Raghu G. Raj

Carter Lyons, Raghu G. Raj, Margaret Cheney

Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections within the compound Gaussian (CG) class of distributions. The CG class subsumes many commonly used priors in signal and image reconstruction methods including those of sparsity-based approaches. The first method developed is an iterative algorithm, called generalized compound Gaussian least squares (G-CG-LS), that minimizes a regularized least squares objective function where the regularization enforces a CG prior. G-CG-LS is then unrolled, or unfolded, to furnish our second method, which is a novel deep regularized (DR) neural network, called DR-CG-Net, that learns the prior information. A detailed computational theory on convergence properties of G-CG-LS and thorough numerical experiments for DR-CG-Net are provided. Due to the comprehensive nature of the CG prior, these experiments show that DR-CG-Net outperforms competitive prior art methods in tomographic imaging and compressive sensing, especially in challenging low-training scenarios.

Sophia Li, Max Zhao, Raghu G. Raj et al.

Floods frequently impact regions around the world. Rapid and accurate flood detection is crucial for emergency response and timely mitigation of human and economic loss. The expanding availability of satellite data and advances in artificial intelligence have enhanced monitoring of environmental hazards, but many flood events remain challenging to detect because cloud cover obscures optical satellite imagery. Rambour et al. introduced the SEN12-FLOOD dataset and extracted per-image features using a ResNet-50 convolutional neural network backbone, then fed these features into a gated recurrent unit network to show that temporal information can substantially improve accuracy compared to single-image baselines. More recently, Chamatidis et al. showed that a vision transformer can achieve strong performance with popular convolutional architectures. However, these models typically function as opaque black boxes, making it difficult to interpret their decision boundaries, learned features, and internal reasoning, especially in safety-critical domains like remote sensing. In contrast, topological data analysis (TDA) provides a mathematically grounded framework for capturing global structural features of data. TDA has emerged as a powerful tool for analyzing complex imagery, especially imagery with geometrically interpretable structures, of which floods are a prime candidate. In this work, we systematically evaluate topological descriptors for flood detection using the open-source SEN12-FLOOD dataset. By extracting topological features from each image and incorporating them into neural networks, we demonstrate that topological descriptors carry meaningful flood signals independently and complement existing networks to yield more robust and interpretable flood detection systems.

Carter Lyons, Raghu G. Raj, Margaret Cheney

Algorithm unfolding or unrolling is the technique of constructing a deep neural network (DNN) from an iterative algorithm. Unrolled DNNs often provide better interpretability and superior empirical performance over standard DNNs in signal estimation tasks. An important theoretical question, which has only recently received attention, is the development of generalization error bounds for unrolled DNNs. These bounds deliver theoretical and practical insights into the performance of a DNN on empirical datasets that are distinct from, but sampled from, the probability density generating the DNN training data. In this paper, we develop novel generalization error bounds for a class of unrolled DNNs that are informed by a compound Gaussian prior. These compound Gaussian networks have been shown to outperform comparative standard and unfolded deep neural networks in compressive sensing and tomographic imaging problems. The generalization error bound is formulated by bounding the Rademacher complexity of the class of compound Gaussian network estimates with Dudley's integral. Under realistic conditions, we show that, at worst, the generalization error scales $\mathcal{O}(n\sqrt{\ln(n)})$ in the signal dimension and $\mathcal{O}(($Network Size$)^{3/2})$ in network size.

Owen T. Huber, Raghu G. Raj, Tianyu Chen et al.

This paper introduces a novel methodology of adapting the representation of videos based on the dynamics of their scene content variation. In particular, we demonstrate how the clustering of dynamic mode decomposition eigenvalues can be leveraged to learn an adaptive video representation for separating structurally distinct morphologies of a video. We extend the morphological component analysis (MCA) algorithm, which uses multiple predefined incoherent dictionaries and a sparsity prior to separate distinct sources in signals, by introducing our novel eigenspace clustering technique to obtain data-driven MCA dictionaries, which we call dynamic morphological component analysis (DMCA). After deriving our novel algorithm, we offer a motivational example of DMCA applied to a still image, then demonstrate DMCA's effectiveness in denoising applications on videos from the Adobe 240fps dataset. Afterwards, we provide an example of DMCA enhancing the signal-to-noise ratio of a faint target summed with a sea state, and conclude the paper by applying DMCA to separate a bicycle from wind clutter in inverse synthetic aperture radar images.

Carter Lyons, Raghu G. Raj, Margaret Cheney

For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized least squares objective function where the regularization is based on a compound Gaussian prior distribution. The compound Gaussian prior subsumes many of the commonly used priors in image reconstruction, including those of sparsity-based approaches. The developed iterative algorithm gives rise to the paper's second new approach, which is a deep neural network that corresponds to an "unrolling" or "unfolding" of the iterative algorithm. Unrolled deep neural networks have interpretable layers and outperform standard deep learning methods. This paper includes a detailed computational theory that provides insight into the construction and performance of both algorithms. The conclusion is that both algorithms outperform other state-of-the-art approaches to tomographic image formation and compressive sensing, especially in the difficult regime of low training.

Raghu G. Raj

We present a novel variation of online kernel machines in which we exploit a consensus based optimization mechanism to guide the evolution of decision functions drawn from a reproducing kernel Hilbert space, which efficiently models the observed stationary process.

