection failure of active and non-active users can be kept
below any desired threshold regardless of the number of users. The only price
to pay is delay, i.e. the number of time-slots over which cross-detection is
performed. We achieve this by jointly exploring the effect of measure
concentration in time and frequency and careful system parameter scaling. iii)
Third, we prove that parallel to activity detection active users can carry one
symbol per pilot resource and time-slot so it supports so-called one-shot
messaging.
The key to proving these results are new concentration results for sequences
of randomly sub-sampled FFTs detecting the sparse vectors "en bloc".
Eventually, we show by simulations that the system is scalable resulting in a
coarsely 30-fold capacity increase compared to standard OFDM
Semi-device-dependent blind quantum tomography
Extracting tomographic information about quantum states is a crucial task in
the quest towards devising high-precision quantum devices. Current schemes
typically require measurement devices for tomography that are a priori
calibrated to a high precision. Ironically, the accuracy of the measurement
calibration is fundamentally limited by the accuracy of state preparation,
establishing a vicious cycle. Here, we prove that this cycle can be broken and
the fundamental dependence on the measurement devices significantly relaxed. We
show that exploiting the natural low-rank structure of quantum states of
interest suffices to arrive at a highly scalable blind tomography scheme with a
classically efficient post-processing algorithm. We further improve the
efficiency of our scheme by making use of the sparse structure of the
calibrations. This is achieved by relaxing the blind quantum tomography problem
to the task of de-mixing a sparse sum of low-rank quantum states. Building on
techniques from model-based compressed sensing, we prove that the proposed
algorithm recovers a low-rank quantum state and the calibration provided that
the measurement model exhibits a restricted isometry property. For generic
measurements, we show that our algorithm requires a close-to-optimal number
measurement settings for solving the blind tomography task. Complementing these
conceptual and mathematical insights, we numerically demonstrate that blind
quantum tomography is possible by exploiting low-rank assumptions in a
practical setting inspired by an implementation of trapped ions using
constrained alternating optimization.Comment: 22 pages, 8 Figure
A Deep Learning Approach for Vital Signs Compression and Energy Efficient Delivery in mhealth Systems
© 2013 IEEE. Due to the increasing number of chronic disease patients, continuous health monitoring has become the top priority for health-care providers and has posed a major stimulus for the development of scalable and energy efficient mobile health systems. Collected data in such systems are highly critical and can be affected by wireless network conditions, which in return, motivates the need for a preprocessing stage that optimizes data delivery in an adaptive manner with respect to network dynamics. We present in this paper adaptive single and multiple modality data compression schemes based on deep learning approach, which consider acquired data characteristics and network dynamics for providing energy efficient data delivery. Results indicate that: 1) the proposed adaptive single modality compression scheme outperforms conventional compression methods by 13.24% and 43.75% reductions in distortion and processing time, respectively; 2) the proposed adaptive multiple modality compression further decreases the distortion by 3.71% and 72.37% when compared with the proposed single modality scheme and conventional methods through leveraging inter-modality correlations; and 3) adaptive multiple modality compression demonstrates its efficiency in terms of energy consumption, computational complexity, and responding to different network states. Hence, our approach is suitable for mobile health applications (mHealth), where the smart preprocessing of vital signs can enhance energy consumption, reduce storage, and cut down transmission delays to the mHealth cloud.This work was supported by NPRP through the Qatar National Research Fund (a member of the Qatar Foundation) under Grant 7-684-1-127
Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
In this paper, we put forth a long short-term memory (LSTM) nudging framework
for the enhancement of reduced order models (ROMs) of fluid flows utilizing
noisy measurements. We build on the fact that in a realistic application, there
are uncertainties in initial conditions, boundary conditions, model parameters,
and/or field measurements. Moreover, conventional nonlinear ROMs based on
Galerkin projection (GROMs) suffer from imperfection and solution instabilities
due to the modal truncation, especially for advection-dominated flows with slow
decay in the Kolmogorov width. In the presented LSTM-Nudge approach, we fuse
forecasts from a combination of imperfect GROM and uncertain state estimates,
with sparse Eulerian sensor measurements to provide more reliable predictions
in a dynamical data assimilation framework. We illustrate the idea with the
viscous Burgers problem, as a benchmark test bed with quadratic nonlinearity
and Laplacian dissipation. We investigate the effects of measurements noise and
state estimate uncertainty on the performance of the LSTM-Nudge behavior. We
also demonstrate that it can sufficiently handle different levels of temporal
and spatial measurement sparsity. This first step in our assessment of the
proposed model shows that the LSTM nudging could represent a viable realtime
predictive tool in emerging digital twin systems
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