Fast Reconstruction of SAR Images with Phase Error Using Sparse Representation

In the past years, a number of algorithms have been introduced for synthesis aperture radar (SAR) imaging. However, they all suffer from the same problem: The data size to process is considerably large. In recent years, compressive sensing and sparse representation of the signal in SAR has gained a significant research interest. This method offers the advantage of reducing the sampling rate, but also suffers from speed processing limitation and it needs a huge amount of memory to reconstruct the image. On the other hand, inaccuracy in SAR model induces phase error to the results and makes the reconstructed image blurry. Existing sparse methods in the presence of phase error, have high computational cost and need a lot of processing time. In addition, these methods take up a considerable space in the memory for saving the measurement matrix. In this paper, a fast method is proposed to reduce the computational cost of image reconstruction, based on the signal sparsity in the presence of phase error. The proposed method consists of substituting accurate observations of sparsity methods with approximated observations of matched filter methods. In this method the output of Range-Doppler matched filter is reconstructed with sparse representation and error phase is estimated simultaneously. This method leads to a nonconvex optimization problem and to solve that, we use the majorisation minimization method. The phase error and reconstructed image are estimated in an iterative procedure. The use of approximated observation, eliminates the need for carrying out big matrix multiplications and Fast Fourier Transformation, as a low computational cost operation, can be employed instead. In addition to computation speed, this method does not need any memory space for saving measurement matrix. In our numerical simulations, we compared the speed of processing and the mean square error (MSE) of reconstructed image for the proposed method with the state-of-the-art sparse method for different sizes of image and under-sampling rates. It is shown in simulations that the reconstructed image from our method has a slightly lower quality and higher MSE, because of the sidelobes effect of the matched filter output. However, in certain conditions the speed of the proposed method is more than a hundred times faster than the compared method. The achieved processing speed with no need for the memory to store the measurement matrix at the expense of slightly lower image quality, would be acceptable for most applications.