Figen S. Oktem

Irfan Manisali, Okyanus Oral, Figen S. Oktem

Near-field multiple-input multiple-output (MIMO) radar imaging systems have recently gained significant attention. In this paper, we develop novel non-iterative deep learning-based reconstruction methods for real-time near-field MIMO imaging. The goal is to achieve high image quality with low computational cost at compressive settings. The developed approaches have two stages. In the first approach, physics-based initial stage performs adjoint operation to back-project the measurements to the image-space, and deep neural network (DNN)-based second stage converts the 3D backprojected measurements to a magnitude-only reflectivity image. Since scene reflectivities often have random phase, DNN processes directly the magnitude of the adjoint result. As DNN, 3D U-Net is used to jointly exploit range and cross-range correlations. To comparatively evaluate the significance of exploiting physics in a learning-based approach, two additional approaches that replace the physics-based first stage with fully connected layers are also developed as purely learning-based methods. The performance is also analyzed by changing the DNN architecture for the second stage to include complex-valued processing (instead of magnitude-only processing), 2D convolution kernels (instead of 3D), and ResNet architecture (instead of U-Net). Moreover, we develop a synthesizer to generate large-scale dataset for training with 3D extended targets. We illustrate the performance through experimental data and extensive simulations. The results show the effectiveness of the developed physics-based learned reconstruction approach in terms of both run-time and image quality at highly compressive settings. Our source codes and dataset are made available at GitHub.

Okyanus Oral, Figen S. Oktem

Near-field radar imaging systems are used in a wide range of applications such as concealed weapon detection and medical diagnosis. In this paper, we consider the problem of reconstructing the three-dimensional (3D) complex-valued reflectivity distribution of the near-field scene by enforcing regularization on its magnitude. We solve this inverse problem by using the alternating direction method of multipliers (ADMM) framework. For this, we provide a general expression for the proximal mapping associated with such regularization functionals. This equivalently corresponds to the solution of a complex-valued denoising problem which involves regularization on the magnitude. By utilizing this expression, we develop a novel and efficient plug-and-play (PnP) reconstruction method that consists of simple update steps. Due to the success of data-adaptive deep priors in imaging, we also train a 3D deep denoiser to exploit within the developed PnP framework. The effectiveness of the developed approach is demonstrated for multiple-input multiple-output (MIMO) imaging under various compressive and noisy observation scenarios using both simulated and experimental data. The performance is also compared with the commonly used direct inversion and sparsity-based reconstruction approaches. The results demonstrate that the developed technique not only provides state-of-the-art performance for 3D real-world targets, but also enables fast computation. Our approach provides a unified general framework to effectively handle arbitrary regularization on the magnitude of a complex-valued unknown and is equally applicable to other radar image formation problems (including SAR).

Cagatay Isil, Figen S. Oktem

In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear and ill-posed nature. Recently, learning-based approaches have emerged as powerful alternatives to the analytical methods for several inverse problems. In the context of phase retrieval, a novel plug-and-play approach that exploits learning-based prior and efficient update steps has been presented at the Computational Optical Sensing and Imaging topical meeting, with demonstrated state-of-the-art performance. The key idea was to incorporate learning-based prior to the Gerchberg-Saxton type algorithms through plug-and-play regularization. In this paper, we present the mathematical development of the method including the derivation of its analytical update steps based on half-quadratic splitting and comparatively evaluate its performance through extensive simulations on a large test dataset. The results show the effectiveness of the method in terms of both image quality, computational efficiency, and robustness to initialization and noise.

Mehmet Onurcan Kaya, Figen S. Oktem

Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior sampling framework of Denoising Diffusion Restoration Models (DDRM) for the solution of nonlinear phase retrieval problem, which requires reconstructing an image from its noisy intensity-only measurements such as Fourier intensity. The approach combines the model-based alternating-projection methods with the DDRM to utilize pretrained unconditional diffusion priors for phase retrieval. The performance is demonstrated through both simulations and experimental data. Results demonstrate the potential of this approach for improving the alternating-projection methods as well as its limitations.

Mehmet Onurcan Kaya, Figen S. Oktem

Phase retrieval involves recovering a signal from intensity-only measurements, crucial in many fields such as imaging, holography, optical computing, crystallography, and microscopy. Although there are several well-known phase retrieval algorithms, including classical iterative solvers, the reconstruction performance often remains sensitive to initialization and measurement noise. Recently, image-to-image diffusion models have gained traction in various image reconstruction tasks, yielding significant theoretical insights and practical breakthroughs. In this work, we introduce a novel phase retrieval approach based on an image-to-image diffusion framework called Inversion by Direct Iteration. Our method begins with an enhanced initialization stage that leverages a hybrid iterative technique, combining the Hybrid Input-Output and Error Reduction methods and incorporating a novel acceleration mechanism to obtain a robust crude estimate. Then, it iteratively refines this initial crude estimate using the learned image-to-image pipeline. Our method achieves substantial improvements in both training efficiency and reconstruction quality. Furthermore, our approach utilizes aggregation techniques to refine quality metrics and demonstrates superior results compared to both classical and contemporary techniques. This highlights its potential for effective and efficient phase retrieval across various applications.

Mehmet Onurcan Kaya, Figen S. Oktem

We propose a novel framework for phase retrieval that leverages Langevin dynamics to enable efficient posterior sampling, yielding reconstructions that explicitly balance distortion and perceptual quality. Unlike conventional approaches that prioritize pixel-wise accuracy, our method navigates the perception-distortion tradeoff through a principled combination of stochastic sampling, learned denoising, and model-based updates. The framework comprises three variants of increasing complexity, integrating theoretically grounded Langevin inference, adaptive noise schedule learning, parallel reconstruction sampling, and warm-start initialization from classical solvers. Extensive experiments demonstrate that our method achieves state-of-the-art performance across multiple benchmarks, both in terms of fidelity and perceptual quality.

Çağatay Işıl, Figen S. Oktem, Aykut Koç

Classical phase retrieval problem is the recovery of a constrained image from the magnitude of its Fourier transform. Although there are several well-known phase retrieval algorithms including the hybrid input-output (HIO) method, the reconstruction performance is generally sensitive to initialization and measurement noise. Recently, deep neural networks (DNNs) have been shown to provide state-of-the-art performance in solving several inverse problems such as denoising, deconvolution, and superresolution. In this work, we develop a phase retrieval algorithm that utilizes two DNNs together with the model-based HIO method. First, a DNN is trained to remove the HIO artifacts and is used iteratively with the HIO method to improve the reconstructions. After this iterative phase, a second DNN is trained to remove the remaining artifacts. Numerical results demonstrate the effectiveness of ourapproach, which has little additional computational cost compared to the HIO method. Our approach not only achieves state-of-the-art reconstruction performance but also is more robust to different initialization and noise levels.