Browsing by Author "Papanicolaou, George"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Coherent Interferometric Imaging, Time Gating and Beamforming(2010-12) Borcea, Liliana; Garnier, Josselin; Papanicolaou, George; Tsogka, ChrysoulaCoherent interferometric imaging is based on the backpropagation of local space-time cross correlations of array data and was introduced in order to improve images when the medium between the array and the object to be imaged is inhomogeneous and unknown [Borcea et al., Inverse Problems, 21 (2005), 1419]. Although this method has been shown to be effective and is well founded theoretically, the coherent interferometric imaging function is computationally expensive and therefore difficult to use. In this paper we show that this function is equivalent to a windowed beamformer energy function, that is, a quadratic function that involves only time gating and time delaying signals in emission and in reception. In this form the coherent interferometric imaging can be implemented efficiently both in hardware and software, that is, at a computational cost that is comparable to the usual beamforming and migration imaging methods. We also revisit the trade-off between enhanced image stability and loss of resolution in coherent interferometry from the point of view of its equivalence to a windowed beamformer energy imaging function.Item Synthetic Aperture Radar Imaging and Motion Estimation via Robust Principal Component Analysis(arXiv, 2012-08-22) Borcea, Liliana; Callaghan, Thomas; Papanicolaou, GeorgeWe consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving antenna emitting and receiving signals. We address two challenges: (1) the detection of moving targets in the complex scene and (2) the separation of the echoes from the stationary targets and those from the moving targets. Such separation allows high resolution imaging of the stationary scene and motion estimation with the echoes from the moving targets alone. We show that the robust principal component analysis (PCA) method which decomposes a matrix in two parts, one low rank and one sparse, can be used for motion detection and data separation. The matrix that is decomposed is the pulse and range compressed SAR data indexed by two discrete time variables: the slow time, which parametrizes the location of the antenna, and the fast time, which parametrizes the echoes received between successive emissions from the antenna. We present an analysis of the rank of the data matrix to motivate the use of the robust PCA method. We also show with numerical simulations that successful data separation with robust PCA requires proper data windowing. Results of motion estimation and imaging with the separated data are presented, as well.