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

ABSTRACT Weighted median filters are increasingly being used in signal processing applications and thus fast implementations are of importance. This paper introduces a fast algorithm to compute the weighted median of N samples which has linear time and space complexity as opposed to O(N logN) which is the time complexity of traditional sorting algorithms. The proposed algorithm is based on Quickselect which is closely related to the well known Quicksort. We compare the runtime and the complexity to Floyd and Rivest's algorithm SELECT which to date has been the fastest median finding algorithm and show that our algorithm is up to 30% faster.

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    ABSTRACT: In this paper, we address the compressive sensing signal reconstruction problem by solving an ℓ0-regularized Least Absolute Deviation (LAD) regression problem. A coordinate descent algorithm is developed to solve this ℓ0-LAD optimization problem leading to a two-stage 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 shifted-and-scaled 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; 59:2585-2601. · 2.81 Impact Factor


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