Computational Imaging Through Atmospheric Turbulence

Since the seminal work of Andrey Kolmogorov in the early 1940's, imaging through atmospheric turbulence has grown from a pure scientific pursuit to an important subject across a multitude of civilian, space-mission, and national security applications. Fueled by the recent advancement of deep learning, the field is further experiencing a new wave of momentum. However, for these deep learning methods to perform well, new efforts are needed to build faster and more accurate computational models while at the same time maximizing the performance of image reconstruction. The book is written primarily for image processing engineers, computer vision scientists, and engineering students who are interested in the field of atmospheric turbulence, statistical optics, and image processing. The book can be used as a graduate text, or advanced topic classes for undergraduates.

Spatio-Temporal Turbulence Mitigation: A Translational Perspective

Recovering images distorted by atmospheric turbulence is a challenging inverse problem due to the stochastic nature of turbulence. Although numerous turbulence mitigation (TM) algorithms have been proposed, their efficiency and generalization to real-world dynamic scenarios remain severely limited. Building upon the intuitions of classical TM algorithms, we present the Deep Atmospheric TUrbulence Mitigation network (DATUM). DATUM aims to overcome major challenges when transitioning from classical to deep learning approaches. By carefully integrating the merits of classical multi-frame TM methods into a deep network structure, we demonstrate that DATUM can efficiently perform long-range temporal aggregation using a recurrent fashion, while deformable attention and temporal-channel attention seamlessly facilitate pixel registration and lucky imaging. With additional supervision, tilt and blur degradation can be jointly mitigated. These inductive biases empower DATUM to significantly outperform existing methods while delivering a tenfold increase in processing speed. A large-scale training dataset, ATSyn, is presented as a co-invention to enable generalization in real turbulence. Our code and datasets will be available at \href{https://xg416.github.io/DATUM}{\textcolor{pink}{https://xg416.github.io/DATUM}}

FarSight: A Physics-Driven Whole-Body Biometric System at Large Distance and Altitude

Whole-body biometric recognition is an important area of research due to its vast applications in law enforcement, border security, and surveillance. This paper presents the end-to-end design, development and evaluation of FarSight, an innovative software system designed for whole-body (fusion of face, gait and body shape) biometric recognition. FarSight accepts videos from elevated platforms and drones as input and outputs a candidate list of identities from a gallery. The system is designed to address several challenges, including (i) low-quality imagery, (ii) large yaw and pitch angles, (iii) robust feature extraction to accommodate large intra-person variabilities and large inter-person similarities, and (iv) the large domain gap between training and test sets. FarSight combines the physics of imaging and deep learning models to enhance image restoration and biometric feature encoding. We test FarSight's effectiveness using the newly acquired IARPA Biometric Recognition and Identification at Altitude and Range (BRIAR) dataset. Notably, FarSight demonstrated a substantial performance increase on the BRIAR dataset, with gains of +11.82% Rank-20 identification and +11.3% TAR@1% FAR.

Scattering and Gathering for Spatially Varying Blurs

A spatially varying blur kernel $h(\mathbf{x},\mathbf{u})$ is specified by an input coordinate $\mathbf{u} \in \mathbb{R}^2$ and an output coordinate $\mathbf{x} \in \mathbb{R}^2$. For computational efficiency, we sometimes write $h(\mathbf{x},\mathbf{u})$ as a linear combination of spatially invariant basis functions. The associated pixelwise coefficients, however, can be indexed by either the input coordinate or the output coordinate. While appearing subtle, the two indexing schemes will lead to two different forms of convolutions known as scattering and gathering, respectively. We discuss the origin of the operations. We discuss conditions under which the two operations are identical. We show that scattering is more suitable for simulating how light propagates and gathering is more suitable for image filtering such as denoising.

Real-Time Dense Field Phase-to-Space Simulation of Imaging through Atmospheric Turbulence

Numerical simulation of atmospheric turbulence is one of the biggest bottlenecks in developing computational techniques for solving the inverse problem in long-range imaging. The classical split-step method is based upon numerical wave propagation which splits the propagation path into many segments and propagates every pixel in each segment individually via the Fresnel integral. This repeated evaluation becomes increasingly time-consuming for larger images. As a result, the split-step simulation is often done only on a sparse grid of points followed by an interpolation to the other pixels. Even so, the computation is expensive for real-time applications. In this paper, we present a new simulation method that enables \emph{real-time} processing over a \emph{dense} grid of points. Building upon the recently developed multi-aperture model and the phase-to-space transform, we overcome the memory bottleneck in drawing random samples from the Zernike correlation tensor. We show that the cross-correlation of the Zernike modes has an insignificant contribution to the statistics of the random samples. By approximating these cross-correlation blocks in the Zernike tensor, we restore the homogeneity of the tensor which then enables Fourier-based random sampling. On a $512\times512$ image, the new simulator achieves 0.025 seconds per frame over a dense field. On a $3840 \times 2160$ image which would have taken 13 hours to simulate using the split-step method, the new simulator can run at approximately 60 seconds per frame.

