2,463 research outputs found
Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements
The measurement matrix employed in compressive sensing typically cannot be known precisely a priori, and must be estimated via calibration. One may take multiple compressive measurements, from which the measurement matrix and underlying signals may be estimated jointly. This is of interest as well when the measurement matrix may change as a function of the details of what is measured. This problem has been considered recently for Gaussian measurement noise, and here we develop this idea with application to Poisson systems. An optimization-based algorithm is proposed, and associated theoretical performance guarantees are established based on newly derived concentration-of-measure results. A Bayesian model is then introduced, to improve exibility and generality. Connections between the optimization-based methods and the Bayesian model are developed, and example results are presented for a real compressive x-ray imaging system
Photon counting compressive depth mapping
We demonstrate a compressed sensing, photon counting lidar system based on
the single-pixel camera. Our technique recovers both depth and intensity maps
from a single under-sampled set of incoherent, linear projections of a scene of
interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional
reconstructions are required to image a three-dimensional scene. We demonstrate
intensity imaging and depth mapping at 256 x 256 pixel transverse resolution
with acquisition times as short as 3 seconds. We also show novelty filtering,
reconstructing only the difference between two instances of a scene. Finally,
we acquire 32 x 32 pixel real-time video for three-dimensional object tracking
at 14 frames-per-second.Comment: 16 pages, 8 figure
Computational multi-depth single-photon imaging
We present an imaging framework that is able to accurately reconstruct multiple depths at individual pixels from single-photon observations. Our active imaging method models the single-photon detection statistics from multiple reflectors within a pixel, and it also exploits the fact that a multi-depth profile at each pixel can be expressed as a sparse signal. We interpret the multi-depth reconstruction problem as a sparse deconvolution problem using single-photon observations, create a convex problem through discretization and relaxation, and use a modified iterative shrinkage-thresholding algorithm to efficiently solve for the optimal multi-depth solution. We experimentally demonstrate that the proposed framework is able to accurately reconstruct the depth features of an object that is behind a partially-reflecting scatterer and 4 m away from the imager with root mean-square error of 11 cm, using only 19 signal photon detections per pixel in the presence of moderate background light. In terms of root mean-square error, this is a factor of 4.2 improvement over the conventional method of Gaussian-mixture fitting for multi-depth recovery.This material is based upon work supported in part by a Samsung Scholarship, the US National Science Foundation under Grant No. 1422034, and the MIT Lincoln Laboratory Advanced Concepts Committee. We thank Dheera Venkatraman for his assistance with the experiments. (Samsung Scholarship; 1422034 - US National Science Foundation; MIT Lincoln Laboratory Advanced Concepts Committee)Accepted manuscrip
Matrix Completion-Based Channel Estimation for MmWave Communication Systems With Array-Inherent Impairments
Hybrid massive MIMO structures with reduced hardware complexity and power
consumption have been widely studied as a potential candidate for millimeter
wave (mmWave) communications. Channel estimators that require knowledge of the
array response, such as those using compressive sensing (CS) methods, may
suffer from performance degradation when array-inherent impairments bring
unknown phase errors and gain errors to the antenna elements. In this paper, we
design matrix completion (MC)-based channel estimation schemes which are robust
against the array-inherent impairments. We first design an open-loop training
scheme that can sample entries from the effective channel matrix randomly and
is compatible with the phase shifter-based hybrid system. Leveraging the
low-rank property of the effective channel matrix, we then design a channel
estimator based on the generalized conditional gradient (GCG) framework and the
alternating minimization (AltMin) approach. The resulting estimator is immune
to array-inherent impairments and can be implemented to systems with any array
shapes for its independence of the array response. In addition, we extend our
design to sample a transformed channel matrix following the concept of
inductive matrix completion (IMC), which can be solved efficiently using our
proposed estimator and achieve similar performance with a lower requirement of
the dynamic range of the transmission power per antenna. Numerical results
demonstrate the advantages of our proposed MC-based channel estimators in terms
of estimation performance, computational complexity and robustness against
array-inherent impairments over the orthogonal matching pursuit (OMP)-based CS
channel estimator.Comment: This work has been submitted to the IEEE for possible publication.
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