Hyperspectral sensing in the long-wave infrared (LWIR) domain is complicated by the ambiguity between a material’s temperature and its emissivity—a problem known as temperature-emissivity separation (TES). In this letter, we develop a Bayesian approach to the TES problem that disambiguates emissivity values through a novel prior that uses a copula-based Markov chain model. While supporting efficient posterior inference through the forward-backward algorithm, the proposed copula chain improves emissivity retrieval performance by enforcing physical$[{0, 1}]$emissivity bounds and capturing interband correlation. Numerical results demonstrate significant improvement over the existing methods, including a 54% reduction in emissivity estimation error relative to the least-squares TES (LS-TES) algorithm for a 20 microflick noise level. Finally, the posterior uncertainty characterization of the proposed Bayesian algorithm is expected to aid subsequent exploitation tasks, such as material classification and sensor fusion.

Exploitation of hyperspectral long-wave infrared (LWIR) data often involves an emissivity retrieval process where ground-surface emissivity is estimated from at-sensor radiance measurements. Emissivity retrieval consists of both atmospheric compensation and temperature separation, however the presence of spatial-spectral distortion or small spectral calibration errors can engender large errors in emissivity retrieval. In this paper we propose an efficient emissivity retrieval algorithm that jointly performs atmospheric compensation and temperature-emissivity separation while compensating for spectral uncertainty that may exist due to smile or calibration artifacts. Without relying on particular in-scene materials, such as blackbodies or in-library elements, the proposed algorithm estimates unique spectral response function (SRF) band centers and bandwidths at each spatial-spectral index of the focal plane array (FPA) in order to compensate for optical distortions. Like the automatic retrieval of temperature and emissivity using spectral smoothness (ARTEMISS) method, the approach utilizes a spectral smoothness form of regularization. The proposed algorithm, decoding infrared atmospheres in ARTEMISS (DIANA), relies on a deep neural network decoder in order to efficiently model a sequence of SRF-weighted transmission-upwelling-downwelling (TUD) vectors applicable across the FPA and employs a genetic algorithm to perform the high-dimensional inference task. Experimental results on synthetic and measured data quantify performance in a range of environmental conditions and distortion levels, while results from measured data highlight a 26-31% average reduction in emissivity estimation error relative to existing algorithms.

Models of endmember variability capture the notion that multiple spectra may represent a single class or material, and while these models are physically realistic, they often give rise to excessive computational complexity during the spectral unmixing process. In this letter, we present a computationally tractable supervised unmixing method that uses Gauss-Markov processes to model endmember variability and interband correlation properties within endmembers. We use a probabilistic graphical model over multiple Gauss-Markov processes to capture the mixing effects of a spectral sensor and employ sum-product message passing to develop an accelerated statistical unmixing algorithm. The computational complexity of the proposed unmixing algorithm is only linear in the number of bands, making it suitable for both hyperspectral (hundreds of bands) and ultraspectral (thousands of bands) applications. Unmixing examples with measured reflectance spectra show sizable performance improvements when accounting for interband correlation using the proposed method, and empirical results quantify orders of magnitude reduction in complexity compared to alternative methods.

In this work, we present a novel technique for image recovery from highly undersampled phase contrast magnetic resonance imaging (PC-MRI) data. Our approach is holistic and includes modeling of the underlying physics, optimized sampling strategies, and design of a novel inversion algorithm. We capture the unique magnitude and phase structure of PC-MRI data as a non-Gaussian conditional mixture density. We then create a factor graph that describes the joint posterior probability of the inference variables given the noisy measurements. A combination of standard belief propagation and generalized approximate message passing (GAMP) is used to form an iterative inversion algorithm capable of producing MAP or MMSE estimates of the signal of interest. Using the proposed technique, we demonstrate high-fidelity PC-MRI recovery for simulated and phantom data undersampled by a factor of ten.

In this letter, we present an autofocus routine for backprojection imagery from spotlight-mode synthetic aperture radar data. The approach is based on maximizing image sharpness and supports the flexible collection and imaging geometries of BP, including wide-angle apertures and the ability to image directly onto a digital elevation map. While image-quality-based autofocus approaches can be computationally intensive, in the backprojection setting, we demonstrate a natural geometric interpretation that allows for optimal single-pulse phase corrections to be derived in closed form as the solution of a quartic polynomial. The approach is applicable to focusing standard backprojection imagery, as well as providing incremental focusing in sequential imaging applications based on autoregressive backprojection. An example demonstrates the efficacy of the approach applied to real data for a wide-aperture backprojection image.

Hyperspectral change detection (HSCD) provides an avenue for detecting subtle targets in complex backgrounds. Complicating the problem of change detection is the presence of shadow, illumination, and atmospheric differences, as well as misregistration and parallax error, which often produce the appearance of change. Recent development of a model-based (MB) approach to HSCD has demonstrated potential improvement for mitigating false alarms due specifically to shadow differences using calibrated data. Further development and application of the MB approach is provided here. The method is extended for use on both uncalibrated and relatively calibrated hyperspectral data and is applied to airborne hyperspectral imagery collected using the Hyperspectral Digital Imagery Collection Experiment visible to short-wave infrared sensor and uncalibrated tower imagery collected by the Air Force Research Laboratory.

