Learning High-dimensional Generalized Linear Autoregressive Models.

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector could correspond to a different node in a network, and the parameters of an autoregressive model would correspond to the impact of the network structure on the time series evolution. Often these models are used successfully in practice to learn the structure of social, epidemiological, financial, or biological neural networks. However, little is known about statistical guarantees on estimates of such models in non-Gaussian settings. This paper addresses the inference of the autoregressive parameters and associated network structure within a generalized linear model framework that includes Poisson and Bernoulli autoregressive processes. At the heart of this analysis is a sparsity-regularized maximum likelihood estimator. While sparsity-regularization is well-studied in the statistics and machine learning communities, those analysis methods cannot be applied to autoregressive generalized linear models because of the correlations and potential heteroscedasticity inherent in the observations. Sample complexity bounds are derived using a combination of martingale concentration inequalities and modern empirical process techniques for dependent random variables. These bounds, which are supported by several simulation studies, characterize the impact of various network parameters on estimator performance.

Approach to simultaneously denoise and invert backscatter and extinction from photon-limited atmospheric lidar observations.

Atmospheric lidar observations provide a unique capability to directly observe the vertical column of cloud and aerosol scattering properties. Detector and solar-background noise, however, hinder the ability of lidar systems to provide reliable backscatter and extinction cross-section estimates. Standard methods for solving this inverse problem are most effective with high signal-to-noise ratio observations that are only available at low resolution in uniform scenes. This paper describes a novel method for solving the inverse problem with high-resolution, lower signal-to-noise ratio observations that are effective in non-uniform scenes. The novelty is twofold. First, the inferences of the backscatter and extinction are applied to images, whereas current lidar algorithms only use the information content of single profiles. Hence, the latent spatial and temporal information in noisy images are utilized to infer the cross-sections. Second, the noise associated with photon-counting lidar observations can be modeled using a Poisson distribution, and state-of-the-art tools for solving Poisson inverse problems are adapted to the atmospheric lidar problem. It is demonstrated through photon-counting high spectral resolution lidar (HSRL) simulations that the proposed algorithm yields inverted backscatter and extinction cross-sections (per unit volume) with smaller mean squared error values at higher spatial and temporal resolutions, compared to the standard approach. Two case studies of real experimental data are also provided where the proposed algorithm is applied on HSRL observations and the inverted backscatter and extinction cross-sections are compared against the standard approach.

A quantitative microscopic approach to predict local recurrence based on in vivo intraoperative imaging of sarcoma tumor margins.

The goal of resection of soft tissue sarcomas located in the extremity is to preserve limb function while completely excising the tumor with a margin of normal tissue. With surgery alone, one-third of patients with soft tissue sarcoma of the extremity will have local recurrence due to microscopic residual disease in the tumor bed. Currently, a limited number of intraoperative pathology-based techniques are used to assess margin status; however, few have been widely adopted due to sampling error and time constraints. To aid in intraoperative diagnosis, we developed a quantitative optical microscopy toolbox, which includes acriflavine staining, fluorescence microscopy, and analytic techniques called sparse component analysis and circle transform to yield quantitative diagnosis of tumor margins. A series of variables were quantified from images of resected primary sarcomas and used to optimize a multivariate model. The sensitivity and specificity for differentiating positive from negative ex vivo resected tumor margins was 82 and 75%. The utility of this approach was tested by imaging the in vivo tumor cavities from 34 mice after resection of a sarcoma with local recurrence as a bench mark. When applied prospectively to images from the tumor cavity, the sensitivity and specificity for differentiating local recurrence was 78 and 82%. For comparison, if pathology was used to predict local recurrence in this data set, it would achieve a sensitivity of 29% and a specificity of 71%. These results indicate a robust approach for detecting microscopic residual disease, which is an effective predictor of local recurrence.

Multi-excitation Raman spectroscopy technique for fluorescence rejection.

Multi-excitation Raman spectroscopy filters out Raman signals from a fluorescent background by sequentially using multiple excitation frequencies. The filtering method exploits the shift of the Raman spectra with excitation frequency and the static response of the fluorescent background. This technique builds upon previous work which used two slightly shifted excitations, Shifted Excitation Raman Difference Spectroscopy (SERDS), in order to filter the Raman signal. An Expectation-Maximization algorithm is used to estimate the Raman and fluorescence signals from multiple spectra acquired with slightly shifted excitation frequencies. In both simulation and experiment, the efficacy of the algorithm increases with the number of excitation frequencies even when holding the total excitation energy constant, such that the signal to noise ratio is inversely proportional to the number of excitation frequencies. In situations where the intense fluorescence causes significant shot noise compared to the weak Raman signals, the multi-excitation approach is more effective than non-iterative techniques such as polynomial background subtraction.

