Imaging of moving targets with multi-static SAR using an overcomplete
  dictionary

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Abstract

This paper presents a method for imaging of moving targets using multi-static SAR by treating the problem as one of spatial reflectivity signal inversion over an overcomplete dictionary of target velocities. Since SAR sensor returns can be related to the spatial frequency domain projections of the scattering field, we exploit insights from compressed sensing theory to show that moving targets can be effectively imaged with transmitters and receivers randomly dispersed in a multi-static geometry within a narrow forward cone around the scene of interest. Existing approaches to dealing with moving targets in SAR solve a coupled non-linear problem of target scattering and motion estimation typically through matched filtering. In contrast, by using an overcomplete dictionary approach we effectively linearize the forward model and solve the moving target problem as a larger, unified regularized inversion problem subject to sparsity constraints.

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Most cited references 26

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Stable signal recovery from incomplete and inaccurate measurements

Emmanuel Candès, Justin Romberg, Terence Tao (2006)

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Atomic Decomposition by Basis Pursuit

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Is Open Access

Decoding by Linear Programming

Terence Tao, Emmanuel Candès (2005)

This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector \(f \in \R^n\) from corrupted measurements \(y = A f + e\). Here, \(A\) is an \(m\) by \(n\) (coding) matrix and \(e\) is an arbitrary and unknown vector of errors. Is it possible to recover \(f\) exactly from the data \(y\)? We prove that under suitable conditions on the coding matrix \(A\), the input \(f\) is the unique solution to the \(\ell_1\)-minimization problem (\(\|x\|_{\ell_1} := \sum_i |x_i|\)) \[ \min_{g \in \R^n} \| y - Ag \|_{\ell_1} \] provided that the support of the vector of errors is not too large, \(\|e\|_{\ell_0} := |\{i : e_i \neq 0\}| \le \rho \cdot m\) for some \(\rho > 0\). In short, \(f\) can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; \(f\) is recovered exactly even in situations where a significant fraction of the output is corrupted.