Shaun I. Kelly

Advanced image formation and processing of partial synthetic aperture radar data

The authors propose an advanced synthetic aperture radar (SAR) image formation framework based on iterative inversion algorithms that approximately solve a regularised least squares problem. The framework provides improved image reconstructions, compared to the standard methods, in certain imaging scenarios, for example when the SAR data are under-sampled. Iterative algorithms also allow prior information to be used to solve additional problems such as the correction of unknown phase errors in the SAR data. However, for an iterative inversion framework to be feasible, fast algorithms for the generative model and its adjoint must be available. The authors demonstrate how fast, N2 log2 N complexity, (re/back)-projection algorithms can be used as accurate approximations for the generative model and its adjoint, without the limiting geometric approximations of other N2 log2 N methods, for example, the polar format algorithm. Experimental results demonstrate the effectiveness of their framework using publicly available SAR datasets.

Iterative image formation using fast (Re/Back)-projection for spotlight-mode SAR

Iterative SAR image formation can visually improve image reconstructions from under-sampled phase histories by approximately solving a regularised least squares problem. For iterative inversion to be computationally feasible, fast algorithms for the observation matrix and its adjoint must be available. We demonstrate how fast, N2 log2 N complexity, (re/back)-projection algorithms can be used as accurate approximations for the observation matrix and its adjoint, without the limiting assumptions of other N2 log2 N methods, e.g. the polar format algorithm. Experimental results demonstrate the effectiveness of iterative methods using a publicly available SAR dataset. Matlab/C code implementations of the fast (re/back)-projection algorithms used in this paper have been made available.

Sparsity-based autofocus for undersampled synthetic aperture radar

Motivated by the field of compressed sensing and sparse recovery, nonlinear algorithms have been proposed for the reconstruction of synthetic-aperture-radar images when the phase history is undersampled. These algorithms assume exact knowledge of the system acquisition model. In this paper we investigate the effects of acquisition-model phase errors when the phase history is undersampled. We show that the standard methods of autofocus, which are used as a postprocessing step on the reconstructed image, are typically not suitable. Instead of applying autofocus in postprocessing, we propose an algorithm that corrects phase errors during the image reconstruction. The performance of the algorithm is investigated quantitatively and qualitatively through numerical simulations on two practical scenarios where the phase histories contain phase errors and are undersampled.

A sparse regularized model for Raman spectral analysis

Raman spectroscopy has for a long time performed as a common analytical technique in spectroscopic applications. A Raman spectrum depends upon how efficiently a molecule scatters the incident light (electron rich molecules often produce strong signals) which results in difficulties for relating the spectrum to the absolute amounts of present substances. The spectrum is however a stable and accurate representation of the sample measured especially considering that each molecule is associated with a unique spectrum. State-of-the-art spectroscopic calibration methods include the principal component regression (PCR) and partial least squares regression (PLSR) methods which have been proved to be efficient regression methods to realise the quantitative analysis of Raman spectrum. In this paper we consider the problem of Raman spectra deconvolution to analyse the sample composition, as well as possible unknown substances. In particular, we propose a sparse regularized model as a complement to traditional regression methods by leveraging the components sparsity compared to the whole chemical library and the spectra sparsity, given that the chemical fingerprint of each spectrum is mainly determined by the peaks. Experimental results illustrate the effectiveness of this sparse regularized model.

A fast decimation-in-image back-projection algorithm for SAR

Fast back-projection algorithms are required for new modalities of SAR, such as UWB SAR. In this paper we propose a novel algorithm which we call the fast decimation-in-image back-projection algorithm due to its relation to decimation-in-time FFT algorithms. It is the natural dual of existing fast back-projection algorithms which are related to decimation-in-frequency FFT algorithms. The proposed algorithm provides similar speed up to existing algorithms, however, it has additional advantages. The advantages relate to the way in which the algorithm manifests errors. The size and nature of the errors introduced in the proposed algorithm are more desirable than that of existing algorithms.

Phase recovery for 3D SAR range focusing

The problem of calibrating Synthetic Aperture Radar (SAR) data for 3D image formation will be investigated here. A source of errors in modern radar systems is inaccurate range estimations, during the data collection. This is caused by two ambiguities in the platform location and the scene topography map. Such range estimation errors induce some asynchronization in the dechirping process, i.e. a shift in the range direction. When such an error is small, the final image will be blurred and possibly compensated using conventional autofocus techniques. In multipass SAR image formation, this error between the passes is large and we need a different machinery to correct it. We formulate the problem of SAR pulse compression with the range estimation error, in a general setting. The range estimation error appears as some structured phase error in the phase history. We then introduce a new phase recovery technique for compensating the phase error. Some simulation results show the capabilities of the introduced method.

Parallel processing of the fast decimation-in-image back-projection algorithm for SAR

Fast back-projection algorithms provide substantial speedup when compared with the standard back-projection algorithm. However in many potential near-field applications of synthetic aperture radar, further speedup is still required in order to make the application operationally feasible. In this paper we investigate the application of multi-core central processing units and graphic processing units, which are now standard on most scientific workstations, to further speed up a very recently proposed fast back-projection algorithm (the fast decimation-in-image back-projection algorithm).

Compressed sensing in k-space: from magnetic resonance imaging and synthetic aperture radar

We consider two imaging applications of compressed sensing where the acquired data corresponds to samples in the Fourier domain (aka k- space). The rst one is magnetic resonance imaging (MRI), which has been one of the standard examples in the compressed sensing literature. The second one is synthetic aperture radar (SAR). We consider the practical issues of applying compressed sensing ideas in these two applications noting that the physical prossesses involved in these two sensing modalities are very different. We consider the issues of: appropriate image models and sampling strategies, dealing with noise, and the need for calibration.