Robust Transforms Based on the Weighted Median Operator

• Published in: IEEE signal processing letters Vol. 22; no. 1; pp. 120 - 124
• Main Authors: Ramirez, Juan Marcos, Paredes, Jose Luis
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-01-2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Audio denoising; Deviation; Dispersion; Estimation; Fourier transforms; Laplace equations; Mathematical models; Noise; Operators; Regression; robust transforms; Robustness; Signal processing algorithms; Transforms; unitary transforms; weighted median; {\ell _1} -LAD
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2014.2349351

In this letter, we propose a robust algorithm for determining a unitary transform of a discrete-time signal, whose samples are sensed in impulsive noise environments. The proposed algorithm estimates the transformed signal coefficients by solving an ℓ 1 -regularized least absolute deviation (ℓ 1 -LAD) regression problem, leading to the weighted median (WM) as the optimal operator for computing each transform coefficient. Numerical simulations on synthetic data are presented in order to compare the performance of the proposed algorithm to those yielded by previously reported methods. Furthermore, an example of audio denoising using the short time Fourier transform of a digital audio record, in the presence of impulsive noise, is also shown.