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Order statistic filters are used often in the applications of science and engineering problems. This paper investigates the design and training of a feed-forward neural network to approximate minimum, median and maximum operations. The design of order statistic neural network filtering (OSNNF) is further refined by converting the input vectors with elements of real numbers to a set of inputs consisting of ones and zeros, and the neural network is trained to yield a rank vector which can be used to obtain the exact ranked values of the input vector. As a case study, the OSNNF is used to improve the visibility of target echoes masked by clutter in ultrasonic nondestructive testing applications.

Order statistic (OS) processors have been widely used in the field of signal and image processing [1-3]. OS results can be obtained by sorting the elements of an input vector according to the rank of each element. Ranked outputs such as minimum, median and maximum have been used for target detection with applications in radar, sonar and ultrasonic nondestructive testing [4,5]. The problem of sorting has already been solved by sequential and iterative methods such as the bubble sort, selection sort, insertion sort, and quick sort with computational efficiency ranging between O(NlogN) and O(N^{2}) comparisons and swapping operations [

In this paper, feed-forward neural network models [

In practice, it is desirable to develop an efficient neural network model that can be used in finding the estimates of minimum, median, and maximum of the input vectors. To achieve this, simulation data is used in the training phase. The training set of data consists of random numbers with uniform distribution scaled between zero and one. Then, the neural network is trained to yield the ranked output (e.g., the minimum, the median or the maximum value of the input vector with real numbers). In the next section we present the design techniques for the neural network OS filters. Section 3 discusses an improved neural network solution that finds the rank of each input in order to reveal the exact sorted result. Section 4 utilizes these neural network filters to enhance the visibility of target echoes in high scattering clutter using split-spectrum processing (SSP).