A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus. Common techniques that attempt to resolve the antenna ambiguity generally assume an unknown gain and phase error afflicting the radar measurements. However, ensuring identifiability and tractability of the unknown error imposes strict restrictions on the allowable antenna perturbations. Furthermore, these techniques are often not applicable in near-field imaging, where mapping the position ambiguity to phase errors breaks down. In this paper, we propose an alternate formulation where the position error of each antenna is mapped to a spatial shift operator in the image-domain. Thus, the radar autofocus problem becomes a multichannel blind deconvolution problem, in which the radar measurements correspond to observations of a static radar image that is convolved with the spatial shift kernel associated with each antenna. To solve the reformulated problem, we also develop a block coordinate descent framework that leverages the sparsity and piecewise smoothness of the radar scene, as well as the one-sparse property of the two-dimensional shift kernels. We evaluate the performance of our approach using both simulated and experimental radar measurements and demonstrate its superior performance compared with state-of-the-art methods.
More generally, the radar autofocus problem can be viewed as a multichannel blind deconvolution problem, where the distortions due to position errors can be considered as unknown channels acting on the signals that are received in each antenna. Blind deconvolution attempts to separate a signal and a channel from their convolved mixture, i.e., their product in the frequency domain, using assumptions on each of the two. The multi-channel version considers multiple channels affecting the same signal. Solutions to the general multichannel blind deconvolution problem have existed in the literature since the 1990s @cite_24 @cite_36 @cite_0 @cite_43 @cite_18 .
@cite_18 @cite_36 @cite_24 @cite_43 @cite_0
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Inaccuracies in the observation model of the synthetic aperture radar (SAR) due to inaccuracies of the velocity and position of the platform or atmospheric turbulence cause degradations in reconstructed images which necessitate the use of autofocus algorithms. In this paper we propose a novel signal processing algorithm for joint SAR image formation and autofocus in a synthesis dictionary based sparse representation framework. Proposed algorithm can be applied broadly to scenes that exhibit sparsity with respect to any dictionary. This is done by extending our previously developed sparse representation-based SAR imaging framework to joint SAR image formation and autofocus. To this end, the phase error vector is separated from the unknown phase of the complex-valued back-scattered field. Phase error vector is estimated using a MAP estimator and compensated through an iterative algorithm to produce focused images. We demonstrate the effectiveness of the proposed approach on synthetic and real imagery. The phase gradient autofocus (PGA) technique for phase error correction of spotlight mode synthetic aperture radar (SAR) imagery is examined carefully in the context of four fundamental signal processing steps that constitute the algorithm. We demonstrate that excellent results over a wide variety of scene content, and phase error function structure are obtained if and only if all of these steps are included in the processing. Finally, we show that the computational demands of the fun PGA algorithm do not represent a large fraction of the total image formation problem, when mid to large size images are involved. > Motion errors are inevitably introduced when data is acquired and considerably degrade the image quality in terms of geometric resolution, radiometric accuracy and image contrast, especially in high-resolution spotlight synthetic aperture radar (SAR) imagery. In this study, the authors present a novel two-dimensional (2D) autofocus algorithm directly inserted into polar format algorithm, which compensates the envelop error and the phase error sequentially. A coarse error correction is first performed by global positioning system or inertial navigation system in the range-compressed domain, then a new envelop compensation strategy, stage-by-stage approach, is designed, obtaining promising results for removing range cell migration after 2D interpolation. Additionally, a weighed contrast enhancement autofocus algorithm based on spatially variant model is developed to compensate for the residual phase error, which remarkably improves the estimation accuracy. The presented algorithm is very robust to deal with substantial errors over a variety of scenes even in conditions of homogenous areas with no prominent point scatterers and enables the utilisation of fast Fourier transform. The experimental results obtained by the proposed algorithm confirm that the analysis extends well to realistic situations. We introduce a new algorithm for multichannel blind deconvolution. Given the outputs of K linear time- invariant channels driven by a common source, we wish to recover their impulse responses without knowledge of the source signal. Abstractly, this problem amounts to finding a solution to an overdetermined system of quadratic equations. We show how we can recast the problem as solving a system of underdetermined linear equations with a rank constraint. Recent results in the area of low rank recovery have shown that there are effective convex relaxations to problems of this type that are also scalable computationally, allowing us to recover 100s of channel responses after a moderate observation time. We illustrate the effectiveness of our methodology with a numerical simulation of a passive noise imaging" experiment.