We present a concept for UHF/L-band (0.5–2 GHz) remote sensing of Antarctic ice sheet internal temperature using a highly sparse synthetic aperture radiometer constellation. This concept leverages the relative stability of ice sheet thermal emission over long temporal periods to gradually assemble a collection of array baselines which are jointly transformed to develop large image facets. We formulate a calculation of minimum array complexity based on the desired sensitivity, spatial resolution, and time available for observations. We determine from this calculation that such a system can achieve 1–10-km spatial resolution (significantly finer than the program of record) over monthly to yearly timescales with as few as 10–20 elements; even fewer elements are required for observing only the ice sheet center. The inverse problem of reconstructing image facets from mixed-pointing and mixed-configuration observations is posed using a Fourier domain data constraint with a total variational regularization in the image domain. This approach enables image formation from heterogeneous observations while mitigating artifacts. We present a notional constellation design for three satellites which could accomplish the necessary baseline sampling by rotating the phase and semimajor axis of spacecraft relative positions in planar circular orbits (PCOs). We demonstrate image formation by observing system simulations leveraging predictions of Antarctica’s multiwavelength brightness temperature computed from ice sheet thermomechanical and radiative transfer models.

We present the STASIS concept, an innovative approach to developing high spatial resolution maps of Antarctic ice sheet thermal emission at P/L band. Rather than using a large real aperture system, the relative stability of ice sheet temperature over time implies that a sparse array system would be able to gradually build up spatial frequency sampling and generate images with 1K sensitivity at 1-10 km spatial resolution over monthly-seasonal time scales. This contrasts with the requirement for full snapshot spatial frequency coverage required by systems for monitoring soil moisture and ocean salinity Sensitivity heuristic calculations are presented, and simulated interferometric observations are generated incorporating a realistic ice sheet thermal emission model.

We discuss an approach to measuring high-resolution maps of Antarctic ice sheet temperatures using repeat-pass sparsely sampled microwave interferometry. This approach follows from the inference that the relative invariance of ice sheet temperatures on annual timescales obviates the need for high snapshot sensitivity imposed as a requirement for observing more variable regions of the Earth system with interferometers such as SMOS. Such measurements could hypothetically be conducted with spatial resolutions less than 10 km using a small constellation of satellites. We discuss specifically how modifications to sheet-base geothermal heat flux could manifest as observable thermal signatures and a strategy to form images from a mosaic of multiple heterogeneous sparsely sampled observations, and we conclude with comments on necessary areas for future investigations.

Wind velocity estimation is a critical component of weather prediction, but accurately estimating atmospheric winds with in-place instruments is expensive, inefficient, and provides only sparse coverage. Consequently, methods which can extract wind patterns from remote sensing data would offer significant benefits—satellites and satellite-derived data in particular, provide comprehensive coverage of global weather phenomena. In this paper, we develop an optical flow method which successfully extracts dense wind velocity estimates from water vapor data, a commonly estimated quantity by satellites equipped with infrared or microwave instruments. The test-data comes from direct numerical simulations of a mesoscale convective system over the eastern Pacific and provides accompanying ground truth wind velocities, allowing us to quantitatively measure the performance of our methods.

Atmospheric motion vector (AMV) retrieval from water vapor measurements is important in climate research and weather forecasting. However, conventional feature tracking methods for AMV retrievals generate velocity fields with gaps and large errors. In this work, we test the optical flow algorithm by generating a nature run of a convective weather phenomenon, which provides water vapor variables and wind vector fields at various pressure levels. We show that our optical flow algorithm generates superior performance when compared with traditional feature tracking algorithms used in operational centers, generating dense AMVs with no gaps and significantly improving AMV accuracy. The optical flow algorithm performs well down to very low wind speeds and does not require a low-wind cutoff threshold. In our studies, we considered various measurement configurations, including water vapor retrievals at different temporal resolutions and found that the optical flow algorithm is not sensitive to the time interval between images.

This paper explores the application of modern image processing techniques in retrieving high-resolution passive microwave images of the polar ice regions on Earth from sparsely sampled interferometric array measurements. Such observations, sensitive to ice sheet temperature, would be valuable benchmark measurements for ice process models. In this paper, we propose to use a total variation-based method that addresses the challenges associated with large sidelobes and blurry maps resulting from long baseline interferometry. We present a robust algorithm that employs total variation (TV) minimization and the split Bregman optimization. This technique effectively deconvolves images, preserves edges, and minimizes noise amplification without introducing artifacts. To evaluate the algorithm’s performance, we performed tests on a simulated image and a real satellite image of Antarctica. Additionally, we assessed the algorithm’s performance using different interferometric array configurations, including both dense and sparse arrays with varying numbers of elements.

