Robust regression and outlier detection
Robust regression and outlier detection
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution
Signal Processing - Sparse approximations in signal and image processing
A sparse signal reconstruction perspective for source localization with sensor arrays
IEEE Transactions on Signal Processing - Part II
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
On sparse representation in pairs of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Time difference localization in the presence of outliers
Signal Processing
| Hi-index | 35.68 |
Precise localization have attracted considerable interest in the engineering literature. Most publications consider small measurement errors. In this work we discuss localization in the presence of outliers, where several measurements are severely corrupted while sufficient other measurements are reasonably precise. It is known that maximum likelihood or least squares provide poor results under these conditions. On the other hand, robust regression can successfully handle up to 50% outliers but is associated with high complexity. Using the l1 norm as the penalty function provides some immunity from outliers and can be solved efficiently with linear programming methods. We use linear equations to describe the localization problem and then we apply the l1 norm and linear programming to detect the outliers and avoid the wild measurements in the final solution. Our main contribution is an exploitation of recent results in the field of sparse representation to obtain bounds on the number of detectable outliers. The theory is corroborated by simulations and by real data.