Compressive sensing-based synthetic aperture radar (SAR) imaging has shown its superior capability in high-resolution image formation. However, most of those works focus on the scenes that can be sparsely represented in fixed spaces. When dealing with complicated scenes, these fixed spaces lack adaptivity in characterizing varied image contents. To solve this problem, a new compressive sensing-based radar imaging approach with adaptive sparse representation is proposed. Specifically, an autoregressive model is introduced to adaptively exploit the structural sparsity of an image. In addition, similarity among pixels is integrated into the autoregressive model to further promote the capability and thus an adaptive sparse representation facilitated by a weighted autoregressive model is derived. Since the weighted autoregressive model is inherently determined by the unknown image, we propose a joint optimization scheme by iterative SAR imaging and updating of the weighted autoregressive model to solve this problem. Eventually, experimental results demonstrated the validity and generality of the proposed approach.

Canonical multi‐input–multi‐output (MIMO) imaging methods suffer from limited resolution, poor robustness against noise and high computational complexity, especially when the array aperture is limited (affecting angular resolution) and the number of snapshots is limited (affecting Doppler resolution). In this study, the authors discuss a new range‐angle‐Doppler monostatic MIMO imaging method through adaptive estimation of the generalised Cauchy prior distribution (GCD). The superiority of GCD‐based model over existing ℓ _p ‐norm‐based model (which actually assumes the prior as general Gaussian distribution) is theoretically verified through the issue of signal compressibility. The authors adapt a reweighted ℓ ₂ ‐norm iterative algorithm to solve the model. In our model the authors do not pre‐define the scaling factor of the prior distribution and, during the iteration, the authors use a novel ‘quantile‐of‐OS’ method to adaptively estimate the scaling parameter of the prior distribution, enhancing the robustness of the method. Simulation results verify the image quality and speed advantages of the proposed method.

As a new enchanting theory, compressed sensing (CS) demonstrates that a sparse signal can be recovered through a surprisingly small number of linear measurements by solving a problem of ℓ ₁ norm minimisation (which can be thought as a special case of the signomial diversity measures). However, the traditional CS model with ℓ ₁ norm minimisation can not fully exploit the sparsity especially when the degree of sparsity increases or the measurements number reduces. In this study, the Cauchy diversity measures is incorporated into the proposed model to deal with the above difficulties. The simulation results demonstrate that under the same condition, this new model offers a superior reconstruction precision compared with the common used signomial diversity measures.