Computational wave imaging (CWI) extracts hidden structure and physical properties of a volume of material by analyzing wave signals that traverse that volume. Applications include seismic exploration of the Earth's subsurface, acoustic imaging and non-destructive testing in material science, and ultrasound computed tomography in medicine. Current approaches for solving CWI problems can be divided into two categories: those rooted in traditional physics, and those based on deep learning. Physics-based methods stand out for their ability to provide high-resolution and quantitatively accurate estimates of acoustic properties within the medium. However, they can be computationally intensive and are susceptible to ill-posedness and nonconvexity typical of CWI problems. Machine learning-based computational methods have recently emerged, offering a different perspective to address these challenges. Diverse scientific communities have independently pursued the integration of deep learning in CWI. This review discusses how contemporary scientific machine-learning (ML) techniques, and deep neural networks in particular, have been developed to enhance and integrate with traditional physics-based methods for solving CWI problems. We present a structured framework that consolidates existing research spanning multiple domains, including computational imaging, wave physics, and data science. This study concludes with important lessons learned from existing ML-based methods and identifies technical hurdles and emerging trends through a systematic analysis of the extensive literature on this topic.

A closed-form non-parametric detector for rare targets in hyperspectral images is developed, extending the so-called Veritas approach, which until now had been explored only for parametric background models. By treating the typically unknown target fill-factor as known and equal to the smallest value that can be detected at a given level of detectability, an admissible NP detector is obtained. Experimental results on a hyperspectral target detection scenario reveals the potential of the proposed approach, and sets the path for developing more complex but still mathematically and computationally tractable non-parametric admissible detectors based on multiple discrete target fill-factors.

Numerical experiments compare Bayesian and non-Bayesian Generalized Likelihood Ratio Test (GLRT) detection algorithms for opaque sub-pixel hyperspectral targets of unknown abundance. A simplified problem is identified, which allows the full range of Bayesian priors to be explored. When one seeks to minimize the false alarm rate at a fixed detection rate, one finds that GLRT detection outperforms Bayesian detection for any choice of prior. By contrast, when the criterion is detection rate at fixed false alarm rate, Bayesian detection is better. The results hold over a wide range of parameters, and appear to contradict known optimality results for Bayesian detectors. The apparent discrepancy is explained, and a case is made for the practical use of GLRT-based detection statistics.

We investigate the use of Bayesian methods for hyperspectral subpixel target detection, where the uncertainty associated with the target fill factor is “probabilized” by a suitable prior. Specifically, we present a general framework for Bayesian target detection by employing different models for the background distribution, comparing different choices for the Bayesian prior, and investigating different numerical schemes for evaluating the Bayesian integral. The Bayesian methods are furthermore compared to their Generalized Likelihood Ratio Test (GLRT)-based counterparts. Experiments performed over real hyperspectral imagery, with both real and implanted subpixel targets, show that incorporating prior knowledge by means of non-uniform priors emphasizing smaller target fill factors outperforms usage of the “noninformative” uniform prior and enhances Bayes performance beyond the GLRT, a result observed for both parametric and non-parametric background models. We find that even “rough” priors can successfully leverage the context-based information by emphasizing target sizes that are of most interest. We further observe that the Gauss-Legendre numerical integration scheme provides efficient integral approximation while maintaining the desirable admissibility property of Bayesian methods.

Seismic full-waveform inversion (FWI) is a nonlinear computational imaging technique that can provide detailed estimates of subsurface geophysical properties. Solving the FWI problem can be challenging due to its ill-posedness and high computational cost. In this work, we develop a new hybrid computational approach to solve FWI that combines physics-based models with data-driven methodologies. In particular, we develop a data augmentation strategy that can not only improve the representativity of the training set but also incorporate important governing physics into the training process and, therefore, improve the inversion accuracy. To validate the performance, we apply our method to synthetic elastic seismic waveform data generated from a subsurface geologic model built on a carbon sequestration site at Kimberlina, California. We compare our physics-consistent data-driven inversion method to both purely physics-based and purely data-driven approaches and observe that our method yields higher accuracy and greater generalization ability.

