FLANN detector based filtering of images corrupted by impulse noise

Journal of Computer Science, July, 2005 by Banshidhar Majhi, Mowafak Fathi

Abstract: We present a novel non-linear scheme for image restoration based on neuro-detector using Functional Link Artificial Neural Network (FLANN) followed by an improved spatial filter. The method is applied to images corrupted by impulse noise with varying strengths and different noise probability. The neural detector is based on the concept of training or learning by examples. When trained properly, the detector used to detect impulse noise in any image degraded by impulse noise. Hence, the method is suitable for real time image restoration applications. The simulated results obtained from the proposed scheme outperforms existing approaches are highly satisfactory and it outperforms the earlier suggested methods in terms of residual NSR in restored images.

Key words: Impulse Noise, Neural Network, Detection of Impulse Noise, Selective Filtering

INTRODUCTION

When images are acquired and processed, an original image may become degraded in various ways. Degradation may be in the form of random noise and interference, blur induced by camera mis-focus and motion, lens and film nonlinearity, impulse due to recording medium, and other mechanisms. Image restoration methods generally model the degradation process and apply an approximately inverse process to the degraded image to recover the original image [1]. The effectiveness of such image restoration techniques depends on the availability and completeness of knowledge about the degradation process as well as on the structure of the processing scheme implementing the restoration. Various image restoration methods have been proposed in the literature on digital image processing. Descriptions of image restoration techniques can be found in books on image processing such as [2]. Traditional image restoration methods are based on linear processing of image signals. Weiner filters [3] and recursive (Kalman) filters [4] fail under this category.

There are also nonlinear techniques for image restoration. These methods include maximum-likelihood [5] and maximum a posteriori (MAP) estimation technique [6]. Nonlinear methods based on modeling the degraded image, and hence called as model based methods.

However, very few works have been reported for impulse noise removal using nonlinear methods. A Double Derivative based impulse noise detection scheme is reported in [7]. Recently, the authors have proposed a fuzzy logic based impulse noise detection scheme [8], which performs better than the previous method [7] in terms of noise detection capability, edge retention, and noise removal. Another relatively new approach to model based image restoration uses Artificial Neural Network (ANN) filters. Hopfield type recurrent neural networks have been studied for restoration of images degraded by linear distortion [9,10]. ANN is also widely used for impulse noise detection and removal. When the impulse noise is of varying amplitude, a multi layer neural network is required. Such a work is reported in [11], which utilizes Radial Basis Function (RBF) network. In this paper, we propose a functional link neural network (FLANN) to detect the presence of an impulse of varying amplitude and if present, remove it by using improved spatial filtering. This scheme outweighs the earlier scheme proposed [11] in terms of noise rejection in dB. To construct the neural detector, we use supervised learning based on back propagation. It is assumed that the image does not contain any sharp rise or fall in grayness at any of the pixel positions. The details of detection and filtering process of the proposed scheme are given

Proposed Scheme: A general discrete time model for image degradation can be expressed as:

X(m, n) = Y (m, n) (m, n) (1)

where, Y(m, n) represents the original image, X(m, n) is the observed degraded image and (m, n) is the additive impulse noise of varying strengths added with a probability p. Since p << 1, it is desirable to filter only those pixels which are corrupted by noise to minimize blurring in the restored image. To attain this objective we propose a noise detection scheme in the test pixel location, followed by an improved spatial filtering, if at all the test pixel is corrupted. The detection and filtration processes are described below in detail.

Impulse Noise Detection

1. Consider a 3x3 test window XT from X (m, n) as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

2. Compute [sub.i]s, I = 1, ... ,4 as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

3. Pass all [sub.i]s through the FLANN detector which produces the output [O.sub.i,j].

4. The fuzzy rules for the impulse detection in a test pixel [x.sub.i,j] are

* If [O.sub.i,j] is high then the test pixel [x.sub.i,j] is corrupted.

If [O.sub.i,j] is low then the test pixel [x.sub.i,j] is not corrupted.

To obtain a binary decision regarding the presence of the impulse, [D.sub.i, j] is passed through a hard limiter (H) defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where, T is the threshold value.