arXiv subjects

Birsen Yazici

Publications and source records attributed to Birsen Yazici.

16 recordsLinked to original sources

arXiv2026

Online CS-based SAR Edge-Mapping

With modern defense applications increasingly relying on inexpensive, small Unmanned Aerial Vehicles (UAVs), a major challenge lies in designing intelligent and computationally efficient onboard Automatic Target Recognition (ATR) algorithms to carry out operational objectives. This is especially critical in Synthetic Aperture Radar (SAR), where processing techniques such as ATR are often carried out post data collection, requiring onboard systems to bear the memory burden of storing the back-scattered signals. To alleviate this high cost, we propose an online, direct, edge-mapping technique which bypasses the image reconstruction step to classify scenes and targets. Furthermore, by reconstructing the scene as an edge-map we inherently promote sparsity, requiring fewer measurements and computational power than classic SAR reconstruction algorithms such as backprojection.

cs.CV↗

arXiv2026

Online Sparse Synthetic Aperture Radar Imaging

With modern defense applications increasingly relying on inexpensive, autonomous drones, lies the major challenge of designing computationally and memory-efficient onboard algorithms to fulfill mission objectives. This challenge is particularly significant in Synthetic Aperture Radar (SAR), where large volumes of data must be collected and processed for downstream tasks. We propose an online reconstruction method, the Online Fast Iterative Shrinkage-Thresholding Algorithm (Online FISTA), which incrementally reconstructs a scene with limited data through sparse coding. Rather than requiring storage of all received signal data, the algorithm recursively updates storage matrices for each iteration, greatly reducing memory demands. Online SAR image reconstruction facilitates more complex downstream tasks, such as Automatic Target Recognition (ATR), in an online manner, resulting in a more versatile and integrated framework compared to existing post-collection reconstruction and ATR approaches.

cs.CV↗

arXiv2024

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.

eess.SP↗

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.

eess.SP↗

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.

eess.SP↗

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.

eess.SP↗

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.

eess.IV↗

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.

eess.SP↗

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.

cs.IT↗

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.

eess.SP↗

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.

eess.SP↗

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.

eess.SP↗

arXiv2017

Performance Analysis of Convex LRMR based Passive SAR Imaging

Passive synthetic aperture radar (SAR) uses existing signals of opportunity such as communication and broadcasting signals. In our prior work, we have developed a low-rank matrix recovery (LRMR) method that can reconstruct scenes with extended and densely distributed point targets, overcoming shortcomings of conventional methods. The approach is based on correlating two sets of bistatic measurements, which results in a linear mapping of the tensor product of the scene reflectivity with itself. Recognizing this tensor product as a rank-one positive semi-definite (PSD) operator, we pose passive SAR image reconstruction as a LRMR problem with convex relaxation. In this paper, we present a performance analysis of the convex LRMR-based passive SAR image reconstruction method. We use the restricted isometry property (RIP) and show that exact reconstruction is guaranteed under the condition that the pixel spacing or resolution satisfies a certain lower bound. We show that for sufficiently large center frequencies, our method provides superior resolution than that of Fourier based methods, making it a super-resolution technique. Additionally, we show that phaseless imaging is a special case of our passive SAR imaging method. We present extensive numerical simulation to validate our analysis.

cs.CE↗

arXiv2017

Passive Polarimetric Multistatic Radar Detection of Moving Targets

We study the exploitation of polarimetric diversity in passive multistatic radar for detecting moving targets. We first derive a data model that takes into account polarization and anisotropy of targets inherent in multistatic configurations. Unlike conventional isotropic models in which targets are modeled as a collection of uniform spheres, we model targets as a collection of dipole antennas with unknown directions. We consider a multistatic configuration in which each receiver is equipped with a pair of orthogonally polarized antennas, one directed to a scene of interest collecting target-path signal and another one having a direct line-of-sight to a transmitter-of-opportunity collecting direct-path signal. We formulate the detection of moving target problem in a generalized likelihood ratio test framework under the assumption that direct-path signal is available. We show that the result can be reduced to the case in which the direct-path signal is absent. We present a method for estimating the dipole moments of targets. Extensive numerical simulations show the performance of both the detection and the dipole estimation tasks with and without polarimetric diversity.

cs.CE↗

arXiv2017

Doppler Synthetic Aperture Radar Interferometry: A Novel SAR Interferometry for Height Mapping using Ultra-Narrowband Waveforms

This paper introduces a new and novel radar interferometry based on Doppler synthetic aperture radar (Doppler-SAR) paradigm. Conventional SAR interferometry relies on wideband transmitted waveforms to obtain high range resolution. Topography of a surface is directly related to the range difference between two antennas configured at different positions. Doppler-SAR is a novel imaging modality that uses ultra-narrowband continuous waves (UNCW). It takes advantage of high resolution Doppler information provided by UNCWs to form high resolution SAR images. We introduced the theory of Doppler-SAR interferometry. We derived interferometric phase model and develop the equations of height mapping. Unlike conventional SAR interferometry, we show that the topography of a scene is related to the difference in Doppler between two antennas configured at different velocities. While the conventional SAR interferometry uses range, Doppler and Doppler due to interferometric phase in height mapping, Doppler-SAR interferometry uses Doppler, Doppler-rate and Doppler-rate due to interferometric phase in height mapping. We demonstrate our theory in numerical simulations. Doppler-SAR interferometry offers the advantages of long-range, robust, environmentally friendly operations; low-power, low-cost, lightweight systems suitable for low-payload platforms, such as micro-satellites; and passive applications using sources of opportunity transmitting UNCW.

cs.CE↗

arXiv2013

Bistatic Synthetic Aperture Radar Imaging of Moving Targets using Ultra-Narrowband Continuous Waveforms

We consider a synthetic aperture radar (SAR) system that uses ultra-narrowband continuous waveforms (CW) as an illumination source. Such a system has many practical advantages, such as the use of relatively simple, low-cost and low-power transmitters, and in some cases, using the transmitters of opportunity, such as TV, radio stations. Additionally, ultra-narrowband CW signals are suitable for motion estimation due to their ability to acquire high resolution Doppler information. In this paper, we present a novel synthetic aperture imaging method for moving targets using a bi-static SAR system transmitting ultra-narrowband continuous waveforms. Our method exploits the high Doppler resolution provided by ultra-narrowband CW signals to image both the scene reflectivity and to determine the velocity of multiple moving targets. Starting from the first principle, we develop a novel forward model based on the temporal Doppler induced by the movement of antennas and moving targets. We form the reflectivity image of the scene and estimate the motion parameters using a filtered-backprojection technique combined with a contrast optimization method. Analysis of the point spread function of our image formation method shows that reflectivity images are focused when the motion parameters are estimated correctly. We present analysis of the velocity resolution and the resolution of reconstructed reflectivity images. We analyze the error between the correct and reconstructed position of targets due to errors in velocity estimation. Extensive numerical simulations demonstrate the performance of our method and validate the theoretical results.

physics.ins-det↗