arXiv subjects

Bariscan Yonel

Publications and source records attributed to Bariscan Yonel.

12 recordsLinked to original sources

arXiv2026

Doppler Tomography Using Rydberg Sensors

Novel sensors that leverage the quantum properties of atoms for measuring propagating electromagnetic fields are becoming increasingly practical for a variety of applications. These sensors rely on the phenomenon of electromagnetically induced transparency (EIT), which is induced in a confined vapor of alkali atoms when the atoms are excited to a high-energy quantum state, known as a Rydberg state, with multiple resonant optical fields. In this state, the atoms are highly sensitive to electromagnetic radiation and yield a measurement output proportional to the magnitude of an impinging electric field when resonant with a Rydberg-Rydberg transition. In this paper, we consider the use of Rydberg sensors for a tomographic imaging application through a set of modeled system dynamics. Our contribution includes a novel method for placing nulls in the image by modulating the radiated local oscillator (LO) that is used to recover phase information from the received signal. We also present an algorithm for deblurring the image.

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arXiv2023

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.

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arXiv2022

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.

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arXiv2022

Unrolled Wirtinger Flow with Deep Decoding Priors for Phaseless Imaging

We introduce a deep learning (DL) based network and an associated exact recovery theory for imaging from intensity-only measurements. The network architecture uses a recurrent structure that unrolls the Wirtinger Flow (WF) algorithm with a deep decoding prior that 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 models a fixed number of iterations of the underlying optimization algorithm into a recurrent neural network (RNN). Furthermore, it facilitates simultaneous learning of the parameters of the decoding and encoding networks and the RNN. We establish a sufficient condition to guarantee exact recovery under deterministic forward models. Additionally, we demonstrate the relation between the Lipschitz constants of the trained decoding prior and encoding networks to the convergence rate of the WF algorithm. We show the practical applicability of our method in synthetic aperture imaging using high fidelity simulation data from the PCSWAT software. Our numerical study shows that the decoding prior and the encoding network facilitate improvements in sample complexity.

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arXiv2022

Robust Phase Retrieval via Reverse Kullback-Leibler Divergence

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 novel robust phase retrieval algorithms 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 outliers and promoting projections orthogonal to noise subspace. We perform a quantitative analysis demonstrating the robustness of RKLD-based minimization as compared to that of the $\ell_2$ and Poisson loss-based minimization. We present three algorithms based on RKLD minimization, including two with truncation schemes to enhance the robustness to significant contamination. Our numerical study uses data generated based on synthetic coded diffraction patterns and real optical imaging data. The results demonstrate the advantages of our algorithms in terms of sample efficiency, convergence speed, and robustness with respect to outliers over the state-of-the-art techniques.

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arXiv2021

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.

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arXiv2020

A Spectral Estimation Framework for Phase Retrieval via Bregman Divergence Minimization

In this paper, we develop a novel framework to optimally design spectral estimators for phase retrieval given measurements realized from an arbitrary model. We begin by deconstructing spectral methods, and identify the fundamental mechanisms that inherently promote the accuracy of estimates. We then propose a general formalism for spectral estimation as approximate Bregman loss minimization in the range of the lifted forward model that is tractable by a search over rank-1, PSD matrices. Essentially, by the Bregman loss approach we transcend the Euclidean sense alignment based similarity measure between phaseless measurements in favor of appropriate divergence metrics over $\mathbb{R}^M_+$. To this end, we derive spectral methods that perform approximate minimization of KL-divergence, and the Itakura-Saito distance over phaseless measurements by using element-wise sample processing functions. As a result, our formulation relates and extends existing results on model dependent design of optimal sample processing functions in the literature to a model independent sense of optimality. Numerical simulations confirm the effectiveness of our approach in problem settings under synthetic and real data sets.

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arXiv2020

A Deterministic Theory for Exact Non-Convex Phase Retrieval

In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for phase retrieval and identify a novel sufficient condition for universal exact recovery through the lens of low rank matrix recovery theory. Via a perspective in the lifted domain, we show that the convergence of the WF iterates to a true solution is attained geometrically under a single condition on the lifted forward model. As a result, a deterministic relationship between the accuracy of spectral initialization and the validity of {the regularity condition} is derived. In particular, we determine that a certain concentration property on the spectral matrix must hold uniformly with a sufficiently tight constant. This culminates into a sufficient condition that is equivalent to a restricted isometry-type property over rank-1, positive semi-definite matrices, and amounts to a less stringent requirement on the lifted forward model than those of prominent low-rank-matrix-recovery methods in the literature. We characterize the performance limits of our framework in terms of the tightness of the concentration property via novel bounds on the convergence rate and on the signal-to-noise ratio such that the theoretical guarantees are valid using the spectral initialization at the proper sample complexity.

