Additive and exclusive noise suppression by iterative trimmed and truncated mean algorithm

An iterative trimmed and truncated arithmetic mean (ITTM) algorithm is proposed, and the ITTM filters are developed. Here, trimming a sample means removing it and truncating a sample is to replace its value by a threshold. Simultaneously trimming and truncating enable the proposed filters to attenuate the mixed additive and exclusive noise in an effective way. The proposed trimming and truncating rules ensure that the output of the ITTM filter converges to the median. It offers an efficient method to estimate the median without time-consuming data sorting. Theoretical analysis shows that the ITTM filter of size n has a linear computational complexity O(n). Compared to the median filter and the iterative truncated arithmetic mean (ITM) filter, the proposed ITTM filter suppresses noise more effectively in some cases and has lower computational complexity. Experiments on synthetic data and real images verify the filter's properties.

[1]  Xudong Jiang,et al.  Iterative Truncated Arithmetic Mean Filter and Its Properties , 2012, IEEE Transactions on Image Processing.

[2]  Kenneth E. Barner,et al.  Affine order-statistic filters: "medianization" of linear FIR filters , 1998, IEEE Trans. Signal Process..

[3]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[4]  Gonzalo R. Arce,et al.  Fast and Accurate Computation of the Myriad Filter via Branch-and-Bound Search , 2008, IEEE Transactions on Signal Processing.

[5]  Yong Hoon Lee,et al.  Generalized median filtering and related nonlinear filtering techniques , 1985, IEEE Trans. Acoust. Speech Signal Process..

[6]  Dehua Li,et al.  Modified switching median filter for impulse noise removal , 2010, Signal Process..

[7]  Gonzalo R. Arce,et al.  Nonlinear Signal Processing - A Statistical Approach , 2004 .

[8]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[9]  Rui J. P. de Figueiredo,et al.  Adaptive alpha-trimmed mean filters under deviations from assumed noise model , 2004, IEEE Trans. Image Process..

[10]  Wei Wang,et al.  An Efficient Switching Median Filter Based on Local Outlier Factor , 2011, IEEE Signal Processing Letters.

[11]  Xudong Jiang,et al.  Image detail-preserving filter for impulsive noise attenuation , 2003 .

[12]  Patrenahalli M. Narendra,et al.  A Separable Median Filter for Image Noise Smoothing , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Wei An,et al.  Fuzzy Ordering Theory and Its Use in Filter Generalization , 2001, EURASIP J. Adv. Signal Process..

[14]  G. Grimmett,et al.  Probability and random processes , 2002 .

[15]  Ching-Te Chiu,et al.  Switching bilateral filter with a texture/noise detector for universal noise removal , 2010, ICASSP.

[16]  Kenneth E. Barner,et al.  Generalized Mean-Median Filtering for Robust Frequency-Selective Applications , 2007, IEEE Transactions on Signal Processing.

[17]  Srdjan Stankovic,et al.  An Implementation of the L-Estimate Distributions for Analysis of Signals in Heavy-Tailed Noise , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  Wen-June Wang,et al.  Fuzzy reasoning-based directional median filter design , 2009, Signal Process..

[19]  Xudong Jiang,et al.  Interest point detection using rank order LoG filter , 2013, Pattern Recognit..

[20]  Xudong Jiang,et al.  Further Properties and a Fast Realization of the Iterative Truncated Arithmetic Mean Filter , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  Rachid Harba,et al.  A New Adaptive Switching Median Filter , 2010, IEEE Signal Processing Letters.

[22]  Gonzalo R. Arce,et al.  Optimality of the myriad filter in practical impulsive-noise environments , 2001, IEEE Trans. Signal Process..

[23]  Dimitrios Charalampidis.  Steerable Weighted Median Filters , 2010, IEEE Transactions on Image Processing.

[24]  Xudong Jiang,et al.  A novel rank order LoG filter for interest point detection , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[25]  A. Ben Hamza,et al.  Image denoising: a nonlinear robust statistical approach , 2001, IEEE Trans. Signal Process..

[26]  Xudong Jiang,et al.  Weighted Iterative Truncated Mean Filter , 2013, IEEE Transactions on Signal Processing.

[27]  Gonzalo R. Arce,et al.  Fast algorithms for weighted myriad computation by fixed-point search , 2000, IEEE Trans. Signal Process..

[28]  Yong Hoon Lee,et al.  Some statistical properties of alpha-trimmed mean and standard type M filters , 1988, IEEE Trans. Acoust. Speech Signal Process..

[29]  J. Bednar,et al.  Alpha-trimmed means and their relationship to median filters , 1984 .