3,496 research outputs found
Non-Local Compressive Sensing Based SAR Tomography
Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse
reconstruction problem and, hence, can be solved using compressive sensing (CS)
algorithms. This paper proposes solutions for two notorious problems in this
field: 1) TomoSAR requires a high number of data sets, which makes the
technique expensive. However, it can be shown that the number of acquisitions
and the signal-to-noise ratio (SNR) can be traded off against each other,
because it is asymptotically only the product of the number of acquisitions and
SNR that determines the reconstruction quality. We propose to increase SNR by
integrating non-local estimation into the inversion and show that a reasonable
reconstruction of buildings from only seven interferograms is feasible. 2)
CS-based inversion is computationally expensive and therefore barely suitable
for large-scale applications. We introduce a new fast and accurate algorithm
for solving the non-local L1-L2-minimization problem, central to CS-based
reconstruction algorithms. The applicability of the algorithm is demonstrated
using simulated data and TerraSAR-X high-resolution spotlight images over an
area in Munich, Germany.Comment: 10 page
Soft Consistency Reconstruction: A Robust 1-bit Compressive Sensing Algorithm
A class of recovering algorithms for 1-bit compressive sensing (CS) named
Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS
recovery is essentially an optimization problem, we endeavor to improve the
characteristics of the objective function under noisy environments. With a
family of re-designed consistency criteria, SCRs achieve remarkable
counter-noise performance gain over the existing counterparts, thus acquiring
the desired robustness in many real-world applications. The benefits of soft
decisions are exemplified through structural analysis of the objective
function, with intuition described for better understanding. As expected,
through comparisons with existing methods in simulations, SCRs demonstrate
preferable robustness against noise in low signal-to-noise ratio (SNR) regime,
while maintaining comparable performance in high SNR regime
Multiple and single snapshot compressive beamforming
For a sound field observed on a sensor array, compressive sensing (CS)
reconstructs the direction-of-arrival (DOA) of multiple sources using a
sparsity constraint. The DOA estimation is posed as an underdetermined problem
by expressing the acoustic pressure at each sensor as a phase-lagged
superposition of source amplitudes at all hypothetical DOAs. Regularizing with
an -norm constraint renders the problem solvable with convex
optimization, and promoting sparsity gives high-resolution DOA maps. Here, the
sparse source distribution is derived using maximum a posteriori (MAP)
estimates for both single and multiple snapshots. CS does not require inversion
of the data covariance matrix and thus works well even for a single snapshot
where it gives higher resolution than conventional beamforming. For multiple
snapshots, CS outperforms conventional high-resolution methods, even with
coherent arrivals and at low signal-to-noise ratio. The superior resolution of
CS is demonstrated with vertical array data from the SWellEx96 experiment for
coherent multi-paths.Comment: In press Journal of Acoustical Society of Americ
Frequency-modulated continuous-wave LiDAR compressive depth-mapping
We present an inexpensive architecture for converting a frequency-modulated
continuous-wave LiDAR system into a compressive-sensing based depth-mapping
camera. Instead of raster scanning to obtain depth-maps, compressive sensing is
used to significantly reduce the number of measurements. Ideally, our approach
requires two difference detectors. % but can operate with only one at the cost
of doubling the number of measurments. Due to the large flux entering the
detectors, the signal amplification from heterodyne detection, and the effects
of background subtraction from compressive sensing, the system can obtain
higher signal-to-noise ratios over detector-array based schemes while scanning
a scene faster than is possible through raster-scanning. %Moreover, we show how
a single total-variation minimization and two fast least-squares minimizations,
instead of a single complex nonlinear minimization, can efficiently recover
high-resolution depth-maps with minimal computational overhead. Moreover, by
efficiently storing only data points from measurements of an
pixel scene, we can easily extract depths by solving only two linear equations
with efficient convex-optimization methods
Phase Retrieval From Binary Measurements
We consider the problem of signal reconstruction from quadratic measurements
that are encoded as +1 or -1 depending on whether they exceed a predetermined
positive threshold or not. Binary measurements are fast to acquire and
inexpensive in terms of hardware. We formulate the problem of signal
reconstruction using a consistency criterion, wherein one seeks to find a
signal that is in agreement with the measurements. To enforce consistency, we
construct a convex cost using a one-sided quadratic penalty and minimize it
using an iterative accelerated projected gradient-descent (APGD) technique. The
PGD scheme reduces the cost function in each iteration, whereas incorporating
momentum into PGD, notwithstanding the lack of such a descent property,
exhibits faster convergence than PGD empirically. We refer to the resulting
algorithm as binary phase retrieval (BPR). Considering additive white noise
contamination prior to quantization, we also derive the Cramer-Rao Bound (CRB)
for the binary encoding model. Experimental results demonstrate that the BPR
algorithm yields a signal-to- reconstruction error ratio (SRER) of
approximately 25 dB in the absence of noise. In the presence of noise prior to
quantization, the SRER is within 2 to 3 dB of the CRB
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