By Topic

Variance-Component Based Sparse Signal Reconstruction and Model Selection

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Kun Qiu ; Dept. of Electr. & Comput. Eng., Iowa State Univ., Ames, IA, USA ; Dogandzic, A.

We propose a variance-component probabilistic model for sparse signal reconstruction and model selection. The measurements follow an underdetermined linear model, where the unknown regression vector (signal) is sparse or approximately sparse and noise covariance matrix is known up to a constant. The signal is composed of two disjoint parts: a part with significant signal elements and the complementary part with insignificant signal elements that have zero or small values. We assign distinct variance components to the candidates for the significant signal elements and a single variance component to the rest of the signal; consequently, the dimension of our model's parameter space is proportional to the assumed sparsity level of the signal. We derive a generalized maximum-likelihood (GML) rule for selecting the most efficient parameter assignment and signal representation that strikes a balance between the accuracy of data fit and compactness of the parameterization. We prove that, under mild conditions, the GML-optimal index set of the distinct variance components coincides with the support set of the sparsest solution to the underlying underdetermined linear system. Finally, we propose an expansion-compression variance-component based method (ExCoV) that aims at maximizing the GML objective function and provides an approximate GML estimate of the significant signal element set and an empirical Bayesian signal estimate. The ExCoV method is automatic and demands no prior knowledge about signal-sparsity or measurement-noise levels. We also develop a computationally and memory efficient approximate ExCoV scheme suitable for large-scale problems, apply the proposed methods to reconstruct one- and two-dimensional signals from compressive samples, and demonstrate their reconstruction performance via numerical simulations. Compared with the competing approaches, our schemes perform particularly well in challenging scenarios where the noise is large or the number of measure- - ments is small.

Published in:

Signal Processing, IEEE Transactions on  (Volume:58 ,  Issue: 6 )