Volterra Filtering Techniques for Removal of Gaussian and Mixed Gaussian-Impulse Noise

Authors: M. B. Meenavathi, K. Rajesh

Abstract:

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is proposed to optimize the trade-off between noise removal and edge preservation. In this paper, we consider both the Gaussian and mixed Gaussian-impulse noise to test the robustness of the filter. Image enhancement and restoration results using the proposed Volterra filter are found to be superior to those obtained with standard linear and nonlinear filters.

Keywords: Gaussian noise, Image enhancement, Imagerestoration, Linear filters, Nonlinear filters, Volterra series.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080392

References:

[1] Ioannis Pitas, Anastasias N Venetsanopoulos, Nonlinear Digital Filters Principles and Applications (NJ: Springer Publisher, 1990).
[2] Sanjit K. Mitra and Giovanni L .Sicuranza, Nonlinear Image Processing (NJ: Academic Press, 2001).
[3] G.Ramponi and G.L.Sicuranza, Quadratic Digital Filters for Image Processing, IEEE Transactions on Acoustics, Speech and Signal processing, 36(6), 1988, 937-939.
[4] Ian.J.Morrison and Peter J.W.Rayner, The Application of Volterra Series to Signal Estimation, IEEE Transactions on Image Processing, 1991, 1481-1484.
[5] Klaus Rank and Rolf Unbehauen, An Adaptive Recursive 2-D Filter for Removal of Gaussian Noise in Images, IEEE Transactions on Image Processing, 1(3), 1992, 431-436
[6] Robert D.Nowarts, Barry D Van Veen, Reduced Parameter Volterra Filters, IEEE Transactions on Image Processing, 1569-1572, 1995.
[7] Rui J.P.deFigueiredo and Sean C.Matz, Exponential Nonlinear Volterra Filter for Contrast Sharpening in Noisy Images, IEEE Transactions on Image Processing,1996, 2263-2266.
[8] Stefan Thurnhofer and Sanjit K. Mitra, A General Frame work for Quadratic Volterra Filters for Edge Enhancement, IEEE Transactions on Image Processing, 5(6), 1996, 950-962.
[9] S.Haykin, Adaptive Filter Theory, (Englewood Cliffs, NJ: Prentice-Hall, 1996).
[10] C.Kortopoulos and I. Pitas, Constrained adaptive LMS L-filters, Signal Process, 26, 1992, 335-358.
[11] Giovanni F. Ramponi Giovanni L.Sicuranza. A computational method for the design of 2D nonlinear Volterra filters, IEEE Transactions on circuits and systems, 35(9), 1988, 1095-1102.
[12] Giovanni F. Ramponi, Edge extraction by a class of second order nonlinear filters, Electronic letters, 22(9), 1986, 482-484.