We implement and evaluate a Bayesian detector for opaque subpixel hyperspectral targets of unknown abundance. Using both simulated and real hyperspectral backgrounds, we compare this detector to the more conventional generalized likelihood ratio test (GLRT) approach, identifying theoretical differences and observing numerical similarities. Among the theoretical advantages provided by the Bayesian detector is admissibility, which means that no detector can be uniformly superior to it. Potential disadvantages include the need to choose a prior distribution, and the computation required to integrate that distribution. For solid subpixel targets, the uniform prior is a natural choice, and we find that adequately-accurate numerical integration can be achieved with only a few evaluations of the likelihood function. We show results for targets implanted in both simulated and real data.

For additive signals on Gaussian clutter, the optimal detector is a linear matched filter that is adapted to the known signal and the covariance of the background. This adaptive matched filter (AMF) is widely used for gas-phase plume detection, even though the effect of the plume on the background is not strictly additive. Here, a derivation of the matched filter for a strictly absorptive plume produces, even in the weak plume limit, a quadratic filter. Assuming a Gaussian background, we derive two expressions, one based on the locally most powerful (LMP) detector which corresponds to the weak plume limit, and one based on the generalized likelihood ratio test (GLRT). Numerical experiments indicate that, as long as the plume is strong enough to be detected at all, both the GLRT and the linear matched filter outperform the LMP detector.

The generalized likelihood ratio test (GLRT) is used to derive a detector for solid sub-pixel targets in hyperspectral imagery. A closed-form solution is obtained that optimizes the replacement target model when the background is a fat-tailed elliptically-contoured multivariate t-distribution. This generalizes GLRT-based detectors that have previously been derived for the replacement target model with Gaussian background, and for the additive target model with an elliptically-contoured background. Experiments with simulated hyperspectral data illustrate the performance of this detector in various parameter regimes.

In the above paper[1], there are several errors, which we correct here.

We formulate hyperspectral target detection in terms of a local context by modeling the relationship of individual pixels with the annuli of pixels that surround them. A prediction of the center pixel in terms of the annulus pixels provides an estimate of the target-free pixel value, and this estimate can be used as a baseline against which a measurement of that pixel is compared. When the measurement is far from the baseline, that is evidence that the target-free hypothesis is incorrect - and that there is a target at that pixel. The predictor is adaptive to the image, and in this paper, we suggest making it more adaptive by segmenting the image into qualitatively different regions, and learning a new predictor for each region. We learn a new predictor for each segment, and attempt to optimize the segmentation so as to minimize the prediction error, overall. We apply this approach to some well-known hyperspectral datasets, and find that (as expected) the average prediction error is reduced and (less expected) that the “segments” that are discovered are spatially quite scattered, and (in the case with two segments) tend to group image pixels into edges and non-edges.

In hyperspectral target detection, a hyperspectral image is usually collected from an airborne or satellite platform, and the goal is to identify all occurrences of a particular target material within that image. When the target of interest can have a single relatively stable reference spectrum, e.g., as with a chemical plume, then the detection algorithms are relatively straightforward. When the target of interest can be represented by a variety of spectra, then the detection algorithms are more complicated. For variable target spectra, subspace detection approaches are typically used. As the number of target spectra that are needed to describe the target grows, however, so does the size of the target subspace, and so does the number of false detections. Here we present an experiment on the newly developed Simplex ACE detector, where the target subspace is instead represented by a constrained subspace, or simplex. We will show how increased target variability causes Subspace ACE to degrade as the target subspace approaches the entire image subspace, and demonstrate how Simplex ACE is robust to that same variability.

We examine the properties and performance of kernelized anomaly detectors, with an emphasis on the Mahalanobis-distance-based kernel RX (KRX) algorithm. Although the detector generally performs well for high-bandwidth Gaussian kernels, it exhibits problematic (in some cases, catastrophic) performance for distances that are large compared to the bandwidth. By comparing KRX to two other anomaly detectors, we can trace the problem to a projection in feature space, which arises when a pseudoinverse is used on the covariance matrix in that feature space. We show that a regularized variant of KRX overcomes this difficulty and achieves superior performance over a wide range of bandwidths.

