3,438 research outputs found
Acceleration Techniques for Sparse Recovery Based Plane-wave Decomposition of a Sound Field
Plane-wave decomposition by sparse recovery is a reliable and accurate technique for plane-wave decomposition which can be used for source localization, beamforming, etc. In this work, we introduce techniques to accelerate the plane-wave decomposition by sparse recovery. The method consists of two main algorithms which are spherical Fourier transformation (SFT) and sparse recovery. Comparing the two algorithms, the sparse recovery is the most computationally intensive. We implement the SFT on an FPGA and the sparse recovery on a multithreaded computing platform. Then the multithreaded computing platform could be fully utilized for the sparse recovery. On the other hand, implementing the SFT on an FPGA helps to flexibly integrate the microphones and improve the portability of the microphone array. For implementing the SFT on an FPGA, we develop a scalable FPGA design model that enables the quick design of the SFT architecture on FPGAs. The model considers the number of microphones, the number of SFT channels and the cost of the FPGA and provides the design of a resource optimized and cost-effective FPGA architecture as the output. Then we investigate the performance of the sparse recovery algorithm executed on various multithreaded computing platforms (i.e., chip-multiprocessor, multiprocessor, GPU, manycore). Finally, we investigate the influence of modifying the dictionary size on the computational performance and the accuracy of the sparse recovery algorithms. We introduce novel sparse-recovery techniques which use non-uniform dictionaries to improve the performance of the sparse recovery on a parallel architecture
Xampling: Signal Acquisition and Processing in Union of Subspaces
We introduce Xampling, a unified framework for signal acquisition and
processing of signals in a union of subspaces. The main functions of this
framework are two. Analog compression that narrows down the input bandwidth
prior to sampling with commercial devices. A nonlinear algorithm then detects
the input subspace prior to conventional signal processing. A representative
union model of spectrally-sparse signals serves as a test-case to study these
Xampling functions. We adopt three metrics for the choice of analog
compression: robustness to model mismatch, required hardware accuracy and
software complexities. We conduct a comprehensive comparison between two
sub-Nyquist acquisition strategies for spectrally-sparse signals, the random
demodulator and the modulated wideband converter (MWC), in terms of these
metrics and draw operative conclusions regarding the choice of analog
compression. We then address lowrate signal processing and develop an algorithm
for that purpose that enables convenient signal processing at sub-Nyquist rates
from samples obtained by the MWC. We conclude by showing that a variety of
other sampling approaches for different union classes fit nicely into our
framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio
Model-Based Calibration of Filter Imperfections in the Random Demodulator for Compressive Sensing
The random demodulator is a recent compressive sensing architecture providing
efficient sub-Nyquist sampling of sparse band-limited signals. The compressive
sensing paradigm requires an accurate model of the analog front-end to enable
correct signal reconstruction in the digital domain. In practice, hardware
devices such as filters deviate from their desired design behavior due to
component variations. Existing reconstruction algorithms are sensitive to such
deviations, which fall into the more general category of measurement matrix
perturbations. This paper proposes a model-based technique that aims to
calibrate filter model mismatches to facilitate improved signal reconstruction
quality. The mismatch is considered to be an additive error in the discretized
impulse response. We identify the error by sampling a known calibrating signal,
enabling least-squares estimation of the impulse response error. The error
estimate and the known system model are used to calibrate the measurement
matrix. Numerical analysis demonstrates the effectiveness of the calibration
method even for highly deviating low-pass filter responses. The proposed method
performance is also compared to a state of the art method based on discrete
Fourier transform trigonometric interpolation.Comment: 10 pages, 8 figures, submitted to IEEE Transactions on Signal
Processin
Uniform Recovery from Subgaussian Multi-Sensor Measurements
Parallel acquisition systems are employed successfully in a variety of
different sensing applications when a single sensor cannot provide enough
measurements for a high-quality reconstruction. In this paper, we consider
compressed sensing (CS) for parallel acquisition systems when the individual
sensors use subgaussian random sampling. Our main results are a series of
uniform recovery guarantees which relate the number of measurements required to
the basis in which the solution is sparse and certain characteristics of the
multi-sensor system, known as sensor profile matrices. In particular, we derive
sufficient conditions for optimal recovery, in the sense that the number of
measurements required per sensor decreases linearly with the total number of
sensors, and demonstrate explicit examples of multi-sensor systems for which
this holds. We establish these results by proving the so-called Asymmetric
Restricted Isometry Property (ARIP) for the sensing system and use this to
derive both nonuniversal and universal recovery guarantees. Compared to
existing work, our results not only lead to better stability and robustness
estimates but also provide simpler and sharper constants in the measurement
conditions. Finally, we show how the problem of CS with block-diagonal sensing
matrices can be viewed as a particular case of our multi-sensor framework.
Specializing our results to this setting leads to a recovery guarantee that is
at least as good as existing results.Comment: 37 pages, 5 figure
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