Name
Title | ||
|---|---|---|
Bayesian compressed sensing of a highly impulsive signal in heavy-tailed noise using a multivariate Cauchy prior |
Abstract | ||
|---|---|---|
Recent studies reveal that if a signal is highly compressible in some orthonormal basis, then an accurate reconstruction can be obtained from random projections using a very small subset of the projec- tion coefficients, and thus, reducing the complexity of the sensing system. A Bayesian framework was introduced recently with re- spect to the reconstruction of the original (noisy) signal, providing some advantages when compared with reconstruction methods, em- ploying norm-based constrained minimization approaches. These Bayesian methods were designed by using mixtures of Gaussians to approximate the sparsity of the prior distribution of the projection coefficients. However, there are cases in which a signal exhibits a highly impulsive behavior, and thus, resulting in an even sparser co- efficient vector. In this paper, we develop a Bayesian approach for estimating the original signal based on a set of compressed-sensing measurements corrupted by heavy-tailed noise. The prior belief that the vector of projection coefficients should be sparse is enforced by fitting its prior distribution by means of a heavy-tailed multivariate Cauchy distribution. The experimental results show that our pro- posed method achieves an improved reconstruction performance, in terms of a smaller reconstruction error, while increasing the sparsity using less basis functions, compared with the recently introduced Gaussian-based Bayesian implementation. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.5281/zenodo.41590 | EUSIPCO |
Keywords | Field | DocType |
bayes methods,gaussian processes,compressed sensing,minimisation,mixture models,random processes,signal reconstruction,vectors,bayesian compressed sensing,gaussian mixtures,heavy-tailed multivariate cauchy distribution,heavy-tailed noise,highly impulsive signal,norm-based constrained minimization,random projection,sparser coefficient vector | Frequency domain,Mathematical optimization,Multivariate statistics,Algorithm,Cauchy distribution,Gaussian,Orthonormal basis,Basis function,Prior probability,Mathematics,Bayesian probability | Conference |
ISBN | Citations | PageRank |
978-161-7388-76-7 | 3 | 0.56 |
References | Authors | |
8 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| George Tzagkarakis | 1 | 139 | 17.94 |
| P. Tsakalides | 2 | 954 | 120.69 |