Radar data have already proven to be compressible with no significant losses for most of the applications in which it is used. In the framework of information theory, the compressibility of a signal implies that it can be decomposed onto a reduced set of basic elements. Since the same quantity of information is carried by the original signal and its decomposition, it can be deduced that a certain degree of redundancy exists in the explicit representation. According to the theory of compressive sensing (CS), due to this redundancy, it is possible to infer an accurate representation of an unknown compressible signal through a highly incomplete set of measurements. Based on this assumption, this paper proposes a novel method for the focusing of raw data in the framework of radar imaging. The technique presented is introduced as an alternative option to the traditional matched filtering, and it suggests that the new modes of acquisition of data are more efficient in orbital configurations. In this paper, this method is first tested on 1-D simulated signals, and results are discussed. An experiment with synthetic aperture radar (SAR) raw data is also described. Its purpose is to show the potential of CS applied to SAR systems. In particular, we show that an image can be reconstructed, without the loss of resolution, after dropping a large percentage of the received pulses, which would allow the implementation of wide-swath modes without reducing the azimuth resolution.

/pdf/a-novel-strategy-for-radar-imaging-based-on-compressive-4xz9eaeigv.pdf

A Novel Strategy for Radar Imaging Based on Compressive Sensing

http://service.tsi.telecom-paristech.fr/cgi-bin/valipub_download.cgi?dId=23

Application de la transformée de Mellin : étude des lois statistiques de l'imagerie cohérente

This paper aims at introducing the recent theory of compressive sensing to radar imaging systems in order to retrieve the imaged scene with better resolution and a reduced amount of collected samples. As a result of the application of the alternative imaging technique proposed, the use of matched filtering is avoided and the effect of its sidelobes in the images is drastically diminished. Furthermore, the amount of data to be stacked in the sensor and then downlinked to the ground station is meaningfully lower. This permits a more efficient management of resources.

/pdf/a-novel-strategy-for-radar-imaging-based-on-compressive-2e1gb1izlx.pdf

The paper focuses on a flexible model of multidimensional probability density function (pdf) dedicated to describe amplitude distribution of polarimetric SAR data. The model is based on the copula theory for characterizing the dependency between polarimetric channels (HH, VV, HV/VH or the target vector components). The benefit in using copula theory is to extend correlation concept to a wider dependence one, which may not be linear. From this point of view, the model is more flexible than the classical Wishart distribution. But it may include it. The other benefit in using the copula model is to separate the dependence concept from the shape of the marginal pdfs. Hence, this multidimensional characterization may be linked to classical 1D gamma pdf, or to a more flexible Pearson system of distributions. In the case of high resolution data, pdf shapes are becoming of heavy tailed and the Fisher system of distributions seems to be an interesting alternative for such a model. Any parametric 1D model may be used. The paper mainly focuses on the model itself and more precisely on the technique required to construct such multidimensional dependence function. The difficulties arise for copula on 3D in which the dependency is not homogeneous between the components (the link between HH and VV may not be of the same behavior as the one between HH and HV). Illustrations are given on classification and despeckling. Classification will be performed by a stochastic estimation maximisation (SEM). Despeckling will be achieved by a maximum A posteriori technique.

The use of multidimensional copulas to describe amplitude distribution of polarimetric SAR data

This paper relates to three strategies of SAR image lossy compression by wavelet based coders as JPEG2000 and SPIHT. We take into account two aspects: 1) the inherent presence of speckle and its features; 2) filtering effect of lossy compression if applied to noisy images. The first strategy is visually lossless compression. According to the second strategy, a fixed compression ratio (CR) has to be provided. The third strategy is to perform compression in the neighborhood of optimal operation point (OOP). For all strategies, compression with and without logarithmic type homomorphic transform (HT) is considered. It is shown that the use of HT produces several benefits.

Strategies of SAR image lossy compression by JPEG2000 and SPIHT

In the framework of wavelet based SAR compression techniques, this paper proposes a new approach to model subband coefficients marginal distributions. The decomposition scheme involves homomorphic wavelet transform and "second kind statistics" characterization models. Our method has been successfully tested on real data experiments

Homomorphic wavelet transform and new subband statistics models for SAR image compression

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Homomorphic wavelet transform and new subband statistics models for SAR image compression