We present a spatio-temporal super-resolution method for reconstructing a sequence of observations collected by imaging satellites. A sequence of observations is assumed to be defined on a low resolution spatio-temporal grid. It is further assumed that the sequence is generated by blurring of a captured scene with a spatio-temporal convolution kernel and is degraded by noise. Our method simultaneously exhibits deconvolution of the sequence of images from the effects of spatio-temporal blur, denoising of the data, and upsampling of the low-resolution sequence to a high resolution spatiotemporal grid. We perform the super-resolution in the spacetime domain, as opposed to super-resolving the sequence separately and sequentially to a higher spatial and then temporal resolution grid. Simultaneous space-time optimization achieves a more efficient and more accurate reconstruction than reconstructing a sequence frame by frame. The proposed super-resolution methodology is based on total variation regularization and computes the solution using the alternating direction method of multipliers. Numerical results show our approach to be robust and computationally efficient.

The purpose of this work is to use data from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to refine our knowledge of post-launch AIRS point spread functions (PSFs), including suspected changes over the mission. We develop methodology, by deriving mathematical optimization formulation based on variational principles and Sobolev gradient descent, for reconstruction of AIRS spatial response functions. We use the data over the ocean, collected for the duration of a day, to reconstruct a single PSF. We examine the repeatability of our reconstructions by computing PSFs based on data collected during two consecutive days, and also investigating the change in the reconstructions by comparing the reconstructed PSF based on data collected in the beginning and the middle of the mission. We also quantify uncertainties in our reconstruction results.

Small ocean eddies are observed in fine-resolution satellite imagery within the coastal regions and ice margins of the world's oceans. The derivation of surface velocity fields of these features would enable geophysical estimates of the kinematic energy contained within the eddies, leading to improved understanding of the role these eddies play in ocean circulation. In this paper, we develop a method to derive surface velocity fields of small ocean eddies using fine resolution, multi-sensor imagery obtained over short time intervals. We consider the evolving image to be embedded in a deformable medium, and perform image matching using nonlinear viscous fluid registration model. We employ sum of squared differences and mutual information as matching functionals. The physical continuum equation is solved using an efficient multigrid full approximation scheme. We test our method using synthetic aperture radar (SAR) image pairs and show that it produces promising results.

Multi-angle Imaging Spectro-Radiometer (MISR) instrument provides the multi-angle images of aerosols and clouds. There are a multitude of challenges for accurate stereo imaging of clouds and aerosols including the high variation of radiative properties of aerosols and clouds within an image. In this work, we adapt an image model to separate two specific types of clouds frequently appearing in MISR images. Specifically, we separate cirrus and cumulus clouds in the two-dimensional MISR single-channel images. We characterize these two cloud types according to their spatial variations and optical brightness. Cirrus clouds appear smooth and optically thin, while cumulus clouds present high optical oscillations and appear brighter. We adapt the additive piecewise-smooth (APS) model for this cloud separation task. We describe the differences between our results and the results of the previous joint work of the second author on cloud separation.

Due to the limitations of imaging sensors, remote sensing images often have limited resolution. To address this issue, various super-resolution (SR) image reconstruction techniques have been developed to reconstruct a high-resolution image from a sequence of low-resolution, noisy and blurry observations. In this paper, we propose an efficient super-resolution image reconstruction method for geometrically deformed remote sensing images, based on the nonlocal total variation (NLTV) regularization. The proposed minimization problem is solved by a fast primal-dual algorithm. Numerical experiments demonstrate the performance of the proposed method.

This paper introduces a variational method for destriping data acquired by pushbroom-type satellite imaging systems. The model leverages sparsity in signals and is based on current research in sparse optimization and compressed sensing. It is based on the basic principles of regularization and data fidelity with certain constraints using modern methods in variational optimization - namely total variation (TV), both L1and L2fidelity, and the alternating direction method of multipliers (ADMM). The main algorithm in this paper, TV-L1, uses sparsity promoting energy functionals to achieve two important imaging effects. The TV term maintains boundary sharpness of content in the underlying clean image, while the L1fidelity allows for the equitable removal of stripes without over- or under-penalization, providing a more accurate model of presumably independent sensors with unspecified and unrestricted bias distribution. A comparison is made between the TV-L1and TV-L2models to exemplify the qualitative efficacy of an L1striping penalty. The model makes use of novel minimization splittings and proximal mapping operators, successfully yielding more realistic destriped images in very few iterations.