Cellular populations are typically heterogenous collections of cells at different points in their respective cell cycles, each with a cell cycle time that varies from individual to individual. As a result, true single-cell behavior, particularly that which is cell-cycle--dependent, is often obscured in population-level (averaged) measurements. We have developed a simple deconvolution method that can be used to remove the effects of asynchronous variability from population-level time-series data. In this paper, we summarize some recent progress in the development and application of our approach, and provide technical updates that result in increased biological fidelity. We also explore several preliminary validation results and discuss several ongoing applications that highlight the method's usefulness for estimating parameters in differential equation models of single-cell gene regulation.

We consider the problem of parameter estimation for signals characterized by sums of parameterized functions. We present a dynamic dictionary subset selection approach to parameter estimation where we iteratively select a small number of dictionary elements and then alter the parameters of these dictionary elements to achieve better signal model fit. The proposed approach avoids the use of highly oversampled (and highly correlated) dictionary elements, which are needed in fixed dictionary approaches to reduce parameter bias associated with dictionary quantization. We demonstrate estimation performance on a sinusoidal signal estimation example.

Within the hyperspectral community, change detection is a continued area of interest. Interesting changes in imagery typically correspond to changes in material reflectance associated with pixels in the scene. Using a physical model describing the sensor-reaching radiance, change detection can be formulated as a statistical hypothesis test. Complicating the problem of change detection is the presence of shadow, illumination, and atmospheric differences, as well as misregistration and parallax error, which often produce the appearance of change. The proposed physical model incorporates terms to account for both direct and diffuse shadow fractions to help mitigate false alarms associated with shadow differences between scenes. The resulting generalized likelihood ratio test (GLRT) provides an indicator of change at each pixel. The maximum likelihood estimates of the physical model parameters used for the GLRT are obtained from the entire joint data set to take advantage of coupled information existing between pixel measurements. Simulation results using synthetic and real imagery demonstrate the efficacy of the proposed approach.

This paper considers the estimation of shooter locations using a sensor network where each sensor measures the time difference between receptions of a firearm's muzzle blast and a bullet's shockwave. This recently proposed approach has the advantages of reduced hardware complexity and not requiring time synchronization between sensors. The disadvantages are increased computational complexity and a requirement to know the bullet's velocity at all points along the trajectory. This paper proposes to eliminate these disadvantages by intentionally adopting an incorrect model that assumes a constant bullet velocity. The model misspecification naturally induces bias in subsequent maximum likelihood estimates (MLEs). We explore the performance impact of the model misspecification through analytical derivation of the bias and variance of the pseudo MLE. The analytic results are applied to several realistic firearm models and corroborated with simulations.

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure "just-in-time" assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract "single-cell"-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell.

In sensor network self-localization, anchor nodes provide a convenient means to disambiguate scene translation and rotation, thereby affording estimates in an absolute coordinate system. However, localization performance depends on the positions of the anchor nodes relative to the unknown-location nodes. Conventional wisdom in the literature is that anchor nodes should be placed around the perimeter of the network. In this paper, we show analytically why this strategy works well universally. We demonstrate that perimeter placement forces the information provided by the anchor constraints to closely align with the subspace that cannot be estimated from inter-node measurements: the subspace of translations and rotations. Examples quantify the efficacy of perimeter placement of anchors.

This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The location parameters are shown to have a natural decomposition into relative configuration and centroid transformation components based on the influence of measurements and prior information in the problem. A linear representation of the transformation parameter space, which includes rotations and translations, is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). To regularize the absolute localization problem, we consider constraints on the coordinate locations and the impact of these constraints on relative and absolute location error. A geometric interpretation of the constrained Cramer-Rao bound (CRB) is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples illustrate the utility of this error decomposition.

Sensor location information is a prerequisite to the utility of most sensor networks. In this paper we present a robust and low-complexity algorithm to self-localize and orient sensors in a network based on angle-of-arrival (AOA) information. The proposed non-iterative subspace-based method is robust to missing and noisy measurements and works for cases when sensor orientations are either known or unknown. We show that the computational complexity of the algorithm is O (mn2), where m is the number of measurements and n is the total number of sensors. Simulation results demonstrate that the error of the proposed subspace algorithm is only marginally greater than an iterative maximum-likelihood estimator (MLE), while the computational complexity is two orders of magnitude less. Additionally, the iterative MLE is prone to converge to local maxima in the likelihood function without accurate initialization. We illustrate that the proposed subspace method can be used to initialize the MLE and obtain near-Cramér-Rao performance for sensor localization. Finally, the scalability of the subspace algorithm is illustrated by demonstrating how clusters within a large network may be individually localized and then merged.

Self-localization is an important component of distributed sensor systems. The presence of a few highly erroneous measurements, or outliers, results in erroneous sensor location estimates. In this paper, we employ the EM algorithm to iteratively detect outlier measurements and provide robust position estimates of the sensors. The derivation of the algorithm is given, and Monte-Carlo simulations are presented to compare this estimator to others. The performance of the EM-based algorithm is also shown to be close to the Cramer-Rao lower bound for position estimation when perfect knowledge of the outlier process is known.