E_WP1: Sparse Representations and Compressed Sensing

This work package explores low-dimensional signal models for sensing and imaging. Its focus is essentially on the sparsity/compressibility property of most signals, to yield more efficient sensing systems. Although the applications of such models are numerous, the applications which will be initially explored here are wideband RF sub-Nyquist sampling, (3D) Synthetic Aperture Radar and Synthetic Aperture Sonar. The sparse representation and compressed sensing techniques are often computationally complex. They are therefore not good candidates for many real-world problems. A low Size Weight and Power (SWAP) solution for the mentioned application will be explored in this work package. It will also link to WP6, which will explore the possibility of the implementation of such algorithms on the reconfigurable architectures e.g. FPGA's and highly parallel platforms. The canonical compressed sensing setting has some randomness in the sensing stage to guarantee its promised performance. However, a fully random structure in sensing and imaging systems, is not easily achievable in most applications. The hardware or physical constraints, imposed by imaging and sensing systems, will also be explored in order to find the techniques which allow us to use CS well-developed theoretical results, under such constraints.

E_WP 1.1 Efficient subNyquist sampling schemes

We developed and analysed a practical low complexity scheme for subNyquist sampling and a reconstruction system with the particular application of wideband electronic surveillance. We used multi-coset sampling strategies, whose hardware implementation is very similar to classical interleaved ADCs. We are developing a system which can incorporate sophisticated signal detection and separation methods and have the flexibility to switch between continuous wideband surveillance and narrow band full rate sampling to give maximum dynamic range when required. A schematic representation of the system is presented in Figure 1. The goal is to provide the low Size Weight and Power (SWAP) solutions, and to present a subNyquist sampling technique which can be implemented on existing FPGA architectures. The proposed technique (LoCoMC) is based some linear and non-linear computationally cheap operators.

If we compare the proposed sub-Nyquist radar ES and the conventional Rapid Swept Superheterodyne Receiver (RSSR), using some synthetic ES signals, we get the results shown in Figure 2. While some pulses are missing and the processing gain is a bit lost in the RSSR, LoCoMC have some advantages here. Some work in pulse descriptor word extraction is under development.

E_WP 1.2 Compressive Imaging with Sensor Constraints

This work package offers  a number of opportunities to enhance imaging systems such as SAR or multi/hyperspectral imaging. However, most sensing systems impose severe physics constraints on the nature of measurements that can be taken. For example, in low frequency SAR systems it is necessary to notch the transmitted pulses to avoid civilian RF communication bands. The extent to which CS can be adapted to tackle these challenges and how to determine the best strategies to achieve a reasonable resolution in these scenarios will be explored. We have initially started the investigation of video SAR, passive SONAR and low-frequency (3D)SAR applications.

E_WP 1.3 CS, Beyond Imaging

This area of work will look at the potential to extract additional information from the scene beyond simple imaging. Moving targets can appear displaced and defocused in a standard SAR image. Within multi-channel SAR, moving target detection can then be viewed as a joint sparse recovery problem providing joint SAR/GMTI imaging. As most scatterers are not isotropic, the additional structure can be useful for target classification.  This work package is about building structured dictionaries to characterize the anisotropic properties of different scatterers (planar, edge, corner, etc.).  The major challenge would be to achieve this in a robust and computationally simple manner. Such dictionaries could also incorporate spectral dependencies when applied in the context of ultra-wideband SAR. There are similarities to work in synthetic aperture sonar, where the frequency dependence of scatterers has so far been exploited through a biomimetic approach.

Another structure in sparse signals which has been explored in this task, is the non-negative sparse approximation, for Raman spectral decomposition and hyperspectral data representation. In this task, we developed a new Raman spectral decomposition technique, where the task is to find the component of a chemical mixture. We have also introduced some new non-negative greedy sparse approximations which can be used to accelerate such a Raman spectral decomposition and efficient hyperspectral imaging. Application of such methods to the hyperspectral imaging, which is also related to the E_WP1.2, is under development.

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