23,284 research outputs found
Robust Linear Regression Analysis - A Greedy Approach
The task of robust linear estimation in the presence of outliers is of
particular importance in signal processing, statistics and machine learning.
Although the problem has been stated a few decades ago and solved using
classical (considered nowadays) methods, recently it has attracted more
attention in the context of sparse modeling, where several notable
contributions have been made. In the present manuscript, a new approach is
considered in the framework of greedy algorithms. The noise is split into two
components: a) the inlier bounded noise and b) the outliers, which are
explicitly modeled by employing sparsity arguments. Based on this scheme, a
novel efficient algorithm (Greedy Algorithm for Robust Denoising - GARD), is
derived. GARD alternates between a least square optimization criterion and an
Orthogonal Matching Pursuit (OMP) selection step that identifies the outliers.
The case where only outliers are present has been studied separately, where
bounds on the \textit{Restricted Isometry Property} guarantee that the recovery
of the signal via GARD is exact. Moreover, theoretical results concerning
convergence as well as the derivation of error bounds in the case of additional
bounded noise are discussed. Finally, we provide extensive simulations, which
demonstrate the comparative advantages of the new technique
Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Related
This paper considers a recently emerged hyperspectral unmixing formulation
based on sparse regression of a self-dictionary multiple measurement vector
(SD-MMV) model, wherein the measured hyperspectral pixels are used as the
dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is
special in that it allows simultaneous identification of the endmember spectral
signatures and the number of endmembers. Previous SD-MMV studies mainly focus
on convex relaxations. In this study, we explore the alternative of greedy
pursuit, which generally provides efficient and simple algorithms. In
particular, we design a greedy SD-MMV algorithm using simultaneous orthogonal
matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be
closely related to some existing pure pixel search algorithms, especially, the
successive projection algorithm (SPA). Thus, a link between SD-MMV and pure
pixel search is revealed. We then perform exact recovery analyses, and prove
that the proposed greedy algorithm is robust to noise---including its
identification of the (unknown) number of endmembers---under a sufficiently low
noise level. The identification performance of the proposed greedy algorithm is
demonstrated through both synthetic and real-data experiments
Multichannel sparse recovery of complex-valued signals using Huber's criterion
In this paper, we generalize Huber's criterion to multichannel sparse
recovery problem of complex-valued measurements where the objective is to find
good recovery of jointly sparse unknown signal vectors from the given multiple
measurement vectors which are different linear combinations of the same known
elementary vectors. This requires careful characterization of robust
complex-valued loss functions as well as Huber's criterion function for the
multivariate sparse regression problem. We devise a greedy algorithm based on
simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Unlike
the conventional SNIHT method, our algorithm, referred to as HUB-SNIHT, is
robust under heavy-tailed non-Gaussian noise conditions, yet has a negligible
performance loss compared to SNIHT under Gaussian noise. Usefulness of the
method is illustrated in source localization application with sensor arrays.Comment: To appear in CoSeRa'15 (Pisa, Italy, June 16-19, 2015). arXiv admin
note: text overlap with arXiv:1502.0244
Nonparametric Simultaneous Sparse Recovery: an Application to Source Localization
We consider multichannel sparse recovery problem where the objective is to
find good recovery of jointly sparse unknown signal vectors from the given
multiple measurement vectors which are different linear combinations of the
same known elementary vectors. Many popular greedy or convex algorithms perform
poorly under non-Gaussian heavy-tailed noise conditions or in the face of
outliers. In this paper, we propose the usage of mixed norms on
data fidelity (residual matrix) term and the conventional -norm
constraint on the signal matrix to promote row-sparsity. We devise a greedy
pursuit algorithm based on simultaneous normalized iterative hard thresholding
(SNIHT) algorithm. Simulation studies highlight the effectiveness of the
proposed approaches to cope with different noise environments (i.i.d., row
i.i.d, etc) and outliers. Usefulness of the methods are illustrated in source
localization application with sensor arrays.Comment: Paper appears in Proc. European Signal Processing Conference
(EUSIPCO'15), Nice, France, Aug 31 -- Sep 4, 201
Computational Methods for Sparse Solution of Linear Inverse Problems
The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications
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