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Synthetic aperture radar based on the matched filter theory has the ability of obtaining two-di- mensional image of the scattering areas. Nevertheless, the resolution and sidelobe level of SAR imaging is limited by the antenna length and bandwidth of transmitted signal. However, for sparse signals (direct or indirect), sparse imaging methods can break through limitations of the conventional SAR methods. In this paper, we introduce the basic theory of sparse representation and reconstruction, and then analyze several common sparse imaging algorithms: the greed algorithm, the convex optimization algorithm. We apply some of these algorithms into SAR imaging using RadBasedata. The results show the presented method based on sparse construction theory outperforms the conventional SAR method based on MF theory.

Due to the properties of all weather and day-night imaging [

For the moment, the most common and conventional methods for SAR imaging are based on matched filter (MF) theory [

1) The bandwidth of original transmitted signal decides the resolution of the range direction. The antenna length decided by the radar system determines the resolution of the azimuth direction. Therefore, we have great difficulty to achieve the high resolution SAR images with a low bandwidth signal and a short synthetic aperture length.

2) Limiting by the Nyquist rate, a large amount of SAR raw data will be collected which brings to a heavy burden to the radar system naturally.

3) The radar images obtained by conventional SAR imaging algorithm have a severe sidelobe which is a considerable problem to overcome.

In recent years, with the development of compressed sensing (CS) theory [

Some of the applications in radar field are listed as following. Compressive sensing data acquisition and imaging system had been applied in Ground Penetrating Radar (GPR). Through-wall radar imaging with the similar theme had been presented. By transmitting a noise-like signal (specially designed signal), the theory of CS with random convolution was used and high resolution radar was proposed. We can realize the fact that CS has got more and more attention and been more and more popular in radar applications, including relaxation of required measurements, improvement the resolution of radar system, reduction of sidelobe, and suppression of noise.

In some special applications (such as detection of ship on the sea, lights along the airline roads, and distribution of scattering points of warhead etc.), the main scattering targets appear in a sparse way over a big observed scene. The number of dominant scatters is much smaller than the total size of observed scene. In such a situation, SAR raw echo can be regarded as a sparse signal. Obviously, sparse construction method can be applied in SAR imaging widely. In order to explain what kind of method is more accurate, we apply the conventional method and sparse construction method into SAR imaging. The conventional MF method and the sparse construction method are compared in the same situation. The sparse construction method includes OMP, CoSaMP, LASSO, BP etc. Some numerical simulations are presented to evaluate the best method for SAR imaging. The indicators we take to evaluate the quality of SAR imaging include resolution of azimuth and range, sidelobe level and computation complexity etc.

The reminder of the paper is organized as follows. In Section 2, we give a brief description of basic theory of sparse representation and reconstruction. In Section 3, sparse SAR signal imaging through conventional method and sparse method is implemented and we analyze the imaging quality of different method. In Section 4, we get a conclusion that sparse method of BP is a good method for improving resolution and reducing the sidelobe obviously. At the same time, we propose some directions to discover in the following days.

If the signal only has a small number of nonzero vectors, then we consider it as a sparse signal. Usually, some signals is sparse in time domain, but in some transformdomain.

Considering a discrete signal vector

Therefore, the true information contained in signal s lives in at most K dimensions rather than N. The sparse signal s can be expressed as following.

() (1)

The model of signal s can also be expressed as

() (2)

where vector

According to the CS theory, the signal to be measured is acquired by linear projections

where

where

According to the existed theory, the k-sparse

where

However, the minimum

If the observed vector y and the measured matrix

If the noise is taken into consideration, the modified convex problem can be described as follows.

where

Recently, there are several sparse approximation algorithms to recover the sparse signal

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In order to use sparse theory, a linear measurement model of SAR should be created. According to (7), in discrete scenarios the raw echo signal of SAR can be expressed as

So, (8) can be expressed in vector form as

where

Due to the matrix

The real and imaginary part of measured signal can be calculated respectively as

We define the signal

Then (13) can be further replaced as

In order to explain what kind of method is more accurate, we apply the conventional method and sparse construction method into SAR imaging. The conventional MF method and the sparse construction method are compared in the same situation. We take two most common kinds of sparse construction methods, including OMP, BP. Simulations are all based on complex image in frequency domain.

Some numerical simulations with these three methods are presented to find the merits and drawbacks of sparse method and conventional method in SAR imaging. The indicators we have taken to evaluate the quality of SAR imaging include resolution of azimuth and range, side lobe level. Simulation data is a series of complicated point targets generated from RadBase.

AS is shown in Figures 1-6, BP method has a more clear imaging result and better resolution over FFT and

OMP. Imaging result with OMP carry more noise than BP and imaging result by FFT has a high side lobe. Obviously, targets can be distinguished from each other in BP. Convex optimization method outperforms over OMP method and FFT. In Data 1, the regularization parameter

In order to judge the imaging quality more intuitively, we choose the BP algorithm (Data 2, the regularization parameter

The BP method with a proper

The paper presents a series of sparse reconstruction method for SAR imaging. Compared with traditional MF method, the convex optimization method outperforms in high resolution and side lobe suppression and greatly improves the imaging quality. The pre-condition is that the signal is sparse in some domain (such as time, frequency, space etc.). Through a simple new strategy we proposed, we can easily find the best regularization parameter of sparse construction. Results show the effectiveness and feasibility of our method. However, there are still some challenges demanded to overcome in SAR imaging with sparse method. The computation complexity and robustness of sparse construction needs to be improved with noise. How to find a better dictionary D is also an interesting problem for us to solve.

This study we research for the moment is supported by the National Natural Science Foundation of China.

Xiaoxiang Zhu,Guanghu Jin,Feng He,Zhen Dong, (2016) Radar Imaging of Sidelobe Suppression Based on Sparse Regularization. Journal of Computer and Communications,04,108-115. doi: 10.4236/jcc.2016.43017