1,436 research outputs found

    Restoration of multichannel microwave radiometric images

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    A constrained iterative image restoration method is applied to multichannel diffraction-limited imagery. This method is based on the Gerchberg-Papoulis algorithm utilizing incomplete information and partial constraints. The procedure is described using the orthogonal projection operators which project onto two prescribed subspaces iteratively. Some of its properties and limitations are also presented. The selection of appropriate constraints was emphasized in a practical application. Multichannel microwave images, each having different spatial resolution, were restored to a common highest resolution to demonstrate the effectiveness of the method. Both noise-free and noisy images were used in this investigation

    Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation

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    Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment, has been a subject of growing research in the past decades. Here, we introduce a unified framework that ties together the problems of downscaling, data fusion and data assimilation as ill-posed inverse problems. This framework seeks solutions beyond the classic least squares estimation paradigms by imposing proper regularization, which are constraints consistent with the degree of smoothness and probabilistic structure of the underlying state. We review relevant regularization methods in derivative space and extend classic formulations of the aforementioned problems with particular emphasis on hydrologic and atmospheric applications. Informed by the statistical characteristics of the state variable of interest, the central results of the paper suggest that proper regularization can lead to a more accurate and stable recovery of the true state and hence more skillful forecasts. In particular, using the Tikhonov and Huber regularization in the derivative space, the promise of the proposed framework is demonstrated in static downscaling and fusion of synthetic multi-sensor precipitation data, while a data assimilation numerical experiment is presented using the heat equation in a variational setting

    Microlocal ISAR for Low Signal-to-Noise Environments

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    The problem of extracting radar target information from multi-aspect high-range-resolution data is examined. We suggest a new non-imaging approach that is based on microlocal analysis, which is a mathematical theory developed to handle highfrequency asymptotics. In essence, we relate features of the target to high-frequency components of the data. To deal with realistic band-limited data, we propose an iterative algorithm (based on the generalized Radon-Hough transform) in which we estimate the high-frequency features of the data, one after another, and subtract out the corresponding band-limited components. The algorithm has been successfully tested on noisy data, and may have a number of advantages over conventional imaging methods.This work was supported by the Office of Naval Research. M.C. also thanks Gary Hewer and the ASEE Summer Faculty Research Program for supporting her stay at China Lake

    Measurements of rainfall rate, drop size distribution, and variability at middle and higher latitudes: application to the combined DPR-GMI algorithm

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    The Global Precipitation Measurement mission is a major U.S.–Japan joint mission to understand the physics of the Earth’s global precipitation as a key component of its weather, climate, and hydrological systems. The core satellite carries a dual-precipitation radar and an advanced microwave imager which provide measurements to retrieve the drop size distribution (DSD) and rain rates using a Combined Radar-Radiometer Algorithm (CORRA). Our objective is to validate key assumptions and parameterizations in CORRA and enable improved estimation of precipitation products, especially in the middle-to-higher latitudes in both hemispheres. The DSD parameters and statistical relationships between DSD parameters and radar measurements are a central part of the rainfall retrieval algorithm, which is complicated by regimes where DSD measurements are abysmally sparse (over the open ocean). In view of this, we have assembled optical disdrometer datasets gathered by research vessels, ground stations, and aircrafts to simulate radar observables and validate the scattering lookup tables used in CORRA. The joint use of all DSD datasets spans a large range of drop concentrations and characteristic drop diameters. The scaling normalization of DSDs defines an intercept parameter NW, which normalizes the concentrations, and a scaling diameter Dm, which compresses or stretches the diameter coordinate axis. A major finding of this study is that a single relationship between NW and Dm, on average, unifies all datasets included, from stratocumulus to heavier rainfall regimes. A comparison with the NW–Dm relation used as a constraint in versions 6 and 7 of CORRA highlights the scope for improvement of rainfall retrievals for small drops (Dm lt; 1 mm) and large drops (Dm gt; 2 mm). The normalized specific attenuation–reflectivity relationships used in the combined algorithm are also found to match well the equivalent relationships derived using DSDs from the three datasets, suggesting that the currently assumed lookup tables are not a major source of uncertainty in the combined algorithm rainfall estimates