Superimposed video disambiguation for increased field of view.

Many infrared optical systems in wide-ranging applications such as surveillance and security frequently require large fields of view (FOVs). Often this necessitates a focal plane array (FPA) with a large number of pixels, which, in general, is very expensive. In a previous paper, we proposed a method for increasing the FOV without increasing the pixel resolution of the FPA by superimposing multiple sub-images within a static scene and disambiguating the observed data to reconstruct the original scene. This technique, in effect, allows each sub-image of the scene to share a single FPA, thereby increasing the FOV without compromising resolution. In this paper, we demonstrate the increase of FOVs in a realistic setting by physically generating a superimposed video from a single scene using an optical system employing a beamsplitter and a movable mirror. Without prior knowledge of the contents of the scene, we are able to disambiguate the two sub-images, successfully capturing both large-scale features and fine details in each sub-image. We improve upon our previous reconstruction approach by allowing each sub-image to have slowly changing components, carefully exploiting correlations between sequential video frames to achieve small mean errors and to reduce run times. We show the effectiveness of this improved approach by reconstructing the constituent images of a surveillance camera video.

Engineering induction of singular neural rosette emergence within hPSC-derived tissues.

Human pluripotent stem cell (hPSC)-derived neural organoids display unprecedented emergent properties. Yet in contrast to the singular neuroepithelial tube from which the entire central nervous system (CNS) develops in vivo, current organoid protocols yield tissues with multiple neuroepithelial units, a.k.a. neural rosettes, each acting as independent morphogenesis centers and thereby confounding coordinated, reproducible tissue development. Here, we discover that controlling initial tissue morphology can effectively (>80%) induce single neural rosette emergence within hPSC-derived forebrain and spinal tissues. Notably, the optimal tissue morphology for observing singular rosette emergence was distinct for forebrain versus spinal tissues due to previously unknown differences in ROCK-mediated cell contractility. Following release of geometric confinement, the tissues displayed radial outgrowth with maintenance of a singular neuroepithelium and peripheral neuronal differentiation. Thus, we have identified neural tissue morphology as a critical biophysical parameter for controlling in vitro neural tissue morphogenesis furthering advancement towards biomanufacture of CNS tissues with biomimetic anatomy and physiology.

Rapid staining and imaging of subnuclear features to differentiate between malignant and benign breast tissues at a point-of-care setting.

PURPOSE: Histopathology is the clinical standard for tissue diagnosis; however, it requires tissue processing, laboratory personnel and infrastructure, and a highly trained pathologist to diagnose the tissue. Optical microscopy can provide real-time diagnosis, which could be used to inform the management of breast cancer. The goal of this work is to obtain images of tissue morphology through fluorescence microscopy and vital fluorescent stains and to develop a strategy to segment and quantify breast tissue features in order to enable automated tissue diagnosis. METHODS: We combined acriflavine staining, fluorescence microscopy, and a technique called sparse component analysis to segment nuclei and nucleoli, which are collectively referred to as acriflavine positive features (APFs). A series of variables, which included the density, area fraction, diameter, and spacing of APFs, were quantified from images taken from clinical core needle breast biopsies and used to create a multivariate classification model. The model was developed using a training data set and validated using an independent testing data set. RESULTS: The top performing classification model included the density and area fraction of smaller APFs (those less than 7 µm in diameter, which likely correspond to stained nucleoli).When applied to the independent testing set composed of 25 biopsy panels, the model achieved a sensitivity of 82 %, a specificity of 79 %, and an overall accuracy of 80 %. CONCLUSIONS: These results indicate that our quantitative microscopy toolbox is a potentially viable approach for detecting the presence of malignancy in clinical core needle breast biopsies.

Structured Illumination Microscopy and a Quantitative Image Analysis for the Detection of Positive Margins in a Pre-Clinical Genetically Engineered Mouse Model of Sarcoma.