Imaging through the Atmosphere using Turbulence Mitigation Transformer

Restoring images distorted by atmospheric turbulence is a long-standing problem due to the spatially varying nature of the distortion, nonlinearity of the image formation process, and scarcity of training and testing data. Existing methods often have strong statistical assumptions on the distortion model which in many cases will lead to a limited performance in real-world scenarios as they do not generalize. To overcome the challenge, this paper presents an end-to-end physics-driven approach that is efficient and can generalize to real-world turbulence. On the data synthesis front, we significantly increase the image resolution that can be handled by the SOTA turbulence simulator by approximating the random field via wide-sense stationarity. The new data synthesis process enables the generation of large-scale multi-level turbulence and ground truth pairs for training. On the network design front, we propose the turbulence mitigation transformer (TMT), a two stage U-Net shaped multi-frame restoration network which has a noval efficient self-attention mechanism named temporal channel joint attention (TCJA). We also introduce a new training scheme that is enabled by the new simulator, and we design new transformer units to reduce the memory consumption. Experimental results on both static and dynamic scenes are promising, including various real turbulence scenarios.

Accelerating Atmospheric Turbulence Simulation via Learned Phase-to-Space Transform

Fast and accurate simulation of imaging through atmospheric turbulence is essential for developing turbulence mitigation algorithms. Recognizing the limitations of previous approaches, we introduce a new concept known as the phase-to-space (P2S) transform to significantly speed up the simulation. P2S is build upon three ideas: (1) reformulating the spatially varying convolution as a set of invariant convolutions with basis functions, (2) learning the basis function via the known turbulence statistics models, (3) implementing the P2S transform via a light-weight network that directly convert the phase representation to spatial representation. The new simulator offers 300x -- 1000x speed up compared to the mainstream split-step simulators while preserving the essential turbulence statistics.

Image Reconstruction of Static and Dynamic Scenes through Anisoplanatic Turbulence

Ground based long-range passive imaging systems often suffer from degraded image quality due to a turbulent atmosphere. While methods exist for removing such turbulent distortions, many are limited to static sequences which cannot be extended to dynamic scenes. In addition, the physics of the turbulence is often not integrated into the image reconstruction algorithms, making the physics foundations of the methods weak. In this paper, we present a unified method for atmospheric turbulence mitigation in both static and dynamic sequences. We are able to achieve better results compared to existing methods by utilizing (i) a novel space-time non-local averaging method to construct a reliable reference frame, (ii) a geometric consistency and a sharpness metric to generate the lucky frame, (iii) a physics-constrained prior model of the point spread function for blind deconvolution. Experimental results based on synthetic and real long-range turbulence sequences validate the performance of the proposed method.

Simulating Anisoplanatic Turbulence by Sampling Inter-modal and Spatially Correlated Zernike Coefficients

Simulating atmospheric turbulence is an essential task for evaluating turbulence mitigation algorithms and training learning-based methods. Advanced numerical simulators for atmospheric turbulence are available, but they require evaluating wave propagation which is computationally expensive. In this paper, we present a propagation-free method for simulating imaging through turbulence. The key idea behind our work is a new method to draw inter-modal and spatially correlated Zernike coefficients. By establishing the equivalence between the angle-of-arrival correlation by Basu, McCrae and Fiorino (2015) and the multi-aperture correlation by Chanan (1992), we show that the Zernike coefficients can be drawn according to a covariance matrix defining the correlations. We propose fast and scalable sampling strategies to draw these samples. The new method allows us to compress the wave propagation problem into a sampling problem, hence making the new simulator significantly faster than existing ones. Experimental results show that the simulator has an excellent match with the theory and real turbulence data.

Rethinking Atmospheric Turbulence Mitigation

State-of-the-art atmospheric turbulence image restoration methods utilize standard image processing tools such as optical flow, lucky region and blind deconvolution to restore the images. While promising results have been reported over the past decade, many of the methods are agnostic to the physical model that generates the distortion. In this paper, we revisit the turbulence restoration problem by analyzing the reference frame generation and the blind deconvolution steps in a typical restoration pipeline. By leveraging tools in large deviation theory, we rigorously prove the minimum number of frames required to generate a reliable reference for both static and dynamic scenes. We discuss how a turbulence agnostic model can lead to potential flaws, and how to configure a simple spatial-temporal non-local weighted averaging method to generate references. For blind deconvolution, we present a new data-driven prior by analyzing the distributions of the point spread functions. We demonstrate how a simple prior can outperform state-of-the-art blind deconvolution methods.