Robust L-estimation based forms of signal transforms and time-frequency representations

• Published in: IEEE transactions on signal processing Vol. 51; no. 7; pp. 1753 - 1761
• Main Authors: Djurovic, I., Stankovic, L., Bohme, J.F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2003; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Applied sciences; Detection, estimation, filtering, equalization, prediction; Discrete transforms; Estimates; Estimation theory; Exact sciences and technology; Filters; Fourier transforms; Gaussian; Gaussian noise; Impulses; Information, signal and communications theory; Mathematical models; Maximum likelihood estimation; Noise; Noise robustness; Representations; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Telecommunications and information theory; Time frequency analysis; Transforms; Working environment noise; Additive noise; Performance evaluation; Time-frequency analysis; Signal estimation; Estimation theory; Fourier transform; Signal representation; signal transforms; time-frequency representations; Pulse noise; Gaussian noise; robust transforms; noise; median filter; Maximum likelihood; Hadamard transform; Wigner distribution
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2003.812739

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.