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arXiv2019

Exact Imaging of Extended Targets Using Multistatic Interferometric Measurements

In this paper, we present a novel approach that can exactly recover extended targets in wave-based multistatic interferometric imaging, based on Generalized Wirtinger Flow (GWF) theory [1]. Interferometric imaging is a generalization of phase retrieval, which arises from cross-correlation of measurements from pairs of receivers in multistatic configuration. Unlike standard Wirtinger Flow, GWF theory guarantees exact recovery for arbitrary lifted forward models that satisfy the restricted isometry property over rank-1, positive semi-definite (PSD) matrices with a sufficiently small restricted isometry constant (RIC). To this end, we design a deterministic, lifted forward model for interferometric multistatic radar satisfying the exact recovery conditions of the GWF theory. Our results quantify a lower limit on the pixel spacing and the minimal sample complexity for exact multistatic radar imaging via GWF. We provide a numerical study of our RIC and pixel spacing bounds, which shows that GWF can achieve exact recovery with super-resolution. While our primary interest lies in radar imaging, our method is also applicable to other multistatic wave-based imaging problems such as those arising in acoustics and geophysics.

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arXiv2019

A Generalization of Wirtinger Flow for Exact Interferometric Inversion

Interferometric inversion involves recovery of a signal from cross-correlations of its linear transformations. A close relative of interferometric inversion is the generalized phase retrieval problem, which consists of recovering a signal from the auto-correlations of its linear transformations. Recently, significant advancements have been made in phase retrieval methods despite the ill-posed, and non-convex nature of the problem. One such method is Wirtinger Flow (WF), a non-convex optimization framework that provides high probability guarantees of exact recovery under certain measurement models, such as coded diffraction patterns, and Gaussian sampling vectors. In this paper, we develop a generalization of WF for interferometric inversion, which we refer to as Generalized Wirtinger Flow (GWF). GWF theory extends the probabilistic exact recovery results of WF to arbitrary measurement models characterized in the equivalent lifted problem, hence covers a larger class of measurement models. Our framework unifies the theory of low rank matrix recovery (LRMR) and the non-convex optimization approach of WF, thereby establishes theoretical advantages of the non-convex approach over LRMR. We identify a new sufficient condition on the lifted forward model that directly implies exact recovery conditions of standard WF. This condition is less stringent than those of LRMR, which is the state of the art approach for exact interferometric inversion. We establish our sufficient condition for the cross-correlations of linear measurements collected by complex Gaussian sampling vectors, and show that the exact recovery conditions of standard WF imply our sufficient condition. As a result, the regularity condition of WF becomes redundant in solving the interferometric inversion problem. Finally, we demonstrate the effectiveness of GWF numerically in a deterministic multi-static radar imaging scenario.

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arXiv2019

Deep Learning for Waveform Estimation and Imaging in Passive Radar

We consider a bistatic configuration with a stationary transmitter transmitting unknown waveforms of opportunity and a moving receiver, and present a Deep Learning (DL) framework for passive synthetic aperture radar (SAR) imaging. Existing passive radar methods require two or more antennas which are either spatially separated or colocated with sufficient directivity to estimate the underlying waveform prior to imaging. Our approach to passive radar only requires a single receiver, hence reduces cost and increases versatility. We approach DL from an optimization perspective and formulate image reconstruction as a machine learning task. By unfolding the iterations of a proximal gradient descent algorithm, we construct a deep recurrent neural network (RNN) that is parameterized by transmitted waveforms. We cascade the RNN structure with a decoder stage to form a recurrent-auto encoder architecture. We then utilize backpropagation to learn transmitted waveforms by training the network in an unsupervised manner using SAR measurements. The highly non-convex problem of backpropagation is guided to a feasible solution over the parameter space by initializing the network with the known components of the SAR forward model. Moreover, prior information regarding the waveform structure is incorporated during initialization and backpropagation. We demonstrate the effectiveness of the DL-based approach through extensive numerical simulations that show focused, high contrast imagery using a single receiver antenna at realistic SNR levels.

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arXiv2017

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.

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