Nonconvex Sparse Recovery Methods

Critical to accurate reconstruction of sparse signals from low-dimensional observations is the solution of nonlinear optimization problems that promote sparse solutions. Sparse signal recovery is a common problem of many different applications ranging from photography to tomography and from radiology to biology. Within the compressive imaging community, minimizing the $\ell_1$-norm or the total variation (TV) seminorm penalized least-squares problem is the most conventional approach for sparse signal recovery. The least-squares data-fidelity term assumes a Gaussian noise model. However, there are many real-world applications that do not follow Gaussian noise statistics. For an instance, when the number of observed photon counts is relatively low at the camera detector, they are corrupted by Poisson noise. This phenomenon can be seen in a variety of different applications including astronomy, night vision, and medical imaging. Therefore, the contribution of the dissertation to sparse signal recovery is two-fold. First, we propose several nonconvex algorithms operate on Poisson statistics to promote sparsity. Second, we will present methods based on trust-region and alternating minimization techniques for sparse signal recovery under Gaussian statistics. While convex optimization for low-light imaging has received some attention by the imaging community, non-convex optimization techniques for photon-limited imaging are still in their nascent stages. Theoretically, the non-convex $\ell_p$-norm regularization (0 \leq p < 1) would lead to more accurate reconstruction than the convex $\ell_1$-norm relaxation. In this dissertation, we explore sparse Poisson intensity reconstruction methods using gradient based optimization approach with the nonconvex regularization techniques: $\ell_p$-norm, TV$_p$-seminorm, and the \textit{generalized} Shannon entropy. The proposed methods lead to more accurate and high strength reconstructions in medical imaging and computational genomics. In particular, we developed a stage-based nonconvex approach to solve time dependent bioluminescence and fluorescence lifetime imaging problems in the Poisson noise context. In Gaussian noise context, we solve the $\ell_2$-$\ell_1$ and $\ell_2$-$\ell_p$ sparse recovery problems by transforming the objective function into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments with simulated compressive sensing 1D and 2D data are provided to illustrate that our proposed approach eliminates spurious solutions more effectively while improving the computational time to converge in comparison to standard approaches. Moreover, we employ nonconvex $\ell_p$-norm regularization for better recovery and demixing of sparse signals arise in image inpainting and source separation applications

Systematic Review and Comparison of Publicly Available ICU Data Sets-A Decision Guide for Clinicians and Data Scientists.

OBJECTIVE As data science and artificial intelligence continue to rapidly gain traction, the publication of freely available ICU datasets has become invaluable to propel data-driven clinical research. In this guide for clinicians and researchers, we aim to: 1) systematically search and identify all publicly available adult clinical ICU datasets, 2) compare their characteristics, data quality, and richness and critically appraise their strengths and weaknesses, and 3) provide researchers with suggestions, which datasets are appropriate for answering their clinical question. DATA SOURCES A systematic search was performed in Pubmed, ArXiv, MedRxiv, and BioRxiv. STUDY SELECTION We selected all studies that reported on publicly available adult patient-level intensive care datasets. DATA EXTRACTION A total of four publicly available, adult, critical care, patient-level databases were included (Amsterdam University Medical Center data base [AmsterdamUMCdb], eICU Collaborative Research Database eICU CRD], High time-resolution intensive care unit dataset [HiRID], and Medical Information Mart for Intensive Care-IV). Databases were compared using a priori defined categories, including demographics, patient characteristics, and data richness. The study protocol and search strategy were prospectively registered. DATA SYNTHESIS Four ICU databases fulfilled all criteria for inclusion and were queried using SQL (PostgreSQL version 12; PostgreSQL Global Development Group) and analyzed using R (R Foundation for Statistical Computing, Vienna, Austria). The number of unique patient admissions varied between 23,106 (AmsterdamUMCdb) and 200,859 (eICU-CRD). Frequency of laboratory values and vital signs was highest in HiRID, for example, 5.2 (±3.4) lactate values per day and 29.7 (±10.2) systolic blood pressure values per hour. Treatment intensity varied with vasopressor and ventilatory support in 69.0% and 83.0% of patients in AmsterdamUMCdb versus 12.0% and 21.0% in eICU-CRD, respectively. ICU mortality ranged from 5.5% in eICU-CRD to 9.9% in AmsterdamUMCdb. CONCLUSIONS We identified four publicly available adult clinical ICU datasets. Sample size, severity of illness, treatment intensity, and frequency of reported parameters differ markedly between the databases. This should guide clinicians and researchers which databases to best answer their clinical questions

