Conference Paper
A fast weighted median algorithm based on Quickselect
Dept. of Electr. & Comput. Eng., Univ. of Delaware, Delaware, OH, USA
DOI: 10.1109/ICIP.2010.5651855 Conference: Image Processing (ICIP), 2010 17th IEEE International Conference on Source: IEEE Xplore

Conference Paper: Compressive sensing signal reconstruction by weighted median regression estimates.
[Show abstract] [Hide abstract]
ABSTRACT: In this paper, we propose a simple and robust algorithm for compressive sensing (CS) signal reconstruction based on the weighted median (WM) operator. The proposed approach addresses the reconstruction problem by solving a l<sub>0</sub>regularized least absolute deviation (l<sub>0</sub>LAD) regression problem with a tunable regularization parameter, being suitable for applications where the underlying contamination follows a statistical model with heavierthanGaussian tails. The solution to this regularized LAD regression problem is efficiently computed, under a coordinate descent framework, by an iterative algorithm that comprises two stages. In the first stage, an estimation of the sparse signal is found by recasting the reconstruction problem as a parameter location estimation for each entry in the sparse vector leading to the minimization of a sum of weighted absolute deviations. The solution to this onedimensional minimization problem turns out to be the WM operator acting on a shiftedandscaled version of the measurement samples with weights taken from the entries in the measurement matrix. The resultant estimated value is then passed to a second stage that identifies whether the corresponding entry is relevant or not. This stage is achieved by a hard threshold operator with adaptable thresholding parameter that is suitably tuned as the algorithm progresses. This twostage operation, WM operator followed by a hard threshold operator, adds the desired robustness to the estimation of the sparse signal and, at the same time, ensures the sparsity of the solution. Extensive simulations demonstrate the reconstruction capability of the proposed approach under different noise models. We compare the performance of the proposed approach to those yielded by stateoftheart CS reconstruction algorithms showing that our approach achieves a better performance for different noise distributions. In particular, as the distribution tails become heavier the performance gai n achieved by the proposed approach increases significantly.Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010, 1419 March 2010, Sheraton Dallas Hotel, Dallas, Texas, USA; 01/2010  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we address the compressive sensing signal reconstruction problem by solving an ℓ0regularized Least Absolute Deviation (LAD) regression problem. A coordinate descent algorithm is developed to solve this ℓ0LAD optimization problem leading to a twostage operation for signal estimation and basis selection. In the first stage, an estimation of the sparse signal is found by a weighted median operator acting on a shiftedandscaled version of the measurement samples with weights taken from the entries of the projection matrix. The resultant estimated value is then passed to the second stage that tries to identify whether the corresponding entry is relevant or not. This stage is achieved by a hard threshold operator with adaptable thresholding parameter that is suitably tuned as the algorithm progresses.IEEE Transactions on Signal Processing 01/2011; 59:25852601. · 2.81 Impact Factor
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.