A robust version of Principal Component Analysis (PCA) can be constructed via a decomposition of a data matrix into low rank and sparse components, the former representing a low-dimensional linear model of the data, and the latter representing sparse deviations from the low-dimensional subspace. This decomposition has been shown to be highly effective, but the underlying model is not appropriate when the data are not modeled well by a single low-dimensional subspace. We construct a new decomposition corresponding to a more general underlying model consisting of a union of low-dimensional subspaces, and demonstrate the performance on a video background removal problem.

We describe an approach for improving the robustness to misregistration of pixel-wise anomalous change detection (ACD) algorithms. The aim of ACD is to distinguish actual anomalous changes from the irrelevant incidental differences that occur throughout the scene. For such change detection to be effective, it is important that corresponding pixels in the two images of interest correspond to the same location in the scene. Indeed, one of the most confounding sources of incidental differences is the inevitable imprecision in the coregistration of the two images. We address this with small local adjustments to the coregistration which leads to a modified misregistration-insensitive measure of anomalousness. Several variants are considered, and the resulting performance improvements are evaluated using both real and simulated changes, and real and simulated misregistration.

We use singular vectors of the whitened cross-covariance matrix of two hyper-spectral images and the Golub-Kahan permutations in order to obtain equivalent tridiagonal representations of the coefficient matrices for a family of covariance-based quadratic Anomalous Change Detection (ACD) algorithms. Due to the nature of the problem these tridiagonal matrices have block-diagonal structure, which we exploit to derive analytical expressions for the eigenvalues of the coefficient matrices in terms of the singular values of the whitened cross-covariance matrix. The block-diagonal structure of the matrices of the RX, Chronochrome, symmetrized Chronochrome, Whitened Total Least Squares, Hyperbolic and Subpixel Hyperbolic Anomalous change detectors are revealed by the white singular value decomposition and Golub-Kahan transformations. Similarities and differences in the properties of these change detectors are illuminated by their eigenvalue spectra.

We cast anomalous change detection as a binary classification problem, and use a support vector machine (SVM) to build a detector that does not depend on assumptions about the underlying data distribution. To speed up the computation, our SVM is implemented, in part, on a graphical processing unit. Results on real and simulated anomalous changes are used to compare performance to algorithms which effectively assume a Gaussian distribution.

We investigate three algorithms that use the sparse matrix transform (SMT) to produce variance-maximizing linear projections to a lower-dimensional space. The SMT expresses the projection as a sequence of Givens rotations and this enables computationally efficient implementation of the projection operator. The baseline algorithm uses the SMT to directly approximate the optimal solution that is given by principal components analysis (PCA). A variant of the baseline begins with a standard SMT solution, but prunes the sequence of Givens rotations to only include those that contribute to the variance maximization. Finally, a simpler and faster third algorithm is introduced; this also estimates the projection operator with a sequence of Givens rotations, but in this case, the rotations are chosen to optimize a criterion that more directly expresses the dimension reduction criterion.

We introduce a class of statistics for characterizing the periphery of a distribution, and show that these statistics are particularly valuable for problems in target detection. Because so many detection algorithms are rooted in Gaussian statistics, we concentrate on ellipsoidal models of high-dimensional data distributions (that is to say: covariance matrices), but we recommend several alternatives to the sample covariance matrix that more efficiently model the periphery of a distribution, and can more effectively detect anomalous data samples.

We derive a class of algorithms for detecting anomalous changes in hyperspectral image pairs by modeling the data with elliptically contoured (EC) distributions. These algorithms are generalizations of well-known detectors that are obtained when the EC function is Gaussian. The performance of these EC-based anomalous change detectors is assessed on real data using both real and simulated changes. In these experiments, the EC-based detectors substantially outperform their Gaussian counterparts.

We investigate the behavior of a detector for weak gaseous plumes in hyperspectral imagery that can be derived in terms of a generalized likelihood ratio test (GLRT) applied to an elliptically-contoured (EC) model for the distribution of background clutter. Two limiting cases of this EC-GLRT detector are the adaptive matched filter (AMF) and the adaptive coherence estimator (ACE). While the general EC-GLRT detector does not share the specific optimality or invariance properties exhibited by these limiting cases, it provides an in-between model that can be competitive with both of them over a broad range of scenarios.

