A Learning-Aided Unsupervised Method for Sparse Aperture ISAR Imaging and Autofocusing

While recent research on learning-based signal processing has achieved significant success, most of them are supervised and rely on pre-training models on large labeled data. However, the availability of high-quality paired training data is very limited in specific scenarios, such as the images for high-speed targets (e.g., satellites, aircraft) images obtained by the sparse aperture-inverse synthetic aperture radar (SA-ISAR). In this paper, we propose a learning-aided optimization framework (LAOF), which solves inverse problems in an unsupervised style. Specifically, it converts the optimization of the original variable into network optimization using an untrained generative network-based modeling. To ensure convergence, a random prior-based update strategy is proposed that consists of two parts: random prior generation (RPG) and Langevin dynamics-based optimization (LDO). In RPG, the Markov Chain Monte Carlo (MCMC) simulation is adopted to generate random samples from the potential variable distribution as random priors, which are then assigned to the LDO. Within the LDO framework, the update of network parameters is executed by incorporating a random prior term in conjunction with a task-specific data consistency term, thus constituting a Langevin dynamics-based update mechanism. Consequently, this approach effectively mitigates the occurrence of suboptimal local minima. Moreover, there are two applications of our LAOF: Langevin dynamics-based SA-ISAR imaging (LDSI) and MCMC sampling-based phase estimation (MCPE), which are provided for two typical ISAR imaging cases: SA-ISAR imaging without autofocusing (SIWA) and SA-ISAR imaging with autofocusing (SIAF), respectively. Extensive simulations of various scenarios, such as different sparsity rates and SNRs, demonstrate that the proposed method can achieve superior performance compared to existing state-of-the-art methods with modest computational costs.