The images acquired by microwave sensors are blurry and of low-resolution. On the other hand, the images obtained using infrared/visible sensors are of sufficiently high-resolution. In this paper, we develop a data fusion methodology and apply it to enhance resolution of a microwave image using the data from a collocated infrared/visible sensor. Such an approach takes advantage of the spatial resolution of the infrared instrument and the sensing accuracy of the microwave instrument. We tested our method using precipitation scenes captured with the Advanced Microwave Sounding Unit (AMSU) microwave instrument and the Advanced Very High Resolution Radiometer (AVHRR).

We introduce a methodology for separating reflective layers of clouds in Earth remote sensing images. We propose a single-channel layer separation framework and extend it to multispectral layer separation. Efficient alternating minimization and fast operator-splitting methods are used to solve minimization problems. Specifically, we apply our methodology to separate strongly stratified and optically thin upper (cirrus) clouds from optically thick lower convective (cumulus) clouds in atmospheric imagery approximated as additive contributions to the observed signal. After setting up synthetic “truth” scenarios, we evaluate the accuracy of the two-layer separation results while varying the effective opaqueness of each of two types of cloud. We show that multispectral cloud layer separation is consistently more accurate than channel-by-channel cloud layer separation.

In this paper, we introduce methodology for multispectral layer separation. Efficient alternating minimization and fast operator-splitting methods are used to solve minimization problems. Specifically, we apply our methodology to separate strongly stratified and optically thin upper (cirrus) clouds from optically thick lower convective (cumulus) clouds in atmospheric imagery approximated as additive contributions to the observed signal. After setting up synthetic “truth” scenarios, we evaluate the accuracy of the two-layer separation results while varying the effective opaqueness of each of two types of cloud. We show that multispectral cloud layer separation is consistently more accurate than channel-by-channel cloud layer separation.

In this paper, we present a novel framework for constructing large deformation log-unbiased image registration models that generate theoretically and intuitively correct deformation maps. Such registration models do not rely on regridding and are inherently topology preserving. We apply information theory to quantify the magnitude of deformations and examine the statistical distributions of Jacobian maps in the logarithmic space. To demonstrate the power of the proposed framework, we generalize the well known viscous fluid registration model to compute log-unbiased deformations. We tested the proposed method using a pair of binary corpus callosum images, a pair of two-dimensional serial MRI images, and a set of three-dimensional serial MRI brain images. We compared our results to those computed using the viscous fluid registration method, and demonstrated that the proposed method is advantageous when recovering voxel-wise maps of local tissue change.

In [8], the authors proposed the large deformation log-unbiased diffeomorphic nonlinear image registration model which has been successfully used to obtain theoretically and intuitively correct deformation maps. In this paper, we extend this idea to simultaneously registering and tracking deforming objects in a sequence of two or more images. We generalize a level set based Chan-Vese multiphase segmentation model to consider Jacobian fields while segmenting regions of growth and shrinkage in deformations. Deforming objects are thus classified based on magnitude of homogeneous deformation. Numerical experiments demonstrating our results include a pair of two-dimensional synthetic images and pairs of two-dimensional and three-dimensional serial MRI images.

Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on the Jacobian map, which estimates local tissue gain or loss. Here, we provide rigorous mathematical analyses of the Jacobian maps, and use themto motivate a new numerical method to construct unbiased nonlinear image registration. First, we argue that logarithmic transformation is crucial for analyzing Jacobian values representing morphometric differences. We then examine the statistical distributions of log-Jacobian maps by defining the Kullback-Leibler (KL) distance on material density functions arising in continuum-mechanical models. With this framework, unbiased image registration can be constructed by quantifying the symmetric KL-distance between the identity map and the resulting deformation. Implementation details, addressing the proposed unbiased registration as well as the minimization of symmetric image matching functionals, are then discussed and shown to be applicable to other registration methods, such as inverse consistent registration. In the results section, we test the proposed framework, as well as present an illustrative application mapping detailed 3-D brain changes in sequential magnetic resonance imaging scans of a patient diagnosed with semantic dementia. Using permutation tests, we show that the symmetrization of image registration statistically reduces skewness in the log-Jacobian map.