309 research outputs found
Oracle-order Recovery Performance of Greedy Pursuits with Replacement against General Perturbations
Applying the theory of compressive sensing in practice always takes different
kinds of perturbations into consideration. In this paper, the recovery
performance of greedy pursuits with replacement for sparse recovery is analyzed
when both the measurement vector and the sensing matrix are contaminated with
additive perturbations. Specifically, greedy pursuits with replacement include
three algorithms, compressive sampling matching pursuit (CoSaMP), subspace
pursuit (SP), and iterative hard thresholding (IHT), where the support
estimation is evaluated and updated in each iteration. Based on restricted
isometry property, a unified form of the error bounds of these recovery
algorithms is derived under general perturbations for compressible signals. The
results reveal that the recovery performance is stable against both
perturbations. In addition, these bounds are compared with that of oracle
recovery--- least squares solution with the locations of some largest entries
in magnitude known a priori. The comparison shows that the error bounds of
these algorithms only differ in coefficients from the lower bound of oracle
recovery for some certain signal and perturbations, as reveals that
oracle-order recovery performance of greedy pursuits with replacement is
guaranteed. Numerical simulations are performed to verify the conclusions.Comment: 27 pages, 4 figures, 5 table
Interference Removal for Radar/Communication Co-existence: the Random Scattering Case
In this paper we consider an un-cooperative spectrum sharing scenario,
wherein a radar system is to be overlaid to a pre-existing wireless
communication system. Given the order of magnitude of the transmitted powers in
play, we focus on the issue of interference mitigation at the communication
receiver. We explicitly account for the reverberation produced by the
(typically high-power) radar transmitter whose signal hits scattering centers
(whether targets or clutter) producing interference onto the communication
receiver, which is assumed to operate in an un-synchronized and un-coordinated
scenario. We first show that receiver design amounts to solving a non-convex
problem of joint interference removal and data demodulation: next, we introduce
two algorithms, both exploiting sparsity of a proper representation of the
interference and of the vector containing the errors of the data block. The
first algorithm is basically a relaxed constrained Atomic Norm minimization,
while the latter relies on a two-stage processing structure and is based on
alternating minimization. The merits of these algorithms are demonstrated
through extensive simulations: interestingly, the two-stage alternating
minimization algorithm turns out to achieve satisfactory performance with
moderate computational complexity
Study of the gOMP Algorithm for Recovery of Compressed Sensed Hyperspectral Images
Hyperspectral Imaging (HSI) is used in a wide range of applications such as
remote sensing, yet the transmission of the HS images by communication data
links becomes challenging due to the large number of spectral bands that the HS
images contain together with the limited data bandwidth available in real
applications. Compressive Sensing reduces the images by randomly subsampling
the spectral bands of each spatial pixel and then it performs the image
reconstruction of all the bands using recovery algorithms which impose sparsity
in a certain transform domain. Since the image pixels are not strictly sparse,
this work studies a data sparsification pre-processing stage prior to
compression to ensure the sparsity of the pixels. The sparsified images are
compressed and then recovered using the Generalized Orthogonal
Matching Pursuit algorithm (gOMP) characterized by high accuracy, low
computational requirements and fast convergence. The experiments are performed
in five conventional hyperspectral images where the effect of different
sparsification levels in the quality of the uncompressed as well as the
recovered images is studied. It is concluded that the gOMP algorithm
reconstructs the hyperspectral images with higher accuracy as well as faster
convergence when the pixels are highly sparsified and hence at the expense of
reducing the quality of the recovered images with respect to the original
images.Comment: Hyperspectral Imaging, Compressive Sensing, Greedy Algorithms,
Generalized Orthogonal Matching Pursuit (gOMP), Sparsity, Sparsification,
IEEE-copyrighted material (2022), WHISPERS Workshop (13-16 September 2022
- …