Towards Accurate Dielectric Property Retrieval of Biological Tissues for Blood Glucose Monitoring

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A Deterministic Theory for Exact Non-Convex Phase Retrieval

In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for phase retrieval and identify a novel sufficient condition for universal exact recovery through the lens of low rank matrix recovery theory. Via a perspective in the lifted domain, we show that the convergence of the WF iterates to a true solution is attained geometrically under a single condition on the lifted forward model. As a result, a deterministic relationship between the accuracy of spectral initialization and the validity of {the regularity condition} is derived. In particular, we determine that a certain concentration property on the spectral matrix must hold uniformly with a sufficiently tight constant. This culminates into a sufficient condition that is equivalent to a restricted isometry-type property over rank-1, positive semi-definite matrices, and amounts to a less stringent requirement on the lifted forward model than those of prominent low-rank-matrix-recovery methods in the literature. We characterize the performance limits of our framework in terms of the tightness of the concentration property via novel bounds on the convergence rate and on the signal-to-noise ratio such that the theoretical guarantees are valid using the spectral initialization at the proper sample complexity.Comment: In Revision for IEEE Transactions on Signal Processin

Determination of biogeochemical properties of marine particles using above water measurements of the degree of polarization at the Brewster angle

Retrieval of biogeochemical parameters from remotely sensed data in optically complex waters such as those found in coastal zones is a challenging task due to the effects of various water constituents (biogenic, nonalgal and inorganic particles, dissolved matter) on the radiation exiting the ocean. Since scattering by molecules, aerosols, hydrosols and reflection at the sea surface introduce and modify the polarization state of light, the polarized upward radiation contains embedded information about the intrinsic nature of aerosols and suspended matter in the ocean. In this study, shipborne above water angularly resolved visible/near infrared multiband measurements of the degree of polarization are analysed against their corresponding in-situ biogeochemically characterized water samples for the first time. Water samples and radiometric data were collected in the English Channel along an inshore-offshore transect. Angular variations in the degree of polarization P are found to be consistent with theory. Maximum values of P are observed near the Brewster viewing angle in the specular direction. Variations in the degree of polarization at the Brewster angle (PB) with water content revealed that the suspended particulate matter, which is mainly composed of inorganic particles during the experiment, contributes to depolarise the skylight reflection, thus reducing PB. An empirical polarization-based approach is proposed to determine biogeochemical properties of the particles. The concentration of inorganic particles can be estimated using PB to within ±13% based on the dataset used. Larger sets of polarized measurements are recommended to corroborate the tendency observed in this study

Combined CloudSat-CALIPSO-MODIS retrievals of the properties of ice clouds

In this paper, data from spaceborne radar, lidar and infrared radiometers on the “A-Train” of satellites are combined in a variational algorithm to retrieve ice cloud properties. The method allows a seamless retrieval between regions where both radar and lidar are sensitive to the regions where one detects the cloud. We first implement a cloud phase identification method, including identification of supercooled water layers using the lidar signal and temperature to discriminate ice from liquid. We also include rigorous calculation of errors assigned in the variational scheme. We estimate the impact of the microphysical assumptions on the algorithm when radiances are not assimilated by evaluating the impact of the change in the area-diameter and the density-diameter relationships in the retrieval of cloud properties. We show that changes to these assumptions affect the radar-only and lidar-only retrieval more than the radar-lidar retrieval, although the lidar-only extinction retrieval is only weakly affected. We also show that making use of the molecular lidar signal beyond the cloud as a constraint on optical depth, when ice clouds are sufficiently thin to allow the lidar signal to penetrate them entirely, improves the retrieved extinction. When infrared radiances are available, they provide an extra constraint and allow the extinction-to-backscatter ratio to vary linearly with height instead of being constant, which improves the vertical distribution of retrieved cloud properties

Scientific Objectives, Measurement Needs, and Challenges Motivating the PARAGON Aerosol Initiative

Aerosols are involved in a complex set of processes that operate across many spatial and temporal scales. Understanding these processes, and ensuring their accurate representation in models of transport, radiation transfer, and climate, requires knowledge of aerosol physical, chemical, and optical properties and the distributions of these properties in space and time. To derive aerosol climate forcing, aerosol optical and microphysical properties and their spatial and temporal distributions, and aerosol interactions with clouds, need to be understood. Such data are also required in conjunction with size-resolved chemical composition in order to evaluate chemical transport models and to distinguish natural and anthropogenic forcing. Other basic parameters needed for modeling the radiative influences of aerosols are surface reflectivity and three-dimensional cloud fields. This large suite of parameters mandates an integrated observing and modeling system of commensurate scope. The Progressive Aerosol Retrieval and Assimilation Global Observing Network (PARAGON) concept, designed to meet this requirement, is motivated by the need to understand climate system sensitivity to changes in atmospheric constituents, to reduce climate model uncertainties, and to analyze diverse collections of data pertaining to aerosols. This paper highlights several challenges resulting from the complexity of the problem. Approaches for dealing with them are offered in the set of companion papers

Satellite estimates of wide-range suspended sediment concentrations in Changjiang (Yangtze) estuary using MERIS data

The Changjiang (Yangtze) estuarine and coastal waters are characterized by suspended sediments over a wide range of concentrations from 20 to 2,500 mg l-1. Suspended sediment plays important roles in the estuarine and coastal system and environment. Previous algorithms for satellite estimates of suspended sediment concentration (SSC) showed a great limitation in that only low to moderate concentrations (up to 50 mg l-1) could be reliably estimated. In this study, we developed a semi-empirical radiative transfer (SERT) model with physically based empirical coefficients to estimate SSC from MERIS data over turbid waters with a much wider range of SSC. The model was based on the Kubelka–Munk two-stream approximation of radiative transfer theory and calibrated using datasets from in situ measurements and outdoor controlled tank experiments. The results show that the sensitivity and saturation level of remote-sensing reflectance to SSC are dependent on wavelengths and SSC levels. Therefore, the SERT model, coupled with a multi-conditional algorithm scheme adapted to satellite retrieval of wide-range SSC, was proposed. Results suggest that this method is more effective and accurate in the estimation of SSC over turbid water