3 research outputs found
An overview of robust compressive sensing of sparse signals in impulsive noise
While compressive sensing (CS) has traditionally relied on L2 as an error norm, a broad spectrum of applications has emerged where robust estimators are required. Among those, applications where the sampling process is performed in the presence of impulsive noise, or where the sampling of the high-dimensional sparse signals requires the preservation of a distance different than L2. This article overviews robust sampling and nonlinear reconstruction strategies for sparse signals based on the Cauchy distribution and the Lorentzian norm for the data fidelity. The derived methods outperform existing compressed sensing techniques in impulsive environ- ments, thus offering a robust framework for CS
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
Robust compressive sensing of sparse signals: A review
Compressive sensing generally relies on the L2-norm for data fidelity, whereas in many applications robust estimators are needed. Among the scenarios in which robust performance is required, applications where the sampling process is performed in the presence of impulsive noise, i.e. measurements are corrupted by outliers, are of particular importance. This article overviews robust nonlinear reconstruction strategies for sparse signals based on replacing the commonly used L2-norm by M-estimators as data fidelity functions. The derived methods outperform existing compressed sensing techniques in impulsive environments, while achieving good performance in light-tailed environments, thus offering a robust framework for CS