4,453 research outputs found
Conjugate Gradient Iterative Hard Thresholding:\ud Observed Noise Stability for Compressed Sensing
Conjugate Gradient Iterative Hard Thresholding (CGIHT) for compressed sensing combines the low per iteration complexity of fast greedy sparse approximation algorithms with the improved convergence rates of more complicated, projection based algorithms. This article shows that CGIHT is robust to\ud
additive noise and is typically the fastest greedy algorithm in the presence of noise
CGIHT: Conjugate Gradient Iterative Hard Thresholding\ud for Compressed Sensing and Matrix Completion
We introduce the Conjugate Gradient Iterative Hard Thresholding (CGIHT) family of algorithms for the efficient solution of constrained underdetermined linear systems of equations arising in compressed sensing, row sparse approximation, and matrix completion. CGIHT is designed to balance the low per iteration complexity of simple hard thresholding algorithms with the fast asymptotic convergence rate of employing the conjugate gradient method. We establish provable recovery guarantees and stability to noise for variants of CGIHT with sufficient conditions in terms of the restricted isometry constants of the sensing operators. Extensive empirical performance comparisons establish significant computational advantages for CGIHT both in terms of the size of problems which can be accurately approximated and in terms of overall computation time
Solar hard X-ray imaging by means of Compressed Sensing and Finite Isotropic Wavelet Transform
This paper shows that compressed sensing realized by means of regularized
deconvolution and the Finite Isotropic Wavelet Transform is effective and
reliable in hard X-ray solar imaging.
The method utilizes the Finite Isotropic Wavelet Transform with Meyer
function as the mother wavelet. Further, compressed sensing is realized by
optimizing a sparsity-promoting regularized objective function by means of the
Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization
parameter is selected by means of the Miller criterion.
The method is applied against both synthetic data mimicking the
Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental
observations provided by the Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI). The performances of the method are compared with the results
provided by standard visibility-based reconstruction methods.
The results show that the application of the sparsity constraint and the use
of a continuous, isotropic framework for the wavelet transform provide a
notable spatial accuracy and significantly reduce the ringing effects due to
the instrument point spread functions
Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion
A spectrally sparse signal of order is a mixture of damped or
undamped complex sinusoids. This paper investigates the problem of
reconstructing spectrally sparse signals from a random subset of regular
time domain samples, which can be reformulated as a low rank Hankel matrix
completion problem. We introduce an iterative hard thresholding (IHT) algorithm
and a fast iterative hard thresholding (FIHT) algorithm for efficient
reconstruction of spectrally sparse signals via low rank Hankel matrix
completion. Theoretical recovery guarantees have been established for FIHT,
showing that number of samples are sufficient for exact
recovery with high probability. Empirical performance comparisons establish
significant computational advantages for IHT and FIHT. In particular, numerical
simulations on D arrays demonstrate the capability of FIHT on handling large
and high-dimensional real data
Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing with Prior Information
Commonly employed reconstruction algorithms in compressed sensing (CS) use
the norm as the metric for the residual error. However, it is well-known
that least squares (LS) based estimators are highly sensitive to outliers
present in the measurement vector leading to a poor performance when the noise
no longer follows the Gaussian assumption but, instead, is better characterized
by heavier-than-Gaussian tailed distributions. In this paper, we propose a
robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse
signals in the presence of impulsive noise. To address this problem, we use a
Lorentzian cost function instead of the cost function employed by the
traditional IHT algorithm. We also modify the algorithm to incorporate prior
signal information in the recovery process. Specifically, we study the case of
CS with partially known support. The proposed algorithm is a fast method with
computational load comparable to the LS based IHT, whilst having the advantage
of robustness against heavy-tailed impulsive noise. Sufficient conditions for
stability are studied and a reconstruction error bound is derived. We also
derive sufficient conditions for stable sparse signal recovery with partially
known support. Theoretical analysis shows that including prior support
information relaxes the conditions for successful reconstruction. Simulation
results demonstrate that the Lorentzian-based IHT algorithm significantly
outperform commonly employed sparse reconstruction techniques in impulsive
environments, while providing comparable performance in less demanding,
light-tailed environments. Numerical results also demonstrate that the
partially known support inclusion improves the performance of the proposed
algorithm, thereby requiring fewer samples to yield an approximate
reconstruction.Comment: 28 pages, 9 figures, accepted in IEEE Transactions on Signal
Processin
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