Abstract Summary: We present a suite of on-line tools to design candidate vaccine proteins, and to assess antigen potential, using coverage of k-mers (as proxies for potential T-cell epitopes) as a metric. The vaccine design tool uses the recently published ‘mosaic’ method to generate protein sequences optimized for coverage of high-frequency k-mers; the coverage-assessment tools facilitate coverage comparisons for any potential antigens. To demonstrate these tools, we designed mosaic protein sets for B-clade HIV-1 Gag, Pol and Nef, and compared them to antigens used in a recent human vaccine trial. Availability: http://hiv.lanl.gov/content/sequence/MOSAIC/ Contact: [email protected] Supplementary information: Supplementary data are available at ftp://ftp-t10.lanl.gov/pub/btk/WebToolsData

We describe a modification of the standard support vector machine (SVM) classifier that exploits the tendency for spatially contiguous pixels to be similarly classified. A quadratic term characterizing the spatial correlations in a multispectral image is added into the standard SVM optimization criterion. The mathematical structure of the SVM programming problem is retained, and the solution can be expressed in terms of the ordinary SVM solution with a modified dot product. The spatial correlations are characterized by a "contiguity matrix" psi whose computation does not require labeled data; thus, the method provides a way to use a mix of labeled and unlabeled data. We present numerical comparisons of classification performance for this contiguity-enhanced SVM against a standard SVM for two multispectral data sets.

To derive a matched filter for detecting a weak target signal in a hyperspectral image, an estimate of the band-to-band covariance of the target-free background scene is required. We investigate the effects of including some of the target signal in the background scene. Although the covariance is contaminated by the presence of a target signal (there is increased variance in the direction of the target signature), we find that the matched filter is not necessarily affected. In fact, if the variation in plume strength is strictly uncorrelated with the variation in background spectra, the matched filter and its signal-to-clutter ratio (SCR) performance will not be impaired. While there is little a priori reason to expect significant correlation between the plume and the background, there usually is some residual correlation, and this correlation leads to a suppressing effect that limits the SCR obtainable even for strong plumes. These effects are described and quantified analytically, and the crucial role of this correlation is illustrated with some numerical examples using simulated plumes superimposed on real hyperspectral imagery. In one example, we observe an order-of-magnitude loss in SCR for a matched filter based on the contaminated covariance.

Online feature selection (OFS) provides an efficient way to sort through a large space of features, particularly in a scenario where the feature space is large and features take a significant amount of memory to store. Image processing operators, and especially combinations of image processing operators, provide a rich space of potential features for use in machine learning for image processing tasks but they are expensive to generate and store. In this paper we apply OFS to the problem of edge detection in grayscale imagery. We use a standard data set and compare our results to those obtained with traditional edge detectors, as well as with results obtained more recently using "statistical edge detection." We compare several different OFS approaches, including hill climbing, best first search, and grafting.

This paper studies the feasibility of enhancing the spatial resolution of multilook Multispectral Thermal Imager (MTI) imagery using an iterative resolution enhancement algorithm known as Projection Onto Convex Sets (POCS). A multiangle satellite image modeling tool is implemented, and simulated multilook MTI imagery is formed to test the resolution enhancement algorithm. Experiments are done to determine the optimal configuration and number of multiangle low-resolution images needed for a quantitative improvement in the spatial resolution of the high-resolution estimate. The issues of atmospheric path radiance and directional reflectance variations are explored to determine their effect on the resolution enhancement performance.

Synchronous firing limits the amount of information that can be extracted by averaging the firing rates of similarly tuned neurons. Here, we show that the loss of such rate-coded information due to synchronous oscillations between retinal ganglion cells can be overcome by exploiting the information encoded by the correlations themselves. Two very different models, one based on axon-mediated inhibitory feedback and the other on oscillatory common input, were used to generate artificial spike trains whose synchronous oscillations were similar to those measured experimentally. Pooled spike trains were summed into a threshold detector whose output was classified using Bayesian discrimination. For a threshold detector with short summation times, realistic oscillatory input yielded superior discrimination of stimulus intensity compared to rate-matched Poisson controls. Even for summation times too long to resolve synchronous inputs, gamma band oscillations still contributed to improved discrimination by reducing the total spike count variability, or Fano factor. In separate experiments in which neurons were synchronized in a stimulus-dependent manner without attendant oscillations, the Fano factor increased markedly with stimulus intensity, implying that stimulus-dependent oscillations can offset the increased variability due to synchrony alone.

