Impulse noise removal using polynomial approximation
Dapeng Zhang · Optical Engineering · 1998
A novel filtering algorithm is presented to restore images cor- rupted 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 deter- mine 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 improve- ments are obtained in comparison with other state-of-the-art algorithms. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)02904-3) Subject terms: image enhancement; image filter; impulse noise; noise detection; noise filtering; polynomial approximation.