Synthetic aperture radar image formation system and method

1. Method for processing an input signal acquired by a synthetic aperture radar (SAR) system, wherein the input signal is saturated, the method comprising the steps of:

estimating an initial reconstruction that generated the input signal;

reproducing the input signal from the reconstruction to generate a reproduced signal;

comparing the reproduced signal with the input signal;

adjusting an estimated reconstruction based on the comparison;

applying an azimuth Fourier transform (FFT) to the input signal;

applying a first chirp scaling to an output of the azimuth FFT;

applying a range FFT to an output of the first chirp scaling;

multiplying an output of the range FFT by a range frequency response;

applying a range inverse FFT (IFFT) to an output of the range frequency response;

applying a second chirp scaling to an output of the range IFFT;

multiplying an output of the second chirp scaling by an azimuth frequency response;

applying an azimuth IFFT to an output of the azimuth frequency response to form the reconstructed SAR image; and

iterating from the reproducing step until a termination condition is reached to form a reconstructed SAR image, wherein the steps are performed in a processor.

2. The method in claim 1 in which the reproducing further comprises the steps of:

applying an azimuth Fourier transform (FFT) to the input signal;

multiplying an output of the azimuth FFT by an azimuth frequency response;

applying a first chirp scaling to an output of the azimuth frequency response;

applying a range FFT to an output of the first chirp scaling;

multiplying an output of the range FFT by a range frequency response;

applying a range inverse FFT (IFFT) to an output of the range frequency response;

applying a second chirp scaling to an output of the range IFFT; and

applying an azimuth IFFT to an output of the second chip scaling to form raw SAR data.

3. The method of claim 1 , in which the adjusting is according to a signal model.

4. The method of claim 1 , in which a signal model is incorporated after the iterations terminate.

5. The methods of claim 3 or 4 , wherein the signal model imposes that a wavelet transform of the reconstructed SAR images or a wavelet transform of a magnitude of the reconstructed SAR image is sparse.

6. The methods of claim 5 , further comprising:

transforming the reconstructed SAR image or the magnitude to produce transformation coefficients;

thresholding the transformation coefficients by setting coefficients with values less than a threshold value to zero; and

inverse transforming the thresholded coefficients to form the reconstructed SAR image.

7. The method of claim 1 , further comprising:

reducing ghost images.

8. The method of claim 7 , in which reducing further comprises the steps of:

identifying locations of the ghost images; and

removing the ghost images from the locations.

9. The method of claim 7 , in which reducing is applied during the adjusting.

10. The method of claim 7 , in which reducing is applied after the iterating.

11. The method of claim 1 in which the comparing enforces a saturation consistency.

12. The method of claim 1 in which adjusting is performed using a gradient descent.

13. The method of claim 12 in which the gradient descent uses a line search.