Deep Denoising Prior-Based Spectral Estimation for Phaseless Synthetic Aperture Radar

Incoherent processing for synthetic aperture radar (SAR) is a promising approach that enables low implementation costs, simplified hardware designs and operations in high frequency spectrum compared to the conventional imaging methods using coherent processing. Existing non-convex phaseless imaging algorithms offer recovery guarantees over limited range of forward models. In recent years, several deep learning (DL) based techniques have been introduced with the goal of extending applicability of phaseless imaging techniques to wave-based imaging modalities by addressing fundamental challenges, such as, lack of redundancy, non-uniqueness issues encountered commonly with inverse scattering models. In this paper, we introduce a DL-based phaseless SAR imaging approach that is designed under the premise that the spectral estimation technique, widely used for initializing non-convex phase retrieval algorithms, has significance far beyond generating good initial points. We extend the iterative power method for spectral estimation by using deep denoisers at each iteration, and subsequently design a deep imaging network within the plug-and-play framework. Finally, we verify the feasibility of our approach using synthetic SAR measurements.

Interferometric Passive Radar Imaging with Deep Denoising Priors

Passive radar has key advantages over its active counterpart in terms of cost and stealth. In this paper, we address passive radar imaging problem by interferometric inversion using a spectral estimation method with a priori information within a deep learning (DL) framework. Cross-correlating the received signals from different look directions mitigates the influence of shared transmitter related phase components despite lack of a cooperative transmitter, and permits tractable inference via interferometric inversion. We thereon leverage deep architectures for modeling a priori information and for improving sample efficiency of state-of-the-art methods. Our approach comprises of an iterative algorithm based on generalizing the power method, and applies denoisers using plug-and-play (PnP) and regularization by denoising (RED) techniques. We evaluate our approach using simulated data for passive synthetic aperture radar (SAR) by using convolutional neural networks (CNN) as denoisers. The numerical experiments show that our method can achieve faster reconstruction and superior image quality in sample starved regimes than the state-of-the-art passive interferometric imaging algorithms.

Robust Phase Retrieval via Reverse Kullback-Leibler Divergence and Wirtinger Flow

Robustness to noise and outliers is a desirable trait in phase retrieval algorithms for many applications in imaging and signal processing. In this paper, we develop a novel robust phase retrieval algorithm based on the minimization of reverse Kullback-Leibler divergence (RKLD) within the Wirtinger Flow (WF) framework. We use RKLD over intensity-only measurements in two distinct ways: i) to design a novel initial estimate based on minimum distortion design of spectral estimates, and ii) as a loss function for iterative refinement based on WF. The RKLD-based loss function offers implicit regularization by processing data at the logarithmic scale and provides the following benefits: suppressing the influence of large magnitude errors and promoting projections orthogonal to noise subspace. We present three algorithms based on RKLD minimization, including two with truncation schemes to enhance the robustness to significant contamination. Our numerical study demonstrates the advantages of our algorithms in terms of sample efficiency, convergence speed, and robustness to outliers over the state-of-the-art techniques using both synthetic and real optical imaging data.

Unrolled Wirtinger Flow with Deep Priors for Phaseless Imaging

We introduce a deep learning (DL) based network for imaging from measurement intensities. The network architecture uses a recurrent structure that unrolls the Wirtinger Flow (WF) algorithm with a deep prior which enables performing the algorithm updates in a lower dimensional encoded image space. We use a separate deep network (DN), referred to as the encoding network, for transforming the spectral initialization used in the WF algorithm to an appropriate initial value for the encoded domain. The unrolling scheme that models a fixed number of iterations of the underlying algorithm into a recurrent neural network (RNN) enable us to simultaneously learn the parameters of the prior network, the encoding network and the RNN during training. We establish sufficient conditions on the network to guarantee exact recovery under deterministic forward models and demonstrate the relation between the Lipschitz constants of the trained prior and encoding networks to the convergence rate. We show the practical applicability of our method on synthetic aperture imaging using high fidelity simulation data from the PCSWAT software. Our numerical study shows that the deep prior facilitates improvements in sample complexity.

Phase-Space Function Recovery for Moving Target Imaging in SAR by Convex Optimization

In this paper, we present an approach for ground moving target imaging (GMTI) and velocity recovery using synthetic aperture radar. We formulate the GMTI problem as the recovery of a phase-space reflectivity (PSR) function which represents the strengths and velocities of the scatterers in a scene of interest. We show that the discretized PSR matrix can be decomposed into a rank-one, and a highly sparse component corresponding to the stationary and moving scatterers, respectively. We then recover the two distinct components by solving a constrained optimization problem that admits computationally efficient convex solvers within the proximal gradient descent and alternating direction method of multipliers frameworks. Using the structural properties of the PSR matrix, we alleviate the computationally expensive steps associated with rank-constraints, such as singular value thresholding. Our optimization-based approach has several advantages over state-of-the-art GMTI methods, including computational efficiency, applicability to dense target environments, and arbitrary imaging configurations. We present extensive simulations to assess the robustness of our approach to both additive noise and clutter, with increasing number of moving targets. We show that both solvers perform well in dense moving target environments, and low-signal-to-clutter ratios without the need for additional clutter suppression techniques.

Deep Learning for Passive Synthetic Aperture Radar

We introduce a deep learning (DL) framework for inverse problems in imaging, and demonstrate the advantages and applicability of this approach in passive synthetic aperture radar (SAR) image reconstruction. We interpret image recon- struction as a machine learning task and utilize deep networks as forward and inverse solvers for imaging. Specifically, we design a recurrent neural network (RNN) architecture as an inverse solver based on the iterations of proximal gradient descent optimization methods. We further adapt the RNN architecture to image reconstruction problems by transforming the network into a recurrent auto-encoder, thereby allowing for unsupervised training. Our DL based inverse solver is particularly suitable for a class of image formation problems in which the forward model is only partially known. The ability to learn forward models and hyper parameters combined with unsupervised training approach establish our recurrent auto-encoder suitable for real world applications. We demonstrate the performance of our method in passive SAR image reconstruction. In this regime a source of opportunity, with unknown location and transmitted waveform, is used to illuminate a scene of interest. We investigate recurrent auto- encoder architecture based on the 1 and 0 constrained least- squares problem. We present a projected stochastic gradient descent based training scheme which incorporates constraints of the unknown model parameters. We demonstrate through extensive numerical simulations that our DL based approach out performs conventional sparse coding methods in terms of computation and reconstructed image quality, specifically, when no information about the transmitter is available.