High-frequency oscillatory potentials (HFOPs) in the vertebrate retina are stimulus specific. The phases of HFOPs recorded at any given retinal location drift randomly over time, but regions activated by the same stimulus tend to remain phase locked with approximately zero lag, whereas regions activated by spatially separate stimuli are typically uncorrelated. Based on retinal anatomy, we previously postulated that HFOPs are mediated by feedback from a class of axon-bearing amacrine cells that receive excitation from neighboring ganglion cells-via gap junctions-and make inhibitory synapses back onto the surrounding ganglion cells. Using a computer model, we show here that such circuitry can account for the stimulus specificity of HFOPs in response to both high- and low-contrast features. Phase locking between pairs of model ganglion cells did not depend critically on their separation distance, but on whether the applied stimulus created a continuous path between them. The degree of phase locking between spatially separate stimuli was reduced by lateral inhibition, which created a buffer zone around strongly activated regions. Stimulating the inhibited region between spatially separate stimuli increased their degree of phase locking proportionately. Our results suggest several experimental strategies for testing the hypothesis that stimulus-specific HFOPs arise from axon-mediated feedback in the inner retina.

Moving stimuli elicit oscillatory responses from retinal ganglion cells at frequencies between 60-100 Hz. We used a computer model of the inner retina to investigate whether the additional firing synchrony resulting from stimulus-evoked high frequency oscillations could contribute to the detection of moving bars. The responses of the model ganglion cells were similar to those of cat alpha cells. Event trains from the model ganglion cells simulated by moving bars were summed into a threshold detector with short integration window (2-4 msec) whose output was classified by an ideal observer. To isolate the contribution from firing correlations, the model ganglion cells were replaced by independent Poisson generators with matched time-dependent event rates. Compared to this control, firing correlations between the model ganglion cells allowed for improved detection of moving stimuli.

Batch implementations of support vector regression (SVR) are inefficient when used in an on-line setting because they must be retrained from scratch every time the training set is modified. Following an incremental support vector classification algorithm introduced by Cauwenberghs and Poggio (2001), we have developed an accurate on-line support vector regression (AOSVR) that efficiently updates a trained SVR function whenever a sample is added to or removed from the training set. The updated SVR function is identical to that produced by a batch algorithm. Applications of AOSVR in both on-line and cross-validation scenarios are presented. In both scenarios, numerical experiments indicate that AOSVR is faster than batch SVR algorithms with both cold and warm start.

Abstract — We have developed an automated feature detection/classification system, called Genie (GENetic Imagery Exploitation), which has been designed to generate image processing pipelines for a variety of feature detection/classification tasks. Genie is a hybrid evolutionary algorithm that addresses the general problem of finding features of interest in multi-spectral remotely-sensed images. We describe our system in detail together with experiments involving comparisons of Genie with several conventional supervised classification techniques, for a number of classification tasks using multi-spectral remotely-sensed imagery.

In mapping the k-means algorithm to FPGA hardware, we examined algorithm level transforms that dramatically increased the achievable parallelism. We apply the k-means algorithm to multi-spectral and hyper-spectral images, which have tens to hundreds of channels per pixel of data. K-means is an iterative algorithm that assigns assigns to each pixel a label indicating which of K clusters the pixel belongs to.

The use of matched filters on hyperspectral data has made it possible to detect faint signatures. This study uses a modified k-means clustering to improve matched filter performance. Several simple bivariate cases are examined in detail, and the interaction of filtering and partitioning is discussed. The authors show that clustering can reduce within-class variance and group pixels with similar correlation structures. Both of these features improve filter performance. The traditional k-means algorithm is modified to work with a sample of the image at each iteration and is tested against two hyperspectral datasets. A new "extreme" centroid initialization technique is introduced and shown to speed convergence. Several matched filtering formulations (the simple matched filter, the clutter matched filter, and the saturated matched filter) are compared for a variety of number of classes and synthetic hyperspectral images. The performance of the various clutter matched filter formulations is similar, all are about an order of magnitude better than the simple matched filter. Clustering is found to improve the performance of all matched filter formulations by a factor of two to five. Clustering in conjunction with clutter matched filtering can improve fifty-fold over the simple case, enabling very weak signals to be detected in hyperspectral images.