The synthetic aperture radar (SAR) system is a powerful tool for observing the Earth under all weather conditions. In recent years, SAR imaging has been rapidly gaining prominence in applications such as remote sensing, surface surveillance and automatic target recognition. Segmentation of SAR images is a critical preliminary operation in various SAR images processing applications, such as target detection, recognition, and image compression.

SAR images characteristically have a particular kind of noise, called speckle, which occurs by random interferences, either constructive or destructive, between electromagnetic waves from different reflections in the imaged area. This makes SAR segmentation a difficult task, though several different segmentation methods designed specifically for SAR images have been proposed. Three common methods are optical image segmentation after speckle filter, the multiscale method [1–3], and the neural networks method [4,5].

Artificial neural networks (ANNs) are a class of computational architectures that are composed of interconnected, simple processing nodes with weighted interconnections. Neural networks have proven to be a popular tool for knowledge extraction, pattern matching, and classification due to their capability of learning from examples with both linear and nonlinear relationships between the input and output signals. However, ANNs have limited ability to characterize local features, such as discontinuities in curvature, jumps in value or other edges, so these algorithma are not well suited for speckled SAR images. The wavelet transform, on the other hand, is efficient in representing and detecting local features in images due to the spatial and frequency localization properties of wavelet bases [6]. With the detection of local features, an object can be easily recognized. Many new algorithms based on wavelet transform have been developed to solve SAR image segmentation problems [7,8]. However, the feature-matching of these algorithms have some shortcomings. In order to ensure the reliability of the matching results, they all require an enormous number of scales to construct the time-frequency features at various scales during the classification process. Each scale corresponds to convolving the signal with a wavelet function; hence a large number of convolutions are needed for these algorithms, which make them computationally inefficient.

In this paper, a wavelet neural network (WNN) method is proposed for SAR image segmentation, which takes full advantages of the partial-resolution characteristic of the wavelet transform and the nonlinear mapping behavior of artificial neural networks.

This paper is organized as follows. In the next section, we will describe quadtree interpretation of SAR imagery and its mixture multiscale autoregressive (MMAR) modeling. In Section 3, we will propose a hybrid method based on the GA algorithm and EM algorithm for the MMAR model. In Section 4, we will present the experimental results. In Section 5, we will present a short conclusion concerning our algorithm.

In signal analysis applications, it is necessary to extract signal features with Fourier transformation, but it is only a time domain transform, which has no time-frequency localization features. The theory of wavelet transformation was first proposed in the field of multi-resolution analysis; among others, it has been applied to image and signal processing. A continuous wavelet transform (CWT) can decompose a signal into a set of finite basis functions, which can uncover transient characteristics in the signal. Wavelet analysis is the breaking up of a signal into dilations and translation versions of the original wavelet, referred to as the mother wavelet. The wavelet must be oscillatory, have amplitudes that quickly decay to zero, and have at least one vanishing moment. Wavelet coefficients W_x(a, τ) are produced through the convolution of a mother wavelet function ψ(t) with the analyzed signal f(t), it is: (1) W x   ( a , τ ) = 1 | a |   ∫   f ( t ) ψ ( t − τ a ) dtwhere a and τ denote the scale and local center of the analyzing wavelet. By adjusting the scale, a, a series of different frequency components in the signal can be obtained.

Several wavelet mother functions have been proposed in the wavelet theory. Each mother function has its suitable application. In this work, the wavelet employed is the Morlet Wavelet, due to its directional selectiveness capability of detecting oriented features, fine tuning to specific frequencies and its good localization in time and frequency [9]. This is a sinusoidal signal modulated by a Gaussian wave. It is characterized for its narrow frequency response, which offers a higher spectral resolution than the Mexican Hat wavelet. This wavelet is particularly useful for filtering out the background noise of the images. In this paper, the Morlet wavelet is applied as: (2) ψ a , τ   ( t ) = e − t i 2 / 2   cos ( 5 t i )where t i = t − τ a.

We applied the proposed method to two SAR images sized 256 × 256 pixels [Figure 2(a)] to demonstrate the differences between the Morlet and Mexihat procedures; these images include two regions.

First, about 100 samples were selected as the training data. In our experiment, the initial value of t_k is decided by Equation (6)d_k = 2, and ω is a random value between −0.5∼0.5. When the neuron number of the wavelet layer is 25, the segmentation results are best. The compared segmentation results are shown in Figure 2, with (b) showing the Mexihat Wavelet mother function as the transfer function of the second layer and (c) showing the Morlet Wavelet as the transfer function of the second layer. Table 1 is a comparison of the mean square of the above images. It shows that the accuracy ratio of the WNN using Morlet as the transfer function is higher than that of the WNN using Mexihat as the transfer function. Figure 3 is the convergence curve of the WNN training algorithm, which shows the error is almost 10⁻² by the 25^th iteration.

In this paper, an effective wavelet neural network for SAR image segmentation is proposed. The method not only has the feature of multiscale analysis, but also has a good performance in classification. Experimental results show that using Morlet as the transfer function is better than using Mexihat. WNN is an effective and accurate method for SAR image segmentation.