John McKay, Raghu G. Raj, Vishal Monga

Any image recovery algorithm attempts to achieve the highest quality reconstruction in a timely manner. The former can be achieved in several ways, among which are by incorporating Bayesian priors that exploit natural image tendencies to cue in on relevant phenomena. The Hierarchical Bayesian MAP (HB-MAP) is one such approach which is known to produce compelling results albeit at a substantial computational cost. We look to provide further analysis and insights into what makes the HB-MAP work. While retaining the proficient nature of HB-MAP's Type-I estimation, we propose a stochastic approximation-based approach to Type-II estimation. The resulting algorithm, fast stochastic HB-MAP (fsHBMAP), takes dramatically fewer operations while retaining high reconstruction quality. We employ our fsHBMAP scheme towards the problem of tomographic imaging and demonstrate that fsHBMAP furnishes promising results when compared to many competing methods.

John McKay, Isaac Gerg, Vishal Monga et al.

Finding mines in Sonar imagery is a significant problem with a great deal of relevance for seafaring military and commercial endeavors. Unfortunately, the lack of enormous Sonar image data sets has prevented automatic target recognition (ATR) algorithms from some of the same advances seen in other computer vision fields. Namely, the boom in convolutional neural nets (CNNs) which have been able to achieve incredible results - even surpassing human actors - has not been an easily feasible route for many practitioners of Sonar ATR. We demonstrate the power of one avenue to incorporating CNNs into Sonar ATR: transfer learning. We first show how well a straightforward, flexible CNN feature-extraction strategy can be used to obtain impressive if not state-of-the-art results. Secondly, we propose a way to utilize the powerful transfer learning approach towards multiple instance target detection and identification within a provided synthetic aperture Sonar data set.

John McKay, Vishal Monga, Raghu G. Raj

Sonar imaging has seen vast improvements over the last few decades due in part to advances in synthetic aperture Sonar (SAS). Sophisticated classification techniques can now be used in Sonar automatic target recognition (ATR) to locate mines and other threatening objects. Among the most promising of these methods is sparse reconstruction-based classification (SRC) which has shown an impressive resiliency to noise, blur, and occlusion. We present a coherent strategy for expanding upon SRC for Sonar ATR that retains SRC's robustness while also being able to handle targets with diverse geometric arrangements, bothersome Rayleigh noise, and unavoidable background clutter. Our method, pose corrected sparsity (PCS), incorporates a novel interpretation of a spike and slab probability distribution towards use as a Bayesian prior for class-specific discrimination in combination with a dictionary learning scheme for localized patch extractions. Additionally, PCS offers the potential for anomaly detection in order to avoid false identifications of tested objects from outside the training set with no additional training required. Compelling results are shown using a database provided by the United States Naval Surface Warfare Center.

John McKay, Anne Gelb, Vishal Monga et al.

Recent progress in synthetic aperture sonar (SAS) technology and processing has led to significant advances in underwater imaging, outperforming previously common approaches in both accuracy and efficiency. There are, however, inherent limitations to current SAS reconstruction methodology. In particular, popular and efficient Fourier domain SAS methods require a 2D interpolation which is often ill conditioned and inaccurate, inevitably reducing robustness with regard to speckle and inaccurate sound-speed estimation. To overcome these issues, we propose using the frame theoretic convolution gridding (FTCG) algorithm to handle the non-uniform Fourier data. FTCG extends upon non-uniform fast Fourier transform (NUFFT) algorithms by casting the NUFFT as an approximation problem given Fourier frame data. The FTCG has been show to yield improved accuracy at little more computational cost. Using simulated data, we outline how the FTCG can be used to enhance current SAS processing.

John McKay, Vishal Monga, Raghu Raj

Advancements in Sonar image capture have opened the door to powerful classification schemes for automatic target recognition (ATR. Recent work has particularly seen the application of sparse reconstruction-based classification (SRC) to sonar ATR, which provides compelling accuracy rates even in the presence of noise and blur. Existing sparsity based sonar ATR techniques however assume that the test images exhibit geometric pose that is consistent with respect to the training set. This work addresses the outstanding open challenge of handling inconsistently posed test sonar images relative to training. We develop a new localized block-based dictionary design that can enable geometric, i.e. pose robustness. Further, a dictionary learning method is incorporated to increase performance and efficiency. The proposed SRC with Localized Pose Management (LPM), is shown to outperform the state of the art SIFT feature and SVM approach, due to its power to discern background clutter in Sonar images.

John McKay, Raghu Raj, Vishal Monga et al.

Advancements in Sonar image capture have enabled researchers to apply sophisticated object identification algorithms in order to locate targets of interest in images such as mines. Despite progress in this field, modern sonar automatic target recognition (ATR) approaches lack robustness to the amount of noise one would expect in real-world scenarios, the capability to handle blurring incurred from the physics of image capture, and the ability to excel with relatively few training samples. We address these challenges by adapting modern sparsity-based techniques with dictionaries comprising of training from each class. We develop new discriminative (as opposed to generative) sparse representations which can help automatically classify targets in Sonar imaging. Using a simulated SAS data set from the Naval Surface Warfare Center (NSWC), we obtained compelling classification rates for multi-class problems even in cases with considerable noise and sparsity in training samples.