Analysis of Discrepancies Between Pulse Oximetry and Arterial Oxygen Saturation Measurements by Race and Ethnicity and Association With Organ Dysfunction and Mortality

IMPORTANCE Discrepancies in oxygen saturation measured by pulse oximetry (Spo(2)), when compared with arterial oxygen saturation (Sao(2)) measured by arterial blood gas (ABG), may differentially affect patients according to race and ethnicity. However, the association of these disparities with health outcomes is unknown.OBJECTIVE To examine racial and ethnic discrepancies between Sao(2) and Spo(2) measures and their associations with clinical outcomes.DESIGN, SETTING, AND PARTICIPANTS This multicenter, retrospective, cross-sectional study included 3 publicly available electronic health record (EHR) databases (ie, the Electronic Intensive Care Unit-Clinical Research Database and Medical Information Mart for Intensive Care III and IV) as well as Emory Healthcare (2014-2021) and Grady Memorial (2014-2020) databases, spanning 215 hospitals and 382 ICUs. From 141 600 hospital encounters with recorded ABG measurements, 87 971 participants with first ABG measurements and an Spo(2) of at least 88% within 5 minutes before the ABG test were included.EXPOSURES Patients with hidden hypoxemia (ie, Spo(2) >= 88% but Sao(2) <88%).MAIN OUTCOMES AND MEASURES Outcomes, stratified by race and ethnicity, were Sao(2) for each Spo(2), hidden hypoxemia prevalence, initial demographic characteristics (age, sex), clinical outcomes (in-hospital mortality, length of stay), organ dysfunction by scores (Sequential Organ Failure Assessment [SOFA]), and laboratory values (lactate and creatinine levels) before and 24 hours after the ABG measurement.RESULTS The first Spo(2)-Sao(2) pairs from 87 971 patient encounters (27 713 [42.9%] women; mean [SE] age, 62.2 [17.0] years; 1919 [2.3%] Asian patients; 26 032 [29.6%] Black patients; 2397 [2.7%] Hispanic patients, and 57 632 [65.5%] White patients) were analyzed, with 4859 (5.5%) having hidden hypoxemia. Hidden hypoxemia was observed in all subgroups with varying incidence (Black: 1785 [6.8%]; Hispanic: 160 [6.0%]; Asian: 92 [4.8%]; White: 2822 [4.9%]) and was associated with greater organ dysfunction 24 hours after the ABG measurement, as evidenced by higher mean (SE) SOFA scores (7.2 [0.1] vs 6.29 [0.02]) and higher in-hospital mortality (eg, among Black patients: 369 [21.1%] vs 3557 [15.0%]; P < .001). Furthermore, patients with hidden hypoxemia had higher mean (SE) lactate levels before (3.15 [0.09] mg/dL vs 2.66 [0.02] mg/dL) and 24 hours after (2.83 [0.14] mg/dL vs 2.27 [0.02] mg/dL) the ABG test, with less lactate clearance (-0.54 [0.12] mg/dL vs -0.79 [0.03] mg/dL).CONCLUSIONS AND RELEVANCE In this study, there was greater variability in oxygen saturation levels for a given Spo(2) level in patients who self-identified as Black, followed by Hispanic, Asian, and White. Patients with and without hidden hypoxemia were demographically and clinically similar at baseline ABG measurement by SOFA scores, but those with hidden hypoxemia subsequently experienced higher organ dysfunction scores and higher in-hospital mortality.Analysis and support of clinical decision makingDevelopment and application of statistical models for medical scientific researc