Local directional denoising

Denoising of complex-valued signals involves the relationships between the real and imaginary parts of the signal. The authors introduce the idea of local directional thresholding, well-suited to signals that are bidirectional overall but unidirectional at any one time, such as Doppler ultrasound, and show its efficacy on synthetic and real data.

[1]  T. R. Downie,et al.  The discrete multiple wavelet transform and thresholding methods , 1998, IEEE Trans. Signal Process..

[2]  C. Sidney Burrus,et al.  Complex wavelet transforms with allpass filters , 2003, Signal Process..

[3]  B. Silverman,et al.  The Stationary Wavelet Transform and some Statistical Applications , 1995 .

[4]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[5]  Sofia C. Olhede,et al.  'Analytic' wavelet thresholding , 2004 .

[6]  I. Johnstone,et al.  Adapting to unknown sparsity by controlling the false discovery rate , 2005, math/0505374.

[7]  Fabrice Labeau,et al.  Discrete Time Signal Processing , 2004 .

[8]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[9]  Sylvain Sardy.  Minimax threshold for denoising complex signals with Waveshrink , 2000, IEEE Trans. Signal Process..

[10]  Jr. S. Marple,et al.  Computing the discrete-time 'analytic' signal via FFT , 1999, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[11]  Richard G. Baraniuk,et al.  Multiple Window Time Varying Spectrum Estimation , 2000 .

[12]  C. Burrus,et al.  Noise reduction using an undecimated discrete wavelet transform , 1996, IEEE Signal Processing Letters.

[13]  Mark A. Poletti,et al.  The homomorphic analytic signal , 1997, IEEE Trans. Signal Process..

[14]  Michael R. Chernick,et al.  Wavelet Methods for Time Series Analysis , 2001, Technometrics.

[15]  A. T. Walden,et al.  Polarization phase relationships via multiple Morse wavelets. II. Data analysis , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[16]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[17]  N. Kingsbury.  Image processing with complex wavelets , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  G. Nason,et al.  Real nonparametric regression using complex wavelets , 2004 .

[19]  P. Abry,et al.  Multiresolution transient detection , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[20]  M. Shaker Sabri,et al.  Discrete Hilbert transform filtering , 1976, ICASSP.

[21]  D. Donoho,et al.  Translation-Invariant DeNoising , 1995 .

[22]  Sofia C. Olhede,et al.  Noise reduction in directional signals using multiple Morse wavelets illustrated on quadrature Doppler ultrasound , 2003, IEEE Transactions on Biomedical Engineering.