Gradient algorithm based ISAR image reconstruction from the incomplete dataset

In the inverse synthetic aperture radar (ISAR) number of target reflectors is small resulting in the fact that ISAR images are sparse. Since the ISAR image is obtained using the Fourier transform of the input signal then this problems can be treated within processing of sparse signals. The compressive sensing (CS) theory proves that, under some conditions, exact reconstruction of sparse signals is possible based on the reduced set of observations. Here we will present a gradient based reconstruction algorithm and apply it to the several ISAR setups. In contrast to the common reconstruction algorithms where the signal in its sparsity domain is reconstructed, this algorithm solves minimization in an indirect way, by calculating the missing samples/measurements. Obtained results show that the presented simple reconstruction algorithm is reliable and robust. Common problems in ISAR imaging, like uncompensated motion or target nonuniform motion, make ISAR image only approximately sparse. The presented procedure can provide useful results in these cases as well.