Performance analysis of the two-state signal-dependent rank order mean filter

One well-studied image processing task is the removal of impulse noise from images. Impulse noise can be introduced during image capture, during transmission, or during storage. The signal-dependent rank order mean (SD-ROM) filter has been shown to be effective at removing impulses from 2-D scalar- valued signals. Excellent results were presented for both a two-state and a multi-state version of the filter. The two- state SD-ROM filter relies on the selection of a set of threshold values. In this paper, we examine the performance of the algorithm with respect to the thresholds. We take three different approaches. First, we discuss the performance of the algorithm with respect to its root signals. Second, we present a probabilistic model for the SD-ROM filter. This model characterizes the performance of the algorithm in terms of the probability of detecting a corrupted pixel while avoiding uncorrupted pixels. Finally, we apply the insight gained from the root signal analysis and the statistical model to optimized thresholds found using a computerized search algorithm for a large number of images and noise conditions.

[1]  Sanjit K. Mitra,et al.  An efficient method for the removal of impulse noise from speech and audio signals , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[2]  J. Astola,et al.  Fundamentals of Nonlinear Digital Filtering , 1997 .

[3]  John W. Tukey,et al.  Nonlinear (nonsuperposable) methods for smoothing data , 1974 .

[4]  Sanjit K. Mitra,et al.  A simple algorithm for restoration of images corrupted by streaks , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[5]  Y. Neuvo,et al.  An efficient tool for analyzing weighted median filters , 1994 .

[6]  G. Eichmann,et al.  Vector median filters , 1987 .

[7]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[8]  Michael L. Lightstone,et al.  A new efficient approach for the removal of impulse noise from highly corrupted images , 1996, IEEE Trans. Image Process..

[9]  Edward J. Coyle,et al.  Root properties and convergence rates of median filters , 1985, IEEE Trans. Acoust. Speech Signal Process..

[10]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[11]  T. Nodes,et al.  The Output Distribution of Median Type Filters , 1984, IEEE Trans. Commun..

[12]  Yrjö Neuvo,et al.  Detail-preserving median based filters in image processing , 1994, Pattern Recognit. Lett..