Optical
Engineering, vol. 37, no. 4, pp. 1275-1282, Apr. 1998
Impulse Noise Removal
Using Polynomial Approximation
1 Department of Computer Science, City University of Hong Kong,
Hong Kong, China
2 Dept. of Communication & Electronic
Engineering, South China Univ. of Tech., Guangzhou,
China
Abstract:
A novel filtering algorithm is presented to
restore images corrupted by impulsive noise. As a preprocessing procedure of
the noise cancellation filter, an improved impulse detector is used to generate
a binary flag image, which gives each pixel a flag indicating whether it is an
impulse. This flag image has two uses: (1) a pixel is modified only when it is
considered as an impulse; otherwise, it is left unchanged, and (2) only the
values of the good pixels are employed as useful information by the noise
cancellation filter. To remove noises from the corrupted image, we propose a
new filter called a polynomial approximation (PA) filter, which is developed by
modeling a local region with a polynomial that can best approximate the region
under the condition of least squared error. Furthermore, an adaptive approach
is introduced to automatically determine the orders of the polynomials. The
proposed two kinds of PA filters, fixed-order and adaptive-order PA filters,
are tested on images corrupted by both fixed-valued and random-valued impulsive
noise. Major improvements are obtained in comparison with other
state-of-the-art algorithms.