Five different constant false alarm rate (CFAR) radar processing schemes are considered and their performances analyzed in homogeneous and nonhomogeneous backgrounds, the latter specifically being the multiple target environment and regions of clutter transitions. The average detection threshold for each of the CFAR schemes was computed to measure and compare the detection performance in homogeneous noise background. The exponential noise model was used for clear and clutter backgrounds to get closed-form expressions. The processor types compared are: the cell-averaging CFAR, the 'greatest of' CFAR, the 'smallest of' CFAR, the ordered-statistics CFAR, and a modified ordered-statistics processor called the trimmed-mean CFAR. >

Analysis of CFAR processors in homogeneous background

A family of nonlinear filters based on order statistics is presented. A mathematical tool derived through robust estimation theory, order statistics has allowed engineers to develop nonlinear filters with excellent robustness properties. These filters are well suited to digital image processing because they preserve the edges and the fine details of an image much better than conventional linear filters. The probabilistic and deterministic properties of the best known and most widely used filter in this family, the median filter, are discussed. In addition, the authors consider filters that, while not based on order statistics, are related to them through robust estimation theory. A table that ranks nonlinear filters under a variety of performance criteria is included. Most of the topics treated are very active research areas, and the applications are varied, including HDTV, multichannel signal processing of geophysical and ECG/EEG data, and a variety of telecommunications applications. >

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Order statistics in digital image processing

Wavelet-based denoising using subband dependent threshold for ECG signals

Summary form only given. Two approaches have been used in the past to design rank-order-based nonlinear filters to enhance or restore images: the structural approach and the estimation approach. The first approach requires structural descriptions of the image and the process which has altered it, whereas the second required statistical descriptions. The many different classes of rank-order-based filters that have been developed over the last few decades have been reviewed in the context of these two approaches. One of these filter classes, stack filters, has been investigated. These filters, which are defined by a weak superposition property and an ordering property, contain all compositions of 2D rank-order operations. The recently developed theory of minimum-mean-absolute-error (MMAE) stack filtering has been extended to two dimensions. A theory of optimal stack filtering under structural constraints and goals has been developed for the structural approach to image processing. These two optimal stack filtering theories have been combined into a single design theory for rank-order-based filters. >

Optimal stack filtering and the estimation and structural approaches to image processing

Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the median-related filters known as rank-order filters, order-statistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since the days of Fourier, Laplace, and “Convolute.” We trace the development of this theory of nonlinear filtering from its beginnings in the study of noise-removal properties and structural behavior of the median filter to the recently developed theory of optimal stack filtering. The theory of stack filtering provides a point of view which unifies many different filter classes, including morphological filters, so it is discussed in detail. Of particular importance is the way this theory has brought together, in a single analytical framework, both the estimation-based and the structural-based approaches to the design of these filters. Some recent applications of median and stack filters are provided to demonstrate the effectiveness of this approach to nonlinear filtering. They include: the design of an optimal stack filter for image restoration; the use of vector median filters to attenuate impulsive noise in color images and to eliminate cross luminance and cross color in TV images; and the use of median-based filters for image sequence coding, reconstruction, and scan rate conversion in normal TV and HDTV systems.

An overview of median and stack filtering

The statistical properties of two classes of filters generalizing the median filter are considered. The two classes are the alpha-trimmed mean ( alpha -TM) filter and the standard type M(STM) filter, both of which are special cases of the L filter. Results are developed to quantify the white-noise suppression and edge-preservation characteristics of the filters by considering their output sequence error statistics. It is shown that the alpha -TM and STM filters perform better than the running mean and median filters in white noise suppression, while they can be designed to be comparable to the median filter in edge preservation in the presence of noise. >

S.R. Peterson

Papers

Some statistical properties of alpha-trimmed mean and standard type M filters