    A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images

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    Speckle is a granular disturbance, usually modeled as a multiplicative noise, that affects synthetic aperture radar (SAR) images, as well as all coherent images. Over the last three decades, several methods have been proposed for the reduction of speckle, or despeckling, in SAR images. Goal of this paper is making a comprehensive review of despeckling methods since their birth, over thirty years ago, highlighting trends and changing approaches over years. The concept of fully developed speckle is explained. Drawbacks of homomorphic filtering are pointed out. Assets of multiresolution despeckling, as opposite to spatial-domain despeckling, are highlighted. Also advantages of undecimated, or stationary, wavelet transforms over decimated ones are discussed. Bayesian estimators and probability density function (pdf) models in both spatial and multiresolution domains are reviewed. Scale-space varying pdf models, as opposite to scale varying models, are promoted. Promising methods following non-Bayesian approaches, like nonlocal (NL) filtering and total variation (TV) regularization, are reviewed and compared to spatial- and wavelet-domain Bayesian filters. Both established and new trends for assessment of despeckling are presented. A few experiments on simulated data and real COSMO-SkyMed SAR images highlight, on one side the costperformance tradeoff of the different methods, on the other side the effectiveness of solutions purposely designed for SAR heterogeneity and not fully developed speckle. Eventually, upcoming methods based on new concepts of signal processing, like compressive sensing, are foreseen as a new generation of despeckling, after spatial-domain and multiresolution-domain method

    Information retrieval from spaceborne GNSS Reflectometry observations using physics- and learning-based techniques

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    This dissertation proposes a learning-based, physics-aware soil moisture (SM) retrieval algorithm for NASA’s Cyclone Global Navigation Satellite System (CYGNSS) mission. The proposed methodology has been built upon the literature review, analyses, and findings from a number of published studies throughout the dissertation research. Namely, a Sig- nals of Opportunity Coherent Bistatic scattering model (SCoBi) has been first developed at MSU and then its simulator has been open-sourced. Simulated GNSS-Reflectometry (GNSS-R) analyses have been conducted by using SCoBi. Significant findings have been noted such that (1) Although the dominance of either the coherent reflections or incoher- ent scattering over land is a debate, we demonstrated that coherent reflections are stronger for flat and smooth surfaces covered by low-to-moderate vegetation canopy; (2) The influ- ence of several land geophysical parameters such as SM, vegetation water content (VWC), and surface roughness on the bistatic reflectivity was quantified, the dynamic ranges of reflectivity changes due to SM and VWC are much higher than the changes due to the surface roughness. Such findings of these analyses, combined with a comprehensive lit- erature survey, have led to the present inversion algorithm: Physics- and learning-based retrieval of soil moisture information from space-borne GNSS-R measurements that are taken by NASA’s CYGNSS mission. The study is the first work that proposes a machine learning-based, non-parametric, and non-linear regression algorithm for CYGNSS-based soil moisture estimation. The results over point-scale soil moisture observations demon- strate promising performance for applicability to large scales. Potential future work will be extension of the methodology to global scales by training the model with larger and diverse data sets

    Inverse problems in medical ultrasound images - applications to image deconvolution, segmentation and super-resolution

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    In the field of medical image analysis, ultrasound is a core imaging modality employed due to its real time and easy-to-use nature, its non-ionizing and low cost characteristics. Ultrasound imaging is used in numerous clinical applications, such as fetus monitoring, diagnosis of cardiac diseases, flow estimation, etc. Classical applications in ultrasound imaging involve tissue characterization, tissue motion estimation or image quality enhancement (contrast, resolution, signal to noise ratio). However, one of the major problems with ultrasound images, is the presence of noise, having the form of a granular pattern, called speckle. The speckle noise in ultrasound images leads to the relative poor image qualities compared with other medical image modalities, which limits the applications of medical ultrasound imaging. In order to better understand and analyze ultrasound images, several device-based techniques have been developed during last 20 years. The object of this PhD thesis is to propose new image processing methods allowing us to improve ultrasound image quality using postprocessing techniques. First, we propose a Bayesian method for joint deconvolution and segmentation of ultrasound images based on their tight relationship. The problem is formulated as an inverse problem that is solved within a Bayesian framework. Due to the intractability of the posterior distribution associated with the proposed Bayesian model, we investigate a Markov chain Monte Carlo (MCMC) technique which generates samples distributed according to the posterior and use these samples to build estimators of the ultrasound image. In a second step, we propose a fast single image super-resolution framework using a new analytical solution to the l2-l2 problems (i.e., â„“2\ell_2-norm regularized quadratic problems), which is applicable for both medical ultrasound images and piecewise/ natural images. In a third step, blind deconvolution of ultrasound images is studied by considering the following two strategies: i) A Gaussian prior for the PSF is proposed in a Bayesian framework. ii) An alternating optimization method is explored for blind deconvolution of ultrasound

