Rank M-type Filters for Image Denoising

Many different classes of filters have been proposed for removing noise from images (Astola & Kuosmanen, 1997; Bovik, 2000; Kotropoulos & Pitas, 2001). They are classified into several categories depending on specific applications. Linear filters are efficient for Gaussian noise removal but often distort edges and have poor performance against impulsive noise. Nonlinear filters are designed to suppress noise of different nature, they can remove impulsive noise and guarantee detail preservation. Rank order based filters have received considerable attention due to their inherent outlier rejection and detail preservation properties. In the last decade, many useful techniques of multichannel signal processing based on vector processing have been investigated due to the inherent correlation that exists between the image channels compared to traditional component-wise approaches. Many applications of this technique are color image processing, remote sensing, robot vision, biomedical image processing, and high-definition television (HDTV). Different filtering techniques have been proposed for color imaging (Plataniotis & Venetsanopoulos, 2000). Particularly, nonlinear filters applied to color images have been designed to preserve edges and details, and remove impulsive noise. On the other hand, the filters based in the wavelet domain provide a better performance in terms of noise suppression in comparison with different spatial domain filters (Mahbubur Rahman & Kamrul Hasan, 2003). The possibility to process 3D images presents a new application where it is necessary to improve the quality of 3D objects inside the image, suppressing a noise of different nature (impulsive, Gaussian noise, or may be by speckle one) that always affects the communication or acquisition process (Nikolaidis & Pitas, 2001). Multiplicative (speckle) noise is common for any system using a coherent sensor, for example, the ultrasound transducer. Other problem that is not trivial is the adaptation and implementation of the current filters, that have been investigated in different papers in the case of 2D image processing to process objects in 3D by use multiframe methods to increase the signal-tonoise ratio (SNR). This chapter presents the capability features of robust Rank M-Type K-Nearest Neighbor (RMKNN) and Median M-Type L(MML) filters for the removal of impulsive noise in grayscale image processing applications (Gallegos & Ponomaryov, 2004; Gallegos-Funes et al., 2005; Gallegos-Funes et al., 2008). The proposed scheme is based on combined robust R(median, Wilcoxon, Ansari-Bradley-Siegel-Tukey or Mood) and M-estimators, and modification of the KNN and Lfilters that use the RM (Rank M-type) -estimator to calculate