Intraoperative assessment of surgical margins is critical to ensuring residual tumor does not remain in a patient. Previously, we developed a fluorescence structured illumination microscope (SIM) system with a single-shot field of view (FOV) of 2.1 × 1.6 mm (3.4 mm2) and sub-cellular resolution (4.4 µm). The goal of this study was to test the utility of this technology for the detection of residual disease in a genetically engineered mouse model of sarcoma. Primary soft tissue sarcomas were generated in the hindlimb and after the tumor was surgically removed, the relevant margin was stained with acridine orange (AO), a vital stain that brightly stains cell nuclei and fibrous tissues. The tissues were imaged with the SIM system with the primary goal of visualizing fluorescent features from tumor nuclei. Given the heterogeneity of the background tissue (presence of adipose tissue and muscle), an algorithm known as maximally stable extremal regions (MSER) was optimized and applied to the images to specifically segment nuclear features. A logistic regression model was used to classify a tissue site as positive or negative by calculating area fraction and shape of the segmented features that were present and the resulting receiver operator curve (ROC) was generated by varying the probability threshold. Based on the ROC curves, the model was able to classify tumor and normal tissue with 77% sensitivity and 81% specificity (Youden's index). For an unbiased measure of the model performance, it was applied to a separate validation dataset that resulted in 73% sensitivity and 80% specificity. When this approach was applied to representative whole margins, for a tumor probability threshold of 50%, only 1.2% of all regions from the negative margin exceeded this threshold, while over 14.8% of all regions from the positive margin exceeded this threshold.

Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging.

The nonparametric multiscale platelet algorithms presented in this paper, unlike traditional wavelet-based methods, are both well suited to photon-limited medical imaging applications involving Poisson data and capable of better approximating edge contours. This paper introduces platelets, localized functions at various scales, locations, and orientations that produce piece-wise linear image approximations, and a new multiscale image decomposition based on these functions. Platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries. For smoothness measured in certain Hölder classes, it is shown that the error of m-term platelet approximations can decay significantly faster than that of m-term approximations in terms of sinusoids, wavelets, or wedgelets. This suggests that platelets may outperform existing techniques for image denoising and reconstruction. Fast, platelet-based, maximum penalized likelihood methods for photon-limited image denoising, deblurring and tomographic reconstruction problems are developed. Because platelet decompositions of Poisson distributed images are tractable and computationally efficient, existing image reconstruction methods based on expectation-maximization type algorithms can be easily enhanced with platelet techniques. Experimental results suggest that platelet-based methods can outperform standard reconstruction methods currently in use in confocal microscopy, image restoration, and emission tomography.

Quantitative Segmentation of Fluorescence Microscopy Images of Heterogeneous Tissue: Application to the Detection of Residual Disease in Tumor Margins.

PURPOSE: To develop a robust tool for quantitative in situ pathology that allows visualization of heterogeneous tissue morphology and segmentation and quantification of image features. MATERIALS AND METHODS: TISSUE EXCISED FROM A GENETICALLY ENGINEERED MOUSE MODEL OF SARCOMA WAS IMAGED USING A SUBCELLULAR RESOLUTION MICROENDOSCOPE AFTER TOPICAL APPLICATION OF A FLUORESCENT ANATOMICAL CONTRAST AGENT: acriflavine. An algorithm based on sparse component analysis (SCA) and the circle transform (CT) was developed for image segmentation and quantification of distinct tissue types. The accuracy of our approach was quantified through simulations of tumor and muscle images. Specifically, tumor, muscle, and tumor+muscle tissue images were simulated because these tissue types were most commonly observed in sarcoma margins. Simulations were based on tissue characteristics observed in pathology slides. The potential clinical utility of our approach was evaluated by imaging excised margins and the tumor bed in a cohort of mice after surgical resection of sarcoma. RESULTS: Simulation experiments revealed that SCA+CT achieved the lowest errors for larger nuclear sizes and for higher contrast ratios (nuclei intensity/background intensity). For imaging of tumor margins, SCA+CT effectively isolated nuclei from tumor, muscle, adipose, and tumor+muscle tissue types. Differences in density were correctly identified with SCA+CT in a cohort of ex vivo and in vivo images, thus illustrating the diagnostic potential of our approach. CONCLUSION: The combination of a subcellular-resolution microendoscope, acriflavine staining, and SCA+CT can be used to accurately isolate nuclei and quantify their density in anatomical images of heterogeneous tissue.

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.