    Doctor of Philosophy

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    dissertationA database of cirrus particle size distributions (PSDs), with concomitant meteorological variables, has been constructed using data collected with the Twodimensional Stereo (2D-S) probe. Parametric functions are fit to each measured PSD. Full statistical descriptions are given for unimodal fit parameters. Three statistical tests were developed in order to determine the utility of bimodal fits and the efficacy of unimodal fits, and an investigation into the relationship between the parameterized PSDs and several meteorological variables was made. Next, a parameterization of a "universal" cirrus PSD is given. This parameterization constitutes an improvement on earlier works due both to the size of the dataset and to updated instrumentation. Despite earlier works that predicted a gammadistribution tail to the universal ice PSD, it is shown here that the tail is best described by an inverse gamma distribution. A method for predicting any PSD given the universal shape and two independent remote sensing measurements is demonstrated. The constructed PSD database is then used to address a straightforward question: how similar are the statistics of PSD datasets collected using the recently developed 2D-S probe to cirrus PSD datasets collected using older Particle Measuring Systems (PMS) 2D Cloud (2DC) and 2D Precipitation (2DP) probes? It is seen, given the same cloud field and given the same assumptions concerning ice crystal cross-sectional area, density, and radar cross section, that the parameterized 2D-S and the parameterized 2DC predict similar distributions of inferred shortwave extinction coefficient, ice water content, and 94 GHz radar reflectivity. However, the parameterized 2DC predicts a statistically significant higher number of total ice crystals and a larger ratio of small ice crystals to large ice crystals. Finally, the beginnings of two works in their early stages are presented. First, the probability structure of the parameterized PSDs is considered in light of application to the Bayesian inference of cirrus microphysical properties from remote sensing measurements. Then, the collection of measured PSDs, along with a forward model for radar reflectivity, is used to investigate uncertainty in computations of radar reflectivity from modeled moments of cirrus cloud PSDs

    Delineation of Surface Water Features Using RADARSAT-2 Imagery and a TOPAZ Masking Approach over the Prairie Pothole Region in Canada

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    The Prairie Pothole Region (PPR) is one of the most rapidly changing environments in the world. In the PPR of North America, topographic depressions are common, and they are an essential water storage element in the regional hydrological system. The accurate delineation of surface water bodies is important for a variety of reasons, including conservation, environmental management, and better understanding of hydrological and climate modeling. There are numerous surface water bodies across the northern Prairie Region, making it challenging to provide near-real-time monitoring and in situ measurements of the spatial and temporal variation in the surface water area. Satellite remote sensing is the only practical approach to delineating the surface water area of Prairie potholes on an ongoing and cost-effective basis. Optical satellite imagery is able to detect surface water but only under cloud-free conditions, a substantial limitation for operational monitoring of surface water variability. However, as an active sensor, RADARSAT-2 (RS-2) has the ability to provide data for surface water detection that can overcome the limitation of optical sensors. In this research, a threshold-based procedure was developed using Fine Wide (F0W3), Wide (W2) and Standard (S3) modes to delineate the extent of surface water areas in the St. Denis and Smith Creek study basins, Saskatchewan, Canada. RS-2 thresholding results yielded a higher number of apparent water surfaces than were visible in high-resolution optical imagery (SPOT) of comparable resolution acquired at nearly the same time. TOPAZ software was used to determine the maximum possible extent of water ponding on the surface by analyzing high-resolution LiDAR-based DEM data. Removing water bodies outside the depressions mapped by TOPAZ improved the resulting images, which corresponded more closely to the SPOT surface water images. The results demonstrate the potential of TOPAZ masking for RS-2 surface water mapping used for operational purposes

    Recent Techniques for Regularization in Partial Differential Equations and Imaging

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    abstract: Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain. This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges. Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.Dissertation/ThesisDoctoral Dissertation Mathematics 201
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