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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper proposes a wavelet neural network (WNN) for SAR image segmentation by combining the wavelet transform and an artificial neural network. The WNN combines the multiscale analysis ability of the wavelet transform and the classification capability of the artificial neural network by setting the wavelet function as the transfer function of the neural network. Several SAR images are segmented by the network whose transfer functions are the Morlet and Mexihat functions, respectively. The experimental results show the proposed method is very effective and accurate.

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 [

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 [

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 _{x}

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 [

The reason for the application of WNN in case of such a problem as classification is that the feature extraction and representation properties of the wavelet transform are merged into the structure of the ANN to further extend the ability to approximate complicated patterns.

The WNN can be considered an expanded perceptron in which the neurons of the first layer are replaced by wavelet nodes [

The WNN employed in this paper is designed as a three-layer structure with an input layer, a wavelet layer, and an output layer. The topological structure of the WNN is illustrated in _{i}_{1}, _{2}, …., _{n}], the output of the _{i}_{k}_{k}

The output of the third layer is the weighted sum of _{k}

Wavelet network training consists of minimizing the usual least-squares cost function:
_{j}

Due to the fact that wavelets are rapidly vanishing functions, a wavelet may be too local if its dilation parameter is too small and it may sit out of the domain of interest if the translation parameter is not chosen appropriately.

Therefore, it is inadvisable to initialize the dilations and translations randomly, as is usually the case for the weights of a standard neural network with sigmoid activation function. We use the following initialization procedure, setting.

The same value to dilation parameter _{k}_{k}

The partial derivative of parameters

We adjust the parameters by the following equation:
^{T}

We applied the proposed method to two SAR images sized 256 × 256 pixels [

First, about 100 samples were selected as the training data. In our experiment, the initial value of _{k}_{k}^{−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.

The authors would like to thank the anonymous reviewers for their detailed comments and questions which improved the quality of the presentation of this paper. This work is supported in part by the National Natural Science Foundation of China (No. 60872064 No. 60375003), the Tianjin Natural Science Foundation (08JCYBJC12300) (08JCYBJC12200), the Science Foundation of Tianjin University of Technology (2006BA15).

Wavelet Neural Network Structure.

(a) Original SAR image. (b) Segmented image obtained using WNN(Mexihat). (c) Segmented image obtained using WNN(Morlet).

Convergence curve for WNN.

Comparison of mean square of the WNN(Mexihat) and WNN(Morlet).

26.256 | 21.0044 | |